ASTROBIOLOGYVolume 2 Number 3 2002copy Mary Ann Liebert Inc

Does the Rapid Appearance of Life on Earth Suggestthat Life Is Common in the Universe

CHARLES H LINEWEAVER12 and TAMARA M DAVIS1

ABSTRACT

It is sometimes assumed that the rapidity of biogenesis on Earth suggests that life is commonin the Universe Here we critically examine the assumptions inherent in this if-life-evolved-rapidly-life-must-be-common argument We use the observational constraints on the rapid-ity of biogenesis on Earth to infer the probability of biogenesis on terrestrial planets with thesame unknown probability of biogenesis as the Earth We find that on such planets olderthan 1 Gyr the probability of biogenesis is 13 at the 95 confidence level This quan-tifies an important term in the Drake Equation but does not necessarily mean that life is com-mon in the Universe Key Words BiogenesismdashDrake Equation Astrobiology 2 293ndash304

293

THE BIOGENESIS LOTTERY

MUCH OF CURRENT ASTROBIOLOGICAL RESEARCH

is focused on learning more about the earlyevolution of the Earth and about the origin of lifeWe may be able to extrapolate and generalize ourknowledge of how life formed here to how itmight have formed elsewhere Indirect evidencesuggesting that life may be common in the Uni-verse includes

Sun-like stars are common Formation of Earth-like planets in habitable

zones around these stars may be a commonfeature of star formation (Kasting et al 1993Wetherill 1996 Lissauer and Lin 2000 Line-weaver 2001)

Lifersquos chemical ingredientsmdashwater aminoacids and other organic moleculesmdashare com-mon (Cronin 1989 Trimble 1997 Charnley etal 2002)

Sources of free energy such as starlight and re-

ductionndashoxidation pairs are common (Nealsonand Conrad 1999)

It is difficult to translate this circumstantial ev-idence into an estimate of how common life is inthe Universe Without definitive detections of ex-traterrestrial life we can say very little about howcommon it is or even whether it exists Our exis-tence on Earth can tell us little about how com-mon life is in the Universe or about the proba-bility of biogenesis on a terrestrial planet becauseeven if this probability were infinitesimally smalland there were only one life-harboring planet inthe Universe we would of necessity find our-selves on that planet However the rapidity withwhich life appeared on Earth gives us more in-formation If life were rare it would be unlikelythat biogenesis would occur as rapidly as it seemsto have occurred on Earth

Although we do not understand the details ofhow life originated we have some useful obser-vational constraints on how long it took Carbon

1School of Physics University of New South Wales Sydney Australia2Australian Centre for Astrobiology Macquarie University Sydney Australia

isotopic evidence suggests that life existed onEarth 385 billion years ago (Mojzsis et al 1996)High temperatures and large frequent sterilizingimpacts may have frustrated an earlier appear-ance of life (Maher and Stevenson 1988 Sleep et al 1989) If life originated on Earth then in-creasingly tight observational constraints indicatethat biogenesis was rapid (Oberbeck and Fogle-man 1989 Sleep et al 2001) The extraterrestrialimplications of rapid biogenesis on Earth and theextent to which this rapidity suggests that life iscommon in the Universe have not been looked atcarefully and are the focus of this paper

The basic concept is simple Over a given timeperiod more probable events happen more often(and thus more rapidly) than less probableevents Thus the probability of winning a lotterycan be inferred from how quickly a lottery win-ner has won For example suppose we have noidea about the probability q of winning a dailylottery (0 q 1) Suppose a gambler buys a lot-tery ticket every day for 3 days losing on the first2 days and winning on the third We can use thisinformation to infer something about q Specifi-cally in this case we can say that q is more likelyto be about one-third than one-hundredth and isunlikely to be close to 1 [see +(n 5 3 q) in Fig 1]If the gambler can only tell us that he won at leastonce within 3 days then we can no longer ex-clude high values of q with such confidence butthe likelihood of q can still tell us that q 016 atthe 95 confidence level [see +(3 q) in Fig 1and Eq A2 of Appendix]

Suppose there is a group of gamblers all ofwhom have won at least once within N (eg 12)days A gambler is chosen from this group at ran-dom and after carefully examining his tickets hetells us that he won at least once within the first3 daysmdashrelatively early in the 12 days that he hadto have won by to be in the group This is anal-ogous to our situation on Earth We find our-selves in the group of planets on which biogene-sis has necessarily occurred we have of necessitywon the biogenetic lottery some time in the pastAnd we also find that biogenesis has occurredrapidly We won soon after life became possibleon Earth Given the above information about thegambler the likelihood of q is plotted in Fig 1 as+(n 3 N 12 q) and allows us to conclude thatq 012 at the 95 confidence level This statis-tical result applies to a group of gamblers or to agroup of terrestrial planets on which the proba-bility q of biogenesis is unknown as long as q is

approximately the same for each planet in thegroup and approximately the same as it was onEarth In the next section we review the observa-tional constraints on when and how quickly lifeappeared on Earth We then use these constraintsto identify and critically examine selection effectsthat complicate this result Finally we discuss therelationship between our result the Drake Equa-tion and the larger question ldquoHow common islife in the Universerdquo Mathematical details aregiven in the Appendix

OBSERVATIONAL CONSTRAINTS ON THE TIMING OF

TERRESTRIAL BIOGENESIS

If life originated on Earth then during and im-mediately following the Earthrsquos formation there

LINEWEAVER AND DAVIS294

FIG 1 Let the unknown probability of winning adaily lottery be q Suppose a gambler buys a ticket eachday and wins on the third day From this information wecan calculate the likelihood of q [see +(n 5 3 q) above]The most likely value is as expected 13 but we can alsoconclude that 006 q 080 at the 95 confidence level(hatched area) Different scenario Suppose that after 3days the gambler tells us that he won at least once Thelikelihood of q then becomes +(n 3 q) plotted aboveHigh values of q can no longer be excluded and we cansay only that 016 q at the 95 confidence level Dif-ferent scenario (and one more analogous to our situationon Earth) We have a group of gamblers all of whom havewon at least once on or before the Nth (eg 12th) dayOne of them chosen at random (analogous to the Earth)won at least once on or before the third day This is quiteearly since it could have happened any time during the12 days Given this information the likelihood of q be-comes the thick curve labeled ldquo+(n 3 N 12 q)rdquo Inthis case we can say that q 012 at the 95 confidencelevel (gray area) See Appendix for computational details

was a period without life (Dtfrustrated) followedby a period during which life evolved (Dtbiogenesis)followed by a period during which life has beenpresent (Dtlife) The sum of these intervals addsup to the age of the Earth (Fig 2)

Dtfrustrated 1 Dtbiogenesis 1 Dtlife 5 DtEarth (1)

where DtEarth 5 4566 6 0002 Gyr (Allegravegre et al1995) As older fossils and biosignatures havebeen found Dtlife has gotten longer The signifi-cance of large impacts in frustrating or sterilizingprotolife has only recently been appreciated andassessed (Dtfrustrated) Combined these observa-tions indicate that biogenesis was rapid since Dtbiogenesis is caught in the middlemdashthe longer Dtfrustrated and Dtlife get the shorter Dtbiogenesismust get The distinction between how rapid bio-genesis was and when it was is important becauseour result the inferred probability of biogenesisdepends on how rapid it was while only a mar-

ginal selection effect depends on when it was (seeSelection Effects)

The majority of the Earthrsquos mass accreted fromplanetesimals within the first 100 million years ofthe Earthrsquos formation (Halliday 2000) With aninitially molten surface life could not have ap-peared The transition from accretion to heavybombardment included the formation of theMoon by the collision with a Mars-sized object45 Gyr ago (Hartmann and Davis 1975 Canupand Asphaug 2001 Halliday 2001) We can in-fer from the dates and sizes of lunar impact cra-tors whose record goes back to when the Moonformed a solid crust [444 Gyr ago (Sleep et al1989)] that the surface of the Earth was periodi-cally vaporized Since the mass of the Earth is 80times the mass of the Moon impacts on the Earthwere more numerous and more energetic and pe-riodically produced 2000K rock vapor atmos-pheres that lasted for several thousand years(Hartmann et al 2000 Sleep et al 2001) These

IS LIFE COMMON IN THE UNIVERSE 295

FIG 2 We divide the history of the Earth into three epochs Impact frustration Biogenesis and Life The blackcurves show the percentages of terrestial planets with life as a function of time assuming two different probabilitiesof biogenesis (q 5 03 003) within Dtbiogenesis 5 600 Myr The percentages in the histograms on the right (14 and32) are obtained from comparing the subset of planets that have formed life within Dtbiogenesis (middle gray) withthe total number of planets that have life (or have had biogenesis) within 4566 Gyr of their formation (cross-hatched)If q is high (030 thick line) a large fraction (32) of the planets that have evolved life within 4566 Gyr of formationhave life that evolved rapidlymdashwithin Dtbiogenesismdashon their planets If q is low (003 thin line) then a smaller fraction(14) will have life that evolved rapidly These different percentages illustrate the principle that a single observationof rapid terrestrial biogenesis is more likely to be the result of high q This allows us to compute the relative likeli-hood of q and to constrain q (see Fig 4)

conditions were probably an effective and recur-ring autoclave for sterilizing the earliest life formsor more generally frustrating the evolution of lifeA steadily decreasing heavy bombardment con-tinued until 38 Gyr ago

Estimates of the time of the most recent steril-izing impact range between 444 and 37 Gyr ago(Maher and Stevenson 1988 Oberbeck andFogleman 1989 Sleep et al 1989 Halliday 2001)These estimates span the time from the solidifi-cation of the Moonrsquos crust to the end of the lateheavy bombardment Thus life was frustrated forat least the first 01 Gyr and possibly as long asthe first 09 Gyr of the Earthrsquos existence We takeour preferred value as the middle of this rangeDtfrustrated lt 05 6 04 Gyr The range of these es-timates reflects the large uncertainties due tosmall number statistics for the largest impactorsand the uncertainty of the energy required to ster-ilize the Earth completely We do not know wherebiogenesis happened or the extent to which it wasprotected from the effects of impacts Tidal poolshave little protection hydrothermal vents havesome protection while autotrophic thermophilesin subsurface rock under several kilometers ofcrust were probably in effective bomb shelters

The roots of the universal tree of life point toa thermophilic origin (or at least a thermophiliccommon ancestor) for all life on Earth (Pace 1991Stetter 1996) This suggests a hot biogenesis inhydrothermal vents or possibly subsurface rockandor selection for thermophilia by periodictemperature pulses from large impacts If weknew that life evolved on the surface of the Earthand was therefore more susceptible to impactsterilizations life would have been frustratedlonger and our preferred value would be moreprecise Dtfrustrated lt 07 6 02 Gyr

If we accept the carbon isotopic evidence forlife 385 billion years ago (Mojzsis et al 1996)then life has been on Earth at least that long (ieDtlife is at least 385 Gyr) In addition because ofthe Earthrsquos tectonic history this time is also theearliest time we could reasonably hope to find bi-ological evidence from rocks on Earthmdasheven iflife existed earlier With this selection effect inmind (which we know exists at some level) ourpreferred value for the time life has existed onEarth is Dtlife lt 40104

202 GyrIt is possible that biogenesis occurred several

times on Earth For example during the periodDtfrustrated life could have evolved and been ster-ilized multiple times We do not know if this hap-

pened Similar potential sterilizations and bio-geneses could have occurred during the periodDtlife but we do not know For the purposes ofthis analysis we can ignore this complication Weare only interested in the shortest period withinwhich the observations can constrain biogenesisto have occurred Thus Dtbiogenesis is our best ob-servational constraint on any epoch of biogene-sis and this happens to be on the period betweenthe most recent sterilizing impact that is olderthan the oldest evidence we have for life on Earth

Since our preferred values yield Dtfrustrated 1Dtlife lt DtEarth there is little time left for biogen-esis to have occurred This is the basis for thestatement that biogenesis occurred rapidly Sub-stituting our three preferred values DtEarth Dtfrustrated and Dtlife into Eq 1 and solving for Dtbiogenesis yields

Dtbiogenesis 5 01105201 Gyr (2)

Thus we take 600 Myr as a crude estimate ofthe upper limit for the time it took life to appearon Earth Assuming biogenesis took place on thesurface of the Earth Oberbeck and Fogleman(1989) found this maximum time to be 25 MyrMaher and Stevenson (1988) assumed that bio-genesis took somewhere between 01 and 10 Myrdepending on environment while Sleep et al(2001) found a similar range for evolutionarilysignificant periods of clement surface conditionsIndependently biologists specializing in thechemistry of the origin of life have estimated thatthe time required for biogenesis is potentiallyquite short (Miller 1982) and could be 8 Myr(Lazcano and Miller 1994) Thus several lines ofevidence indicate that biogenesis was geologi-cally rapid If biogenesis occurred in the fissuresaround a hydrothermal vent or in subsurfacerocks it was well protected and we can only con-strain biogenesis to have taken less than 600Myr If biogenesis occurred on the surface itprobably took less than 25 Myr In this analy-sis we consider 600 and 25 Myr to represent thehigh and low ends of a plausible range for Dtbiogenesis (Figs 2 and 3 respectively)

These observational constraints on DtfrustratedDtbiogenesis and Dtlife are important because theyquantify how rapidly biogenesis occurred onEarth and enable us to put limits on the proba-bility that biogenesis occurred on other planetsFor example consider a group of terrestrial plan-ets with approximately the same probability of

LINEWEAVER AND DAVIS296

biogenesis ldquoqrdquo as Earth Suppose q 5 030 Attheir formation none of these planets had life Astime passed life arose on more and more of themThe thick line in Fig 2 shows the increasing per-centage of these planets with life as time passesAfter Dtbiogenesis 30 will have life (that is howq 5 030 is defined) After 4566 Gyr 93 willhave life (7 still will not) Of that 93 32 willlike the Earth have had biogenesis within Dtbiogenesis The histogram on the far right of Fig2 represents these numbers Suppose q is only003 Then only 20 will have life after 4566 Gyrand only 14 of those will have had biogenesislike the Earth within Dtbiogenesis Assuming Earthis a random member of the planets with life thesingle observation that biogenesis occurredwithin Dtbiogenesis on Earth indicates that largervalues of q are more likely than small values Thisis the basic idea behind our analysis It is illus-trated in Figs 1 4 and 5 which also show quan-titative constraints on q under the various as-sumptions discussed in the next section

The histograms in Figs 2 and 3 also show thatif q is large the fraction of gamblers or terrestrialplanets who have won after a certain time is large

Suppose the gambler did not know how manygamblers had won by the 12th day but only thathe is a random member of the group that had wonFrom the fact that he won quickly he can infer thatq is large This tells the gambler that after a fewdays a large fraction of lottery ticket buyers are inthe winnersrsquo group He is not alone For the bio-genesis lottery finding large q means that after afew times Dtbiogenesis a large fraction of the terres-trial planets with probability of biogenesis similarto the Earth have (or have had) life

SELECTION EFFECTS

Daily lottery R biogenesis lottery

In the first section we drew parallels betweena daily lottery and a biogenesis lottery Explicitlythese parallels are

The first day of the lottery corresponds to theend of Dtfrustrated the time when conditions be-come clement enough for biogenesis

All the gamblers had the same (but unknown)

IS LIFE COMMON IN THE UNIVERSE 297

FIG 3 Zoomed-in version of Fig 2 with two differences (1) The window for biogenesis shown here is at the shortend of the range permitted by observations Dtbiogenesis 5 25 Myr (2) In Fig 2 by normalizing the histograms to 4566Gyr we have assumed that Earth is a random member of a group of planets at least 4566 Gyr old upon which bio-genesis could have happened anytime up to 4566 after formation including 1 million years ago This ignores thenonobservability-of-recent-biogenesis selection effect Here to minimize the influence of this selection effect we onlyallow biogenesis to occur anytime earlier than 377 Gyr ago [ie within ldquoDt(N 5 4)rdquo] The influence of this normal-ization time Dt(N) is illustrated in Fig 4

chance of winning the lottery each time theybought a ticket (q is the probability of winningper day) This corresponds to a group of ter-restrial planets with approximately the same(but unknown) chance of biogenesis as theEarth (q is the probability of biogenesis withina period of time called here Dtbiogenesis)

We selected a gambler at random from thosewho had won on or before the Nth day Thuswe conditioned on winning before a certaintime This corresponds to assuming that theEarth is a random member of the group of ter-restrial planets that has had biogenesis on orbefore the end of Dt(N) 5 N 3 Dtbiogenesis Con-ditioning on biogenesis before this time corre-

sponds to correcting for the selection effect thatbiogenesis had to have occurred for us to behere

A gambler chosen at random from the groupthat has won within N days found that he hadwon on the first day (n 5 1) This correspondsto finding that biogenesis has occurred rapidlyon Earth that is within Dtbiogenesis

If we set N 5 1 [see Fig 4 +(11 q)] we areconditioning on rapid biogenesis We are con-sidering a group all of whose members havehad rapid biogenesis In this case a randommember having rapid biogenesis can tell usnothing about the probability q To infer some-thing about q we must have N 1

Nonobservability of recent biogenesis

If our conclusions from the daily lottery are toapply to biogenesis on terrestrial planets we need

LINEWEAVER AND DAVIS298

FIG 4 The effect on the likelihood of varying thesomewhat arbitrary number of days that the gamblershave to have won by to be in the group In contrast toFig 1 all the likelihoods of q here are based on the in-formation that a gambler (chosen at random from thegroup whose members have won within N days) has wonon the first day These likelihoods are plotted and labeledldquo+(1N q)rdquo with NIcirc124 In the biogenesis lottery(just as in the daily lottery) N defines the group and is ameasure of the duration biogenesis could have taken[Dt(N) 5 N 3 Dtbiogenesis) For example if N 5 1 we can-not say anything about q since the likelihood +(11 q) isflat (we have conditioned on ldquorapidrdquo biogenesis) Whileif N 5 ` we can put the strongest constraint on q If n 51 (when it could have been much larger 1 n N) wehave more information about q and the likelihood forlarge q is higher (see Appendix Eq A3) The ratio of theprobabilities in the histograms in Fig 3 corresponds tothe ratio of the +(14 q) likelihoods here 3926 5+(14 q 5 030)+(14 q 5 003)5 0690465 15 Thatis with n 5 1 and N 5 4 values of q lt030 are 50 morelikely to be the case than q lt003 [in Fig 3 Dt(N) 5 4 325 Myr] Notice that for 2 N ` the 95 lower limitfor q varies only between 007 and 023

FIG 5 Likelihood of qN In Figs 1 and 4 the likelihoodof q is shown where q is the probability of winning onany one day Here we show likelihoods of qN the un-known probability of winning on or before the Nth dayThis figure shows the effect of varying N The informa-tion used to compute these likelihoods is that a gamblerchosen at random from the group whose members havewon within N days has won on the first day (see Ap-pendix Eqs A6ndashA8) Translated this becomes a planetchosen at random from the group of planets that has hadbiogenesis within Dt(N) 5 N 3 Dtbiogenesis has had bio-genesis within Dtbiogenesis As in Fig 4 if N 5 1 we cansay nothing meaningful about q1 (5 q) However even ifN 5 2 we can make a stronger statement about q2 thanwe could about q q2 013 at the 95 confidence levelThe 95 lower limit on qN increases dramatically as N in-creases constraining qN to be close to 1 The ability to ex-tract a useful constraint even if N is low reduces the in-fluence of the selection effects discussed in the text

to correct for the fact that the evolution of an ob-server takes some time How long it takes ob-serving equipment or complex life or multicel-lular eukaryotes to evolve is difficult to say OnEarth it took 4 Gyr A limited pace of evolutionhas prevented us from looking back at our ownhistory and seeing that biogenesis happened lastyear or even more recently than 2 Gyr ago (weconsider a plausible range for the requisite timeelapsed since biogenesis to be between 2 and 10billion years or Dtevolve 5 416

22 Gyr)This selection effect for nonrecent biogenesis is

selecting for biogenesis to happen a few billionyears before the present regardless of whether ithappened rapidly It is not a selection effect forrapid biogenesis since the longer it took us toevolve to a point when we could measure the ageof the Earth the older the Earth became Simi-larly if biogenesis took 1 Gyr longer than it ac-tually did we would currently find the age of theEarth to be 5566 Gyr (5 4566 1 1) old ldquoWhy isthe Earth 4566 billion years oldrdquo ldquoBecause ittook that long to find it outrdquo The generalizationof this plausible assumption to the ensemble ofterrestrial planets is necessary if the likelihoodsand constraints in Figs 1 4 and 5 are to be ap-plicable to the group of terrestrial planets

Potential problems

Any effect that makes rapid biogenesis a pre-requisite for life would undermine our inferencesfor q For example although it is usually assumedthat the heavy bombardment inhibited biogene-sis energetic impacts may have set up largechemical and thermal disequilibria that playsome crucial role in biogenesis We know so lit-tle about the details of the chemical evolution thatled to life that heat pulses and rapid cooling af-ter large impacts may be part of the preconditionsfor biogenesis If true the time scale of biogene-sis would be linked to the time scale of the ex-ponential decay of bombardment and biogenesiswould (if it occurred at all) be necessarily rapidmost extant life in the Universe would have rapidbiogenesis and little could be inferred about theabsolute value of q from our sample of 1

In a panspermia scenario the rapid appearanceof life on Earth is explained not by rapid terres-trial biogenesis as assumed here but by the ubiq-uity of the ldquoseeds of liferdquo (eg Hoyle and Wick-ramasinghe 1999) An analysis in the context of

a panspermia scenario would be subject to thesame observational constraints as terrestrial bio-genesis and would therefore lead to the same in-ferred probability for the appearance of life onother terrestrial planets

Another potential problem Suppose the auto-catalytic chemical cycles leading to life are expo-nentially sensitive to some still unknown pecu-liarity of the initial conditions on Earth In thiscase to have the same q as the Earth our groupof terrestrial planets may have to be almost in-distinguishable rare clones of Earth That is con-ditioning on planets identical to Earth (ldquosame qrdquo)would be conditioning on rapid biogenesis (N 51) and would prevent us from inferring muchabout q from the observations of rapid biogene-sis on Earth [see +(11 q) in Fig 4]

This is an example of the more general issue ofthe status of the rapidity of biogenesis on EarthDid it have to be rapid If we assume it couldhave been otherwise then we can infer somethingabout q If it had to be that way we cannot Themiddle ground might be the most plausible op-tion Biogenesis did not necessarily have to hap-pen as rapidly as it did but (to be consistent withour existence) it may have had to happen within1 or 2 billion years of the Earthrsquos formation

If this is true we need to look carefully at theinfluence of varying the somewhat arbitrary andcounterfactual duration [Dt(N) 5 N 3 Dtbiogenesis]that biogenesis could have taken on Earth Whatvalues of Dt(N) are plausible and how do theyaffect the results This is done in Fig 4 whichquantifies the degree of variability one can as-sume for the duration of biogenesis and still haveinteresting constraints on q The lower N is theless variability is assumed For example if N 5 2[see +(12 q)] we are assuming that biogenesiscould only have taken as long as 2 3 Dtbiogenesismdashenough variability to be able to say somethingabout q but small enough to maintain the nonob-servability of recent biogenesis

Figure 5 allows us to generalize our inferencesabout q (the probability of biogenesis within Dtbiogenesis) to inferences about qN [the probabil-ity of biogenesis within an arbitrary time Dt(N)]Specifically it shows that we only need to be ableto assume that biogenesis could have been twiceas long as Dtbiogenesis to have interesting con-straints q2 013 at the 95 confidence level [see+(12 qN)] This is the result reported in the ab-stract

IS LIFE COMMON IN THE UNIVERSE 299

HOW COMMON IS LIFE

Relation of our analysis to the Drake Equation

The Drake Equation was devised to address thequestion of ldquoHow many communicative civiliza-tions are in our Galaxyrdquo (eg Sagan 1973) It hasbeen criticized as ldquoa way of compressing a largeamount of ignorance into a small spacerdquo (Olivercited in Dicke 1998) Despite its shortcomings itcontinues to focus the efforts of the search for ex-traterrestrial intelligence (SETI) community Animportant goal of the SETI community is to turnits subjective probabilities into mathematicalprobabilities We have done that here for one ofthe most important terms

We are interested in a simpler question ldquoHowcommon is life in the Universerdquo Our question issimpler because life is more generic than intelli-gent or technological life We modify the DrakeEquation to address our question and introducea parameter F which is a measure of how com-mon life is in the universe F is the fraction of starsin our galaxy today orbited by planets that havehad independent biogenesis

F 5 NlN p 5 fp fe fl (3)

where Nl is the number of stars in our Galaxy or-bited by planets that have had independent bio-genesis N p is the number of stars in our Galaxyfp is the fraction of stars in our Galaxy with plan-etary systems fe is the fraction of these planetarysystems that have a terrestrial planet suitable forlife in the same way as the Earth that is theyhave approximately the same probability q as theEarth and fl is the fraction of these suitable plan-ets on which biogenesis has occurred

Many recent observations of the frequency andage dependence of circumstellar disks aroundyoung stars in star-forming regions support thewidely accepted idea that planet formation is acommon by-product of star formation and thatthe fraction of stars with planetary systems isclose to unity fp lt 1 (eg Habing et al 1999 Mc-Caughrean et al 2000 Meyer and Beckwith2000)

Equation 3 then becomes

F lt fe fl (4)

If F 1022 then 1 of all stars have (or havehad) life and we conclude that life is ldquocommonrdquo

in the Universe If F 10211 we may be the onlylife in the Galaxy and life is ldquorarerdquo

There has been little agreement on the value offl Hart (1996) wrote ldquoThe value of fl is extremelyspeculativerdquo but argued based on the concate-nation of low probabilities that it must be ex-tremely small and thus life elsewhere is improb-able However Shostak (1998) assumed quite theopposite ldquoOn the basis of the rapidity with whichbiology blossomed on Earth we can optimisti-cally speculate that this fraction ( fl ) is also one(100)rdquo Our analysis is a close statistical look atthis optimistic speculation

The relation between the fraction of suitableplanets on which biogenesis has occurred (ldquoflrdquo inthe Drake Equation) and the q analyzed here is

fl(qN) 5 1 2 (1 2 q)N (5)

fl(qDt(N)) 5 1 2 (1 2 q) (6)

fl(qt) 5 1 2 (1 2 q) (7)

where Eq 5 refers to the daily lottery (see Ap-pendix Eq A5) Eq 6 is the translation to the bio-genesis lottery and we obtain Eq 7 by using t 5Dtfrustrated 1 Dt(N) Equation 7 is plotted in Figs2 and 3 Thus in Eq 7 we have expressed the ldquoflrdquoterm of the Drake Equation as a function of timeof the observables Dtfrustrated and Dtbiogenesis andof the probability q for which we have derivedthe relative likelihood In addition since fl(qN) 5qN (see Eq A5) Fig 5 shows the relative likeli-hood of fl and establishes quantitative but model-dependent (specifically N 1-dependent) con-straints on fl For example for terrestrial planetsolder than 1 Gyr (2 3 Dtbiogenesis) fl 13 atthe 95 confidence level

However to go from fl to an answer to the ques-tion ldquoHow common is liferdquo (ie to go from fl toF in Eq 4 we need to know fe the fraction of theseplanetary systems with a terrestrial planet suitablefor life in the same way as the Earth Our under-standing of planet formation is consistent with theidea that ldquoterrestrialrdquo planet formation is a com-mon feature of star formation (Wetherill 1996 Lis-sauer and Lin 2000) The mass histogram of de-tected extrasolar planets peaks at low masses(dNdM ~ M21) and is also consistent with thisidea (Tabachnik and Tremaine 2001 Zucker andMazeh 2001 Lineweaver and Grether 2002)

Our analysis assumed the existence of a group

1t2

D

D

tb

t

i

f

o

r

g

u

e

s

n

tr

e

a

s

t

i

e

s

d 2

1DtbD

io

t(

g

N

en

)

esis 2

LINEWEAVER AND DAVIS300

of terrestrial planets with approximately thesame but unknown (q [ [01]) probability of bio-genesis It is reasonable to postulate the existenceof such a q group since although we do not knowthe details of the chemical evolution that led tolife we have some ideas about the factors in-volved energy flux temperatures the presenceof water planet orbit residence time in the con-tinuously habitable zone mass of the planet at-mospheric composition bombardment rate at theend of planetary accretion and its dependence onthe masses of the large planets in the planetarysystem metallicity of the prestellar molecularcloud crust composition vulcanism basic chem-istry hydration pH and presence of particularclay minerals amino acids and other molecularbuilding blocks for life (Lahav 1999) Since all ormany of these physical variables determine theprobability of biogenesis and since the Earthdoes not seem to be special with respect to anyof them (ie the Earth probably does not occupya thinly populated region of this multidimen-sional parameter space) the assumption that theprobability of biogenesis on these planets wouldbe approximately the same as on Earth is plausi-ble This is equivalent to assuming that q is aldquoslowlyrdquo varying function of environment Iftrue fe and F are not vanishingly small This canbe contrasted with the ldquoexponentially sensitiverdquocase discussed in Potential problems

DISCUSSION

Carter (1983) has pointed out that the time scalefor the evolution of intelligence on the Earth (5Gyr) is comparable to the main sequence lifetimeof the Sun (10 Gyr) Under the assumption thatthese two time scales are independent he arguedthat this would be unlikely to be observed unlessthe average time scale for the evolution of intel-ligence on a terrestrial planet is much longer thanthe main sequence lifetime of the host star [seeLivio (1999) for an objection to the idea that thesetwo time scales are independent] Carterrsquos argu-ment is strengthened by recent models of the ter-restrial biosphere indicating that the gradual in-crease of solar luminosity will make Earthuninhabitable in a billion years or somdashseveral billion years before the Sun leaves the main se-quence (Caldeira and Kasting 1992 Rampinoand Caldeira 1994)

Our analysis is similar in style to Carterrsquos how-

ever we are concerned with the appearance ofthe earliest life forms not the appearance of in-telligent life Subject to the caveats raised in Po-tential problems and by Livio (1999) the implica-tions of our analysis and Carterrsquos are consistentand complementary The appearance of life onterrestrial planets may be common but the ap-pearance of intelligent life may be rare

SUMMARY

Our existence on Earth does not mean that theprobability of biogenesis on a terrestrial planetq is large because if q were infinitesimallysmall and there were only one life-harboringplanet in the Universe we would of necessityfind ourselves on that planet However such ascenario would imply either that Earth has aunique chemistry or that terrestrial biogenesishas taken a long time to occur Neither is sup-ported by the evidence we have Since little canbe said about the probability q of terrestrialbiogenesis from our existence we assume max-imum ignorance 0 q 1 We then use theobservation of rapid terrestrial biogenesis toconstrain q (Fig 4)

We convert the constraints on q into constraintson the fl term of the Drake Equation (the frac-tion of suitable planets that have life) For ter-restrial planets older than 1 Gyr we find thatfl is most probably close to unity and 13 atthe 95 confidence level

If terrestrial planets are common and they haveapproximately the same probability of biogen-esis as the Earth our inference of high q (orhigh qN) indicates that a substantial fraction ofterrestrial planets have life and thus life is com-mon in the UniverseHowever there are assumptions and selection

effects that complicate this result

Although we correct the analysis for the factthat biogenesis is a prerequisite for our exis-tence our result depends on the plausible as-sumption that rapid biogenesis is not such aprerequisite

Although we have evidence that the fraction ofplanets that are ldquoterrestrialrdquo in a broad astro-nomical sense (rocky planet in the continu-ously habitable zone) is large this may be dif-ferent from the fraction of planets that areldquoterrestrialrdquo in a more detailed chemical sense

IS LIFE COMMON IN THE UNIVERSE 301

Although we can make reasonable estimates ofwhat the crusts and atmospheres are made ofwithout detailed knowledge of the steps ofchemical evolution we cannot be sure that as-tronomically terrestrial planets have the sameq as Earth That is the fraction of planets be-longing to the Earthrsquos q group is uncertainThus although we have been able to quantifythe fl term of the Drake Equation using rapidbiogenesis our knowledge of the fe term is stillonly qualitative and inhibits our ability to drawstronger conclusions about how common lifeis in the Universe

APPENDIX LIKELIHOODCOMPUTATIONS

Let the unknown but constant probability ofwinning a daily lottery be q Given the informa-tion that a gambler who buys one ticket each dayfor n days lost on the first n 2 1 days and wonon the nth day we can compute the likelihoodfunction for q (probability of the data given themodel q)

L(n q) 5 (1 2 q)n21q (A1)

This is equal to the fraction of all gamblers whofirst experienced (n21) losses and then wonGiven only the information that the gambler wonat least once on or before the nth day the likeli-hood function for q is

L(n q) 5 1 2 (1 2 q)n (A2)

This is equal to the fraction of all gamblers whohave won at least once on or before the nth dayGiven the information that a group of gamblershave won at least once on or before the Nth dayand that a gambler chosen at random from thisgroup won at least once on or before the nth day(n N) the likelihood of q is

L(n N q) 5 5 (A3)

Out of all the gamblers who have won on or be-fore the Nth day this is the fraction who havewon on or before the nth day Notice that as N Rn the likelihood of low q increases and that if N 5n the likelihood is the same for all q (see Fig 4)As N R ` we have L(n N q) R L(n q)

1 2 (1 2 q)n1 2 (1 2 q)N

L(n q)L(N q)

which yields the tightest constraints on q A nor-malized likelihood + (or probability density) isdefined such that ograve10 +(q)dq 5 1 Thus the renor-malization conversion is

+(x) 5(A4)

The normalized likelihoods for Eqs A1ndashA3 areplotted in Fig 1 for the cases n 5 3 and N 5 12The 95 confidence levels cited are Bayesiancredible intervals based on a uniform prior for q

Although q is the probability of winning thelottery in 1 day we would like to generalize andask what is the probability qN of winning the lot-tery within N days In the analogous biogenesislottery q is the probability of biogenesis on a ter-restrial planet with the same unknown probabil-ity of biogenesis as the Earth The time windowfor biogenesis constrained by observations onEarth Dtbiogenesis corresponds to 1 day for thegambler However we would like to compute thelikelihood of biogenesis after an arbitrary periodof time Dt(N) 5 N 3 Dtbiogenesis Let qN be theprobability of winning on or before the Nth day

qN 5 1 2 (1 2 q)N 5 L(N q) (A5)

(see Eqs A2 and A3) We would like to know thelikelihood of qN rather than limit ourselves to thelikelihood of q (5q1) Suppose the information is the same that was available to computeL(n N q) That information is A randomly cho-sen gambler from the group of gamblers who havewon after N days won on or before the nth dayWe want L(n N qN) The relationship betweenthe likelihood of qN and the likelihood of q is

+(n N qN) dqN 5 +(n N q) dq (A6)

which with dqNdq 5 N(1 2 q)N21 (from Eq A5)becomes

+(n N qN)

5 (A7)

5 (A8)

which is plotted in Fig 5 and has as expected rel-atively larger likelihoods for larger values of qN

+(n N q)N(1 2 q)N21

+(n N q)

dqNdq

+(x)

E1

0L(x)dx

LINEWEAVER AND DAVIS302

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

isotopic evidence suggests that life existed onEarth 385 billion years ago (Mojzsis et al 1996)High temperatures and large frequent sterilizingimpacts may have frustrated an earlier appear-ance of life (Maher and Stevenson 1988 Sleep et al 1989) If life originated on Earth then in-creasingly tight observational constraints indicatethat biogenesis was rapid (Oberbeck and Fogle-man 1989 Sleep et al 2001) The extraterrestrialimplications of rapid biogenesis on Earth and theextent to which this rapidity suggests that life iscommon in the Universe have not been looked atcarefully and are the focus of this paper

The basic concept is simple Over a given timeperiod more probable events happen more often(and thus more rapidly) than less probableevents Thus the probability of winning a lotterycan be inferred from how quickly a lottery win-ner has won For example suppose we have noidea about the probability q of winning a dailylottery (0 q 1) Suppose a gambler buys a lot-tery ticket every day for 3 days losing on the first2 days and winning on the third We can use thisinformation to infer something about q Specifi-cally in this case we can say that q is more likelyto be about one-third than one-hundredth and isunlikely to be close to 1 [see +(n 5 3 q) in Fig 1]If the gambler can only tell us that he won at leastonce within 3 days then we can no longer ex-clude high values of q with such confidence butthe likelihood of q can still tell us that q 016 atthe 95 confidence level [see +(3 q) in Fig 1and Eq A2 of Appendix]

Suppose there is a group of gamblers all ofwhom have won at least once within N (eg 12)days A gambler is chosen from this group at ran-dom and after carefully examining his tickets hetells us that he won at least once within the first3 daysmdashrelatively early in the 12 days that he hadto have won by to be in the group This is anal-ogous to our situation on Earth We find our-selves in the group of planets on which biogene-sis has necessarily occurred we have of necessitywon the biogenetic lottery some time in the pastAnd we also find that biogenesis has occurredrapidly We won soon after life became possibleon Earth Given the above information about thegambler the likelihood of q is plotted in Fig 1 as+(n 3 N 12 q) and allows us to conclude thatq 012 at the 95 confidence level This statis-tical result applies to a group of gamblers or to agroup of terrestrial planets on which the proba-bility q of biogenesis is unknown as long as q is

approximately the same for each planet in thegroup and approximately the same as it was onEarth In the next section we review the observa-tional constraints on when and how quickly lifeappeared on Earth We then use these constraintsto identify and critically examine selection effectsthat complicate this result Finally we discuss therelationship between our result the Drake Equa-tion and the larger question ldquoHow common islife in the Universerdquo Mathematical details aregiven in the Appendix

OBSERVATIONAL CONSTRAINTS ON THE TIMING OF

TERRESTRIAL BIOGENESIS

If life originated on Earth then during and im-mediately following the Earthrsquos formation there

LINEWEAVER AND DAVIS294

FIG 1 Let the unknown probability of winning adaily lottery be q Suppose a gambler buys a ticket eachday and wins on the third day From this information wecan calculate the likelihood of q [see +(n 5 3 q) above]The most likely value is as expected 13 but we can alsoconclude that 006 q 080 at the 95 confidence level(hatched area) Different scenario Suppose that after 3days the gambler tells us that he won at least once Thelikelihood of q then becomes +(n 3 q) plotted aboveHigh values of q can no longer be excluded and we cansay only that 016 q at the 95 confidence level Dif-ferent scenario (and one more analogous to our situationon Earth) We have a group of gamblers all of whom havewon at least once on or before the Nth (eg 12th) dayOne of them chosen at random (analogous to the Earth)won at least once on or before the third day This is quiteearly since it could have happened any time during the12 days Given this information the likelihood of q be-comes the thick curve labeled ldquo+(n 3 N 12 q)rdquo Inthis case we can say that q 012 at the 95 confidencelevel (gray area) See Appendix for computational details

was a period without life (Dtfrustrated) followedby a period during which life evolved (Dtbiogenesis)followed by a period during which life has beenpresent (Dtlife) The sum of these intervals addsup to the age of the Earth (Fig 2)

Dtfrustrated 1 Dtbiogenesis 1 Dtlife 5 DtEarth (1)

where DtEarth 5 4566 6 0002 Gyr (Allegravegre et al1995) As older fossils and biosignatures havebeen found Dtlife has gotten longer The signifi-cance of large impacts in frustrating or sterilizingprotolife has only recently been appreciated andassessed (Dtfrustrated) Combined these observa-tions indicate that biogenesis was rapid since Dtbiogenesis is caught in the middlemdashthe longer Dtfrustrated and Dtlife get the shorter Dtbiogenesismust get The distinction between how rapid bio-genesis was and when it was is important becauseour result the inferred probability of biogenesisdepends on how rapid it was while only a mar-

ginal selection effect depends on when it was (seeSelection Effects)

The majority of the Earthrsquos mass accreted fromplanetesimals within the first 100 million years ofthe Earthrsquos formation (Halliday 2000) With aninitially molten surface life could not have ap-peared The transition from accretion to heavybombardment included the formation of theMoon by the collision with a Mars-sized object45 Gyr ago (Hartmann and Davis 1975 Canupand Asphaug 2001 Halliday 2001) We can in-fer from the dates and sizes of lunar impact cra-tors whose record goes back to when the Moonformed a solid crust [444 Gyr ago (Sleep et al1989)] that the surface of the Earth was periodi-cally vaporized Since the mass of the Earth is 80times the mass of the Moon impacts on the Earthwere more numerous and more energetic and pe-riodically produced 2000K rock vapor atmos-pheres that lasted for several thousand years(Hartmann et al 2000 Sleep et al 2001) These

IS LIFE COMMON IN THE UNIVERSE 295

FIG 2 We divide the history of the Earth into three epochs Impact frustration Biogenesis and Life The blackcurves show the percentages of terrestial planets with life as a function of time assuming two different probabilitiesof biogenesis (q 5 03 003) within Dtbiogenesis 5 600 Myr The percentages in the histograms on the right (14 and32) are obtained from comparing the subset of planets that have formed life within Dtbiogenesis (middle gray) withthe total number of planets that have life (or have had biogenesis) within 4566 Gyr of their formation (cross-hatched)If q is high (030 thick line) a large fraction (32) of the planets that have evolved life within 4566 Gyr of formationhave life that evolved rapidlymdashwithin Dtbiogenesismdashon their planets If q is low (003 thin line) then a smaller fraction(14) will have life that evolved rapidly These different percentages illustrate the principle that a single observationof rapid terrestrial biogenesis is more likely to be the result of high q This allows us to compute the relative likeli-hood of q and to constrain q (see Fig 4)

conditions were probably an effective and recur-ring autoclave for sterilizing the earliest life formsor more generally frustrating the evolution of lifeA steadily decreasing heavy bombardment con-tinued until 38 Gyr ago

Estimates of the time of the most recent steril-izing impact range between 444 and 37 Gyr ago(Maher and Stevenson 1988 Oberbeck andFogleman 1989 Sleep et al 1989 Halliday 2001)These estimates span the time from the solidifi-cation of the Moonrsquos crust to the end of the lateheavy bombardment Thus life was frustrated forat least the first 01 Gyr and possibly as long asthe first 09 Gyr of the Earthrsquos existence We takeour preferred value as the middle of this rangeDtfrustrated lt 05 6 04 Gyr The range of these es-timates reflects the large uncertainties due tosmall number statistics for the largest impactorsand the uncertainty of the energy required to ster-ilize the Earth completely We do not know wherebiogenesis happened or the extent to which it wasprotected from the effects of impacts Tidal poolshave little protection hydrothermal vents havesome protection while autotrophic thermophilesin subsurface rock under several kilometers ofcrust were probably in effective bomb shelters

The roots of the universal tree of life point toa thermophilic origin (or at least a thermophiliccommon ancestor) for all life on Earth (Pace 1991Stetter 1996) This suggests a hot biogenesis inhydrothermal vents or possibly subsurface rockandor selection for thermophilia by periodictemperature pulses from large impacts If weknew that life evolved on the surface of the Earthand was therefore more susceptible to impactsterilizations life would have been frustratedlonger and our preferred value would be moreprecise Dtfrustrated lt 07 6 02 Gyr

If we accept the carbon isotopic evidence forlife 385 billion years ago (Mojzsis et al 1996)then life has been on Earth at least that long (ieDtlife is at least 385 Gyr) In addition because ofthe Earthrsquos tectonic history this time is also theearliest time we could reasonably hope to find bi-ological evidence from rocks on Earthmdasheven iflife existed earlier With this selection effect inmind (which we know exists at some level) ourpreferred value for the time life has existed onEarth is Dtlife lt 40104

202 GyrIt is possible that biogenesis occurred several

times on Earth For example during the periodDtfrustrated life could have evolved and been ster-ilized multiple times We do not know if this hap-

pened Similar potential sterilizations and bio-geneses could have occurred during the periodDtlife but we do not know For the purposes ofthis analysis we can ignore this complication Weare only interested in the shortest period withinwhich the observations can constrain biogenesisto have occurred Thus Dtbiogenesis is our best ob-servational constraint on any epoch of biogene-sis and this happens to be on the period betweenthe most recent sterilizing impact that is olderthan the oldest evidence we have for life on Earth

Since our preferred values yield Dtfrustrated 1Dtlife lt DtEarth there is little time left for biogen-esis to have occurred This is the basis for thestatement that biogenesis occurred rapidly Sub-stituting our three preferred values DtEarth Dtfrustrated and Dtlife into Eq 1 and solving for Dtbiogenesis yields

Dtbiogenesis 5 01105201 Gyr (2)

Thus we take 600 Myr as a crude estimate ofthe upper limit for the time it took life to appearon Earth Assuming biogenesis took place on thesurface of the Earth Oberbeck and Fogleman(1989) found this maximum time to be 25 MyrMaher and Stevenson (1988) assumed that bio-genesis took somewhere between 01 and 10 Myrdepending on environment while Sleep et al(2001) found a similar range for evolutionarilysignificant periods of clement surface conditionsIndependently biologists specializing in thechemistry of the origin of life have estimated thatthe time required for biogenesis is potentiallyquite short (Miller 1982) and could be 8 Myr(Lazcano and Miller 1994) Thus several lines ofevidence indicate that biogenesis was geologi-cally rapid If biogenesis occurred in the fissuresaround a hydrothermal vent or in subsurfacerocks it was well protected and we can only con-strain biogenesis to have taken less than 600Myr If biogenesis occurred on the surface itprobably took less than 25 Myr In this analy-sis we consider 600 and 25 Myr to represent thehigh and low ends of a plausible range for Dtbiogenesis (Figs 2 and 3 respectively)

These observational constraints on DtfrustratedDtbiogenesis and Dtlife are important because theyquantify how rapidly biogenesis occurred onEarth and enable us to put limits on the proba-bility that biogenesis occurred on other planetsFor example consider a group of terrestrial plan-ets with approximately the same probability of

LINEWEAVER AND DAVIS296

biogenesis ldquoqrdquo as Earth Suppose q 5 030 Attheir formation none of these planets had life Astime passed life arose on more and more of themThe thick line in Fig 2 shows the increasing per-centage of these planets with life as time passesAfter Dtbiogenesis 30 will have life (that is howq 5 030 is defined) After 4566 Gyr 93 willhave life (7 still will not) Of that 93 32 willlike the Earth have had biogenesis within Dtbiogenesis The histogram on the far right of Fig2 represents these numbers Suppose q is only003 Then only 20 will have life after 4566 Gyrand only 14 of those will have had biogenesislike the Earth within Dtbiogenesis Assuming Earthis a random member of the planets with life thesingle observation that biogenesis occurredwithin Dtbiogenesis on Earth indicates that largervalues of q are more likely than small values Thisis the basic idea behind our analysis It is illus-trated in Figs 1 4 and 5 which also show quan-titative constraints on q under the various as-sumptions discussed in the next section

The histograms in Figs 2 and 3 also show thatif q is large the fraction of gamblers or terrestrialplanets who have won after a certain time is large

Suppose the gambler did not know how manygamblers had won by the 12th day but only thathe is a random member of the group that had wonFrom the fact that he won quickly he can infer thatq is large This tells the gambler that after a fewdays a large fraction of lottery ticket buyers are inthe winnersrsquo group He is not alone For the bio-genesis lottery finding large q means that after afew times Dtbiogenesis a large fraction of the terres-trial planets with probability of biogenesis similarto the Earth have (or have had) life

SELECTION EFFECTS

Daily lottery R biogenesis lottery

In the first section we drew parallels betweena daily lottery and a biogenesis lottery Explicitlythese parallels are

The first day of the lottery corresponds to theend of Dtfrustrated the time when conditions be-come clement enough for biogenesis

All the gamblers had the same (but unknown)

IS LIFE COMMON IN THE UNIVERSE 297

FIG 3 Zoomed-in version of Fig 2 with two differences (1) The window for biogenesis shown here is at the shortend of the range permitted by observations Dtbiogenesis 5 25 Myr (2) In Fig 2 by normalizing the histograms to 4566Gyr we have assumed that Earth is a random member of a group of planets at least 4566 Gyr old upon which bio-genesis could have happened anytime up to 4566 after formation including 1 million years ago This ignores thenonobservability-of-recent-biogenesis selection effect Here to minimize the influence of this selection effect we onlyallow biogenesis to occur anytime earlier than 377 Gyr ago [ie within ldquoDt(N 5 4)rdquo] The influence of this normal-ization time Dt(N) is illustrated in Fig 4

chance of winning the lottery each time theybought a ticket (q is the probability of winningper day) This corresponds to a group of ter-restrial planets with approximately the same(but unknown) chance of biogenesis as theEarth (q is the probability of biogenesis withina period of time called here Dtbiogenesis)

We selected a gambler at random from thosewho had won on or before the Nth day Thuswe conditioned on winning before a certaintime This corresponds to assuming that theEarth is a random member of the group of ter-restrial planets that has had biogenesis on orbefore the end of Dt(N) 5 N 3 Dtbiogenesis Con-ditioning on biogenesis before this time corre-

sponds to correcting for the selection effect thatbiogenesis had to have occurred for us to behere

A gambler chosen at random from the groupthat has won within N days found that he hadwon on the first day (n 5 1) This correspondsto finding that biogenesis has occurred rapidlyon Earth that is within Dtbiogenesis

If we set N 5 1 [see Fig 4 +(11 q)] we areconditioning on rapid biogenesis We are con-sidering a group all of whose members havehad rapid biogenesis In this case a randommember having rapid biogenesis can tell usnothing about the probability q To infer some-thing about q we must have N 1

Nonobservability of recent biogenesis

If our conclusions from the daily lottery are toapply to biogenesis on terrestrial planets we need

LINEWEAVER AND DAVIS298

FIG 4 The effect on the likelihood of varying thesomewhat arbitrary number of days that the gamblershave to have won by to be in the group In contrast toFig 1 all the likelihoods of q here are based on the in-formation that a gambler (chosen at random from thegroup whose members have won within N days) has wonon the first day These likelihoods are plotted and labeledldquo+(1N q)rdquo with NIcirc124 In the biogenesis lottery(just as in the daily lottery) N defines the group and is ameasure of the duration biogenesis could have taken[Dt(N) 5 N 3 Dtbiogenesis) For example if N 5 1 we can-not say anything about q since the likelihood +(11 q) isflat (we have conditioned on ldquorapidrdquo biogenesis) Whileif N 5 ` we can put the strongest constraint on q If n 51 (when it could have been much larger 1 n N) wehave more information about q and the likelihood forlarge q is higher (see Appendix Eq A3) The ratio of theprobabilities in the histograms in Fig 3 corresponds tothe ratio of the +(14 q) likelihoods here 3926 5+(14 q 5 030)+(14 q 5 003)5 0690465 15 Thatis with n 5 1 and N 5 4 values of q lt030 are 50 morelikely to be the case than q lt003 [in Fig 3 Dt(N) 5 4 325 Myr] Notice that for 2 N ` the 95 lower limitfor q varies only between 007 and 023

FIG 5 Likelihood of qN In Figs 1 and 4 the likelihoodof q is shown where q is the probability of winning onany one day Here we show likelihoods of qN the un-known probability of winning on or before the Nth dayThis figure shows the effect of varying N The informa-tion used to compute these likelihoods is that a gamblerchosen at random from the group whose members havewon within N days has won on the first day (see Ap-pendix Eqs A6ndashA8) Translated this becomes a planetchosen at random from the group of planets that has hadbiogenesis within Dt(N) 5 N 3 Dtbiogenesis has had bio-genesis within Dtbiogenesis As in Fig 4 if N 5 1 we cansay nothing meaningful about q1 (5 q) However even ifN 5 2 we can make a stronger statement about q2 thanwe could about q q2 013 at the 95 confidence levelThe 95 lower limit on qN increases dramatically as N in-creases constraining qN to be close to 1 The ability to ex-tract a useful constraint even if N is low reduces the in-fluence of the selection effects discussed in the text

to correct for the fact that the evolution of an ob-server takes some time How long it takes ob-serving equipment or complex life or multicel-lular eukaryotes to evolve is difficult to say OnEarth it took 4 Gyr A limited pace of evolutionhas prevented us from looking back at our ownhistory and seeing that biogenesis happened lastyear or even more recently than 2 Gyr ago (weconsider a plausible range for the requisite timeelapsed since biogenesis to be between 2 and 10billion years or Dtevolve 5 416

22 Gyr)This selection effect for nonrecent biogenesis is

selecting for biogenesis to happen a few billionyears before the present regardless of whether ithappened rapidly It is not a selection effect forrapid biogenesis since the longer it took us toevolve to a point when we could measure the ageof the Earth the older the Earth became Simi-larly if biogenesis took 1 Gyr longer than it ac-tually did we would currently find the age of theEarth to be 5566 Gyr (5 4566 1 1) old ldquoWhy isthe Earth 4566 billion years oldrdquo ldquoBecause ittook that long to find it outrdquo The generalizationof this plausible assumption to the ensemble ofterrestrial planets is necessary if the likelihoodsand constraints in Figs 1 4 and 5 are to be ap-plicable to the group of terrestrial planets

Potential problems

Any effect that makes rapid biogenesis a pre-requisite for life would undermine our inferencesfor q For example although it is usually assumedthat the heavy bombardment inhibited biogene-sis energetic impacts may have set up largechemical and thermal disequilibria that playsome crucial role in biogenesis We know so lit-tle about the details of the chemical evolution thatled to life that heat pulses and rapid cooling af-ter large impacts may be part of the preconditionsfor biogenesis If true the time scale of biogene-sis would be linked to the time scale of the ex-ponential decay of bombardment and biogenesiswould (if it occurred at all) be necessarily rapidmost extant life in the Universe would have rapidbiogenesis and little could be inferred about theabsolute value of q from our sample of 1

In a panspermia scenario the rapid appearanceof life on Earth is explained not by rapid terres-trial biogenesis as assumed here but by the ubiq-uity of the ldquoseeds of liferdquo (eg Hoyle and Wick-ramasinghe 1999) An analysis in the context of

a panspermia scenario would be subject to thesame observational constraints as terrestrial bio-genesis and would therefore lead to the same in-ferred probability for the appearance of life onother terrestrial planets

Another potential problem Suppose the auto-catalytic chemical cycles leading to life are expo-nentially sensitive to some still unknown pecu-liarity of the initial conditions on Earth In thiscase to have the same q as the Earth our groupof terrestrial planets may have to be almost in-distinguishable rare clones of Earth That is con-ditioning on planets identical to Earth (ldquosame qrdquo)would be conditioning on rapid biogenesis (N 51) and would prevent us from inferring muchabout q from the observations of rapid biogene-sis on Earth [see +(11 q) in Fig 4]

This is an example of the more general issue ofthe status of the rapidity of biogenesis on EarthDid it have to be rapid If we assume it couldhave been otherwise then we can infer somethingabout q If it had to be that way we cannot Themiddle ground might be the most plausible op-tion Biogenesis did not necessarily have to hap-pen as rapidly as it did but (to be consistent withour existence) it may have had to happen within1 or 2 billion years of the Earthrsquos formation

If this is true we need to look carefully at theinfluence of varying the somewhat arbitrary andcounterfactual duration [Dt(N) 5 N 3 Dtbiogenesis]that biogenesis could have taken on Earth Whatvalues of Dt(N) are plausible and how do theyaffect the results This is done in Fig 4 whichquantifies the degree of variability one can as-sume for the duration of biogenesis and still haveinteresting constraints on q The lower N is theless variability is assumed For example if N 5 2[see +(12 q)] we are assuming that biogenesiscould only have taken as long as 2 3 Dtbiogenesismdashenough variability to be able to say somethingabout q but small enough to maintain the nonob-servability of recent biogenesis

Figure 5 allows us to generalize our inferencesabout q (the probability of biogenesis within Dtbiogenesis) to inferences about qN [the probabil-ity of biogenesis within an arbitrary time Dt(N)]Specifically it shows that we only need to be ableto assume that biogenesis could have been twiceas long as Dtbiogenesis to have interesting con-straints q2 013 at the 95 confidence level [see+(12 qN)] This is the result reported in the ab-stract

IS LIFE COMMON IN THE UNIVERSE 299

HOW COMMON IS LIFE

Relation of our analysis to the Drake Equation

The Drake Equation was devised to address thequestion of ldquoHow many communicative civiliza-tions are in our Galaxyrdquo (eg Sagan 1973) It hasbeen criticized as ldquoa way of compressing a largeamount of ignorance into a small spacerdquo (Olivercited in Dicke 1998) Despite its shortcomings itcontinues to focus the efforts of the search for ex-traterrestrial intelligence (SETI) community Animportant goal of the SETI community is to turnits subjective probabilities into mathematicalprobabilities We have done that here for one ofthe most important terms

We are interested in a simpler question ldquoHowcommon is life in the Universerdquo Our question issimpler because life is more generic than intelli-gent or technological life We modify the DrakeEquation to address our question and introducea parameter F which is a measure of how com-mon life is in the universe F is the fraction of starsin our galaxy today orbited by planets that havehad independent biogenesis

F 5 NlN p 5 fp fe fl (3)

where Nl is the number of stars in our Galaxy or-bited by planets that have had independent bio-genesis N p is the number of stars in our Galaxyfp is the fraction of stars in our Galaxy with plan-etary systems fe is the fraction of these planetarysystems that have a terrestrial planet suitable forlife in the same way as the Earth that is theyhave approximately the same probability q as theEarth and fl is the fraction of these suitable plan-ets on which biogenesis has occurred

Many recent observations of the frequency andage dependence of circumstellar disks aroundyoung stars in star-forming regions support thewidely accepted idea that planet formation is acommon by-product of star formation and thatthe fraction of stars with planetary systems isclose to unity fp lt 1 (eg Habing et al 1999 Mc-Caughrean et al 2000 Meyer and Beckwith2000)

Equation 3 then becomes

F lt fe fl (4)

If F 1022 then 1 of all stars have (or havehad) life and we conclude that life is ldquocommonrdquo

in the Universe If F 10211 we may be the onlylife in the Galaxy and life is ldquorarerdquo

There has been little agreement on the value offl Hart (1996) wrote ldquoThe value of fl is extremelyspeculativerdquo but argued based on the concate-nation of low probabilities that it must be ex-tremely small and thus life elsewhere is improb-able However Shostak (1998) assumed quite theopposite ldquoOn the basis of the rapidity with whichbiology blossomed on Earth we can optimisti-cally speculate that this fraction ( fl ) is also one(100)rdquo Our analysis is a close statistical look atthis optimistic speculation

The relation between the fraction of suitableplanets on which biogenesis has occurred (ldquoflrdquo inthe Drake Equation) and the q analyzed here is

fl(qN) 5 1 2 (1 2 q)N (5)

fl(qDt(N)) 5 1 2 (1 2 q) (6)

fl(qt) 5 1 2 (1 2 q) (7)

where Eq 5 refers to the daily lottery (see Ap-pendix Eq A5) Eq 6 is the translation to the bio-genesis lottery and we obtain Eq 7 by using t 5Dtfrustrated 1 Dt(N) Equation 7 is plotted in Figs2 and 3 Thus in Eq 7 we have expressed the ldquoflrdquoterm of the Drake Equation as a function of timeof the observables Dtfrustrated and Dtbiogenesis andof the probability q for which we have derivedthe relative likelihood In addition since fl(qN) 5qN (see Eq A5) Fig 5 shows the relative likeli-hood of fl and establishes quantitative but model-dependent (specifically N 1-dependent) con-straints on fl For example for terrestrial planetsolder than 1 Gyr (2 3 Dtbiogenesis) fl 13 atthe 95 confidence level

However to go from fl to an answer to the ques-tion ldquoHow common is liferdquo (ie to go from fl toF in Eq 4 we need to know fe the fraction of theseplanetary systems with a terrestrial planet suitablefor life in the same way as the Earth Our under-standing of planet formation is consistent with theidea that ldquoterrestrialrdquo planet formation is a com-mon feature of star formation (Wetherill 1996 Lis-sauer and Lin 2000) The mass histogram of de-tected extrasolar planets peaks at low masses(dNdM ~ M21) and is also consistent with thisidea (Tabachnik and Tremaine 2001 Zucker andMazeh 2001 Lineweaver and Grether 2002)

Our analysis assumed the existence of a group

1t2

D

D

tb

t

i

f

o

r

g

u

e

s

n

tr

e

a

s

t

i

e

s

d 2

1DtbD

io

t(

g

N

en

)

esis 2

LINEWEAVER AND DAVIS300

of terrestrial planets with approximately thesame but unknown (q [ [01]) probability of bio-genesis It is reasonable to postulate the existenceof such a q group since although we do not knowthe details of the chemical evolution that led tolife we have some ideas about the factors in-volved energy flux temperatures the presenceof water planet orbit residence time in the con-tinuously habitable zone mass of the planet at-mospheric composition bombardment rate at theend of planetary accretion and its dependence onthe masses of the large planets in the planetarysystem metallicity of the prestellar molecularcloud crust composition vulcanism basic chem-istry hydration pH and presence of particularclay minerals amino acids and other molecularbuilding blocks for life (Lahav 1999) Since all ormany of these physical variables determine theprobability of biogenesis and since the Earthdoes not seem to be special with respect to anyof them (ie the Earth probably does not occupya thinly populated region of this multidimen-sional parameter space) the assumption that theprobability of biogenesis on these planets wouldbe approximately the same as on Earth is plausi-ble This is equivalent to assuming that q is aldquoslowlyrdquo varying function of environment Iftrue fe and F are not vanishingly small This canbe contrasted with the ldquoexponentially sensitiverdquocase discussed in Potential problems

DISCUSSION

Carter (1983) has pointed out that the time scalefor the evolution of intelligence on the Earth (5Gyr) is comparable to the main sequence lifetimeof the Sun (10 Gyr) Under the assumption thatthese two time scales are independent he arguedthat this would be unlikely to be observed unlessthe average time scale for the evolution of intel-ligence on a terrestrial planet is much longer thanthe main sequence lifetime of the host star [seeLivio (1999) for an objection to the idea that thesetwo time scales are independent] Carterrsquos argu-ment is strengthened by recent models of the ter-restrial biosphere indicating that the gradual in-crease of solar luminosity will make Earthuninhabitable in a billion years or somdashseveral billion years before the Sun leaves the main se-quence (Caldeira and Kasting 1992 Rampinoand Caldeira 1994)

Our analysis is similar in style to Carterrsquos how-

ever we are concerned with the appearance ofthe earliest life forms not the appearance of in-telligent life Subject to the caveats raised in Po-tential problems and by Livio (1999) the implica-tions of our analysis and Carterrsquos are consistentand complementary The appearance of life onterrestrial planets may be common but the ap-pearance of intelligent life may be rare

SUMMARY

Our existence on Earth does not mean that theprobability of biogenesis on a terrestrial planetq is large because if q were infinitesimallysmall and there were only one life-harboringplanet in the Universe we would of necessityfind ourselves on that planet However such ascenario would imply either that Earth has aunique chemistry or that terrestrial biogenesishas taken a long time to occur Neither is sup-ported by the evidence we have Since little canbe said about the probability q of terrestrialbiogenesis from our existence we assume max-imum ignorance 0 q 1 We then use theobservation of rapid terrestrial biogenesis toconstrain q (Fig 4)

We convert the constraints on q into constraintson the fl term of the Drake Equation (the frac-tion of suitable planets that have life) For ter-restrial planets older than 1 Gyr we find thatfl is most probably close to unity and 13 atthe 95 confidence level

If terrestrial planets are common and they haveapproximately the same probability of biogen-esis as the Earth our inference of high q (orhigh qN) indicates that a substantial fraction ofterrestrial planets have life and thus life is com-mon in the UniverseHowever there are assumptions and selection

effects that complicate this result

Although we correct the analysis for the factthat biogenesis is a prerequisite for our exis-tence our result depends on the plausible as-sumption that rapid biogenesis is not such aprerequisite

Although we have evidence that the fraction ofplanets that are ldquoterrestrialrdquo in a broad astro-nomical sense (rocky planet in the continu-ously habitable zone) is large this may be dif-ferent from the fraction of planets that areldquoterrestrialrdquo in a more detailed chemical sense

IS LIFE COMMON IN THE UNIVERSE 301

Although we can make reasonable estimates ofwhat the crusts and atmospheres are made ofwithout detailed knowledge of the steps ofchemical evolution we cannot be sure that as-tronomically terrestrial planets have the sameq as Earth That is the fraction of planets be-longing to the Earthrsquos q group is uncertainThus although we have been able to quantifythe fl term of the Drake Equation using rapidbiogenesis our knowledge of the fe term is stillonly qualitative and inhibits our ability to drawstronger conclusions about how common lifeis in the Universe

APPENDIX LIKELIHOODCOMPUTATIONS

Let the unknown but constant probability ofwinning a daily lottery be q Given the informa-tion that a gambler who buys one ticket each dayfor n days lost on the first n 2 1 days and wonon the nth day we can compute the likelihoodfunction for q (probability of the data given themodel q)

L(n q) 5 (1 2 q)n21q (A1)

This is equal to the fraction of all gamblers whofirst experienced (n21) losses and then wonGiven only the information that the gambler wonat least once on or before the nth day the likeli-hood function for q is

L(n q) 5 1 2 (1 2 q)n (A2)

This is equal to the fraction of all gamblers whohave won at least once on or before the nth dayGiven the information that a group of gamblershave won at least once on or before the Nth dayand that a gambler chosen at random from thisgroup won at least once on or before the nth day(n N) the likelihood of q is

L(n N q) 5 5 (A3)

Out of all the gamblers who have won on or be-fore the Nth day this is the fraction who havewon on or before the nth day Notice that as N Rn the likelihood of low q increases and that if N 5n the likelihood is the same for all q (see Fig 4)As N R ` we have L(n N q) R L(n q)

1 2 (1 2 q)n1 2 (1 2 q)N

L(n q)L(N q)

which yields the tightest constraints on q A nor-malized likelihood + (or probability density) isdefined such that ograve10 +(q)dq 5 1 Thus the renor-malization conversion is

+(x) 5(A4)

The normalized likelihoods for Eqs A1ndashA3 areplotted in Fig 1 for the cases n 5 3 and N 5 12The 95 confidence levels cited are Bayesiancredible intervals based on a uniform prior for q

Although q is the probability of winning thelottery in 1 day we would like to generalize andask what is the probability qN of winning the lot-tery within N days In the analogous biogenesislottery q is the probability of biogenesis on a ter-restrial planet with the same unknown probabil-ity of biogenesis as the Earth The time windowfor biogenesis constrained by observations onEarth Dtbiogenesis corresponds to 1 day for thegambler However we would like to compute thelikelihood of biogenesis after an arbitrary periodof time Dt(N) 5 N 3 Dtbiogenesis Let qN be theprobability of winning on or before the Nth day

qN 5 1 2 (1 2 q)N 5 L(N q) (A5)

(see Eqs A2 and A3) We would like to know thelikelihood of qN rather than limit ourselves to thelikelihood of q (5q1) Suppose the information is the same that was available to computeL(n N q) That information is A randomly cho-sen gambler from the group of gamblers who havewon after N days won on or before the nth dayWe want L(n N qN) The relationship betweenthe likelihood of qN and the likelihood of q is

+(n N qN) dqN 5 +(n N q) dq (A6)

which with dqNdq 5 N(1 2 q)N21 (from Eq A5)becomes

+(n N qN)

5 (A7)

5 (A8)

which is plotted in Fig 5 and has as expected rel-atively larger likelihoods for larger values of qN

+(n N q)N(1 2 q)N21

+(n N q)

dqNdq

+(x)

E1

0L(x)dx

LINEWEAVER AND DAVIS302

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

was a period without life (Dtfrustrated) followedby a period during which life evolved (Dtbiogenesis)followed by a period during which life has beenpresent (Dtlife) The sum of these intervals addsup to the age of the Earth (Fig 2)

Dtfrustrated 1 Dtbiogenesis 1 Dtlife 5 DtEarth (1)

where DtEarth 5 4566 6 0002 Gyr (Allegravegre et al1995) As older fossils and biosignatures havebeen found Dtlife has gotten longer The signifi-cance of large impacts in frustrating or sterilizingprotolife has only recently been appreciated andassessed (Dtfrustrated) Combined these observa-tions indicate that biogenesis was rapid since Dtbiogenesis is caught in the middlemdashthe longer Dtfrustrated and Dtlife get the shorter Dtbiogenesismust get The distinction between how rapid bio-genesis was and when it was is important becauseour result the inferred probability of biogenesisdepends on how rapid it was while only a mar-

ginal selection effect depends on when it was (seeSelection Effects)

The majority of the Earthrsquos mass accreted fromplanetesimals within the first 100 million years ofthe Earthrsquos formation (Halliday 2000) With aninitially molten surface life could not have ap-peared The transition from accretion to heavybombardment included the formation of theMoon by the collision with a Mars-sized object45 Gyr ago (Hartmann and Davis 1975 Canupand Asphaug 2001 Halliday 2001) We can in-fer from the dates and sizes of lunar impact cra-tors whose record goes back to when the Moonformed a solid crust [444 Gyr ago (Sleep et al1989)] that the surface of the Earth was periodi-cally vaporized Since the mass of the Earth is 80times the mass of the Moon impacts on the Earthwere more numerous and more energetic and pe-riodically produced 2000K rock vapor atmos-pheres that lasted for several thousand years(Hartmann et al 2000 Sleep et al 2001) These

IS LIFE COMMON IN THE UNIVERSE 295

FIG 2 We divide the history of the Earth into three epochs Impact frustration Biogenesis and Life The blackcurves show the percentages of terrestial planets with life as a function of time assuming two different probabilitiesof biogenesis (q 5 03 003) within Dtbiogenesis 5 600 Myr The percentages in the histograms on the right (14 and32) are obtained from comparing the subset of planets that have formed life within Dtbiogenesis (middle gray) withthe total number of planets that have life (or have had biogenesis) within 4566 Gyr of their formation (cross-hatched)If q is high (030 thick line) a large fraction (32) of the planets that have evolved life within 4566 Gyr of formationhave life that evolved rapidlymdashwithin Dtbiogenesismdashon their planets If q is low (003 thin line) then a smaller fraction(14) will have life that evolved rapidly These different percentages illustrate the principle that a single observationof rapid terrestrial biogenesis is more likely to be the result of high q This allows us to compute the relative likeli-hood of q and to constrain q (see Fig 4)

conditions were probably an effective and recur-ring autoclave for sterilizing the earliest life formsor more generally frustrating the evolution of lifeA steadily decreasing heavy bombardment con-tinued until 38 Gyr ago

Estimates of the time of the most recent steril-izing impact range between 444 and 37 Gyr ago(Maher and Stevenson 1988 Oberbeck andFogleman 1989 Sleep et al 1989 Halliday 2001)These estimates span the time from the solidifi-cation of the Moonrsquos crust to the end of the lateheavy bombardment Thus life was frustrated forat least the first 01 Gyr and possibly as long asthe first 09 Gyr of the Earthrsquos existence We takeour preferred value as the middle of this rangeDtfrustrated lt 05 6 04 Gyr The range of these es-timates reflects the large uncertainties due tosmall number statistics for the largest impactorsand the uncertainty of the energy required to ster-ilize the Earth completely We do not know wherebiogenesis happened or the extent to which it wasprotected from the effects of impacts Tidal poolshave little protection hydrothermal vents havesome protection while autotrophic thermophilesin subsurface rock under several kilometers ofcrust were probably in effective bomb shelters

The roots of the universal tree of life point toa thermophilic origin (or at least a thermophiliccommon ancestor) for all life on Earth (Pace 1991Stetter 1996) This suggests a hot biogenesis inhydrothermal vents or possibly subsurface rockandor selection for thermophilia by periodictemperature pulses from large impacts If weknew that life evolved on the surface of the Earthand was therefore more susceptible to impactsterilizations life would have been frustratedlonger and our preferred value would be moreprecise Dtfrustrated lt 07 6 02 Gyr

If we accept the carbon isotopic evidence forlife 385 billion years ago (Mojzsis et al 1996)then life has been on Earth at least that long (ieDtlife is at least 385 Gyr) In addition because ofthe Earthrsquos tectonic history this time is also theearliest time we could reasonably hope to find bi-ological evidence from rocks on Earthmdasheven iflife existed earlier With this selection effect inmind (which we know exists at some level) ourpreferred value for the time life has existed onEarth is Dtlife lt 40104

202 GyrIt is possible that biogenesis occurred several

times on Earth For example during the periodDtfrustrated life could have evolved and been ster-ilized multiple times We do not know if this hap-

pened Similar potential sterilizations and bio-geneses could have occurred during the periodDtlife but we do not know For the purposes ofthis analysis we can ignore this complication Weare only interested in the shortest period withinwhich the observations can constrain biogenesisto have occurred Thus Dtbiogenesis is our best ob-servational constraint on any epoch of biogene-sis and this happens to be on the period betweenthe most recent sterilizing impact that is olderthan the oldest evidence we have for life on Earth

Since our preferred values yield Dtfrustrated 1Dtlife lt DtEarth there is little time left for biogen-esis to have occurred This is the basis for thestatement that biogenesis occurred rapidly Sub-stituting our three preferred values DtEarth Dtfrustrated and Dtlife into Eq 1 and solving for Dtbiogenesis yields

Dtbiogenesis 5 01105201 Gyr (2)

Thus we take 600 Myr as a crude estimate ofthe upper limit for the time it took life to appearon Earth Assuming biogenesis took place on thesurface of the Earth Oberbeck and Fogleman(1989) found this maximum time to be 25 MyrMaher and Stevenson (1988) assumed that bio-genesis took somewhere between 01 and 10 Myrdepending on environment while Sleep et al(2001) found a similar range for evolutionarilysignificant periods of clement surface conditionsIndependently biologists specializing in thechemistry of the origin of life have estimated thatthe time required for biogenesis is potentiallyquite short (Miller 1982) and could be 8 Myr(Lazcano and Miller 1994) Thus several lines ofevidence indicate that biogenesis was geologi-cally rapid If biogenesis occurred in the fissuresaround a hydrothermal vent or in subsurfacerocks it was well protected and we can only con-strain biogenesis to have taken less than 600Myr If biogenesis occurred on the surface itprobably took less than 25 Myr In this analy-sis we consider 600 and 25 Myr to represent thehigh and low ends of a plausible range for Dtbiogenesis (Figs 2 and 3 respectively)

These observational constraints on DtfrustratedDtbiogenesis and Dtlife are important because theyquantify how rapidly biogenesis occurred onEarth and enable us to put limits on the proba-bility that biogenesis occurred on other planetsFor example consider a group of terrestrial plan-ets with approximately the same probability of

LINEWEAVER AND DAVIS296

biogenesis ldquoqrdquo as Earth Suppose q 5 030 Attheir formation none of these planets had life Astime passed life arose on more and more of themThe thick line in Fig 2 shows the increasing per-centage of these planets with life as time passesAfter Dtbiogenesis 30 will have life (that is howq 5 030 is defined) After 4566 Gyr 93 willhave life (7 still will not) Of that 93 32 willlike the Earth have had biogenesis within Dtbiogenesis The histogram on the far right of Fig2 represents these numbers Suppose q is only003 Then only 20 will have life after 4566 Gyrand only 14 of those will have had biogenesislike the Earth within Dtbiogenesis Assuming Earthis a random member of the planets with life thesingle observation that biogenesis occurredwithin Dtbiogenesis on Earth indicates that largervalues of q are more likely than small values Thisis the basic idea behind our analysis It is illus-trated in Figs 1 4 and 5 which also show quan-titative constraints on q under the various as-sumptions discussed in the next section

The histograms in Figs 2 and 3 also show thatif q is large the fraction of gamblers or terrestrialplanets who have won after a certain time is large

Suppose the gambler did not know how manygamblers had won by the 12th day but only thathe is a random member of the group that had wonFrom the fact that he won quickly he can infer thatq is large This tells the gambler that after a fewdays a large fraction of lottery ticket buyers are inthe winnersrsquo group He is not alone For the bio-genesis lottery finding large q means that after afew times Dtbiogenesis a large fraction of the terres-trial planets with probability of biogenesis similarto the Earth have (or have had) life

SELECTION EFFECTS

Daily lottery R biogenesis lottery

In the first section we drew parallels betweena daily lottery and a biogenesis lottery Explicitlythese parallels are

The first day of the lottery corresponds to theend of Dtfrustrated the time when conditions be-come clement enough for biogenesis

All the gamblers had the same (but unknown)

IS LIFE COMMON IN THE UNIVERSE 297

FIG 3 Zoomed-in version of Fig 2 with two differences (1) The window for biogenesis shown here is at the shortend of the range permitted by observations Dtbiogenesis 5 25 Myr (2) In Fig 2 by normalizing the histograms to 4566Gyr we have assumed that Earth is a random member of a group of planets at least 4566 Gyr old upon which bio-genesis could have happened anytime up to 4566 after formation including 1 million years ago This ignores thenonobservability-of-recent-biogenesis selection effect Here to minimize the influence of this selection effect we onlyallow biogenesis to occur anytime earlier than 377 Gyr ago [ie within ldquoDt(N 5 4)rdquo] The influence of this normal-ization time Dt(N) is illustrated in Fig 4

chance of winning the lottery each time theybought a ticket (q is the probability of winningper day) This corresponds to a group of ter-restrial planets with approximately the same(but unknown) chance of biogenesis as theEarth (q is the probability of biogenesis withina period of time called here Dtbiogenesis)

We selected a gambler at random from thosewho had won on or before the Nth day Thuswe conditioned on winning before a certaintime This corresponds to assuming that theEarth is a random member of the group of ter-restrial planets that has had biogenesis on orbefore the end of Dt(N) 5 N 3 Dtbiogenesis Con-ditioning on biogenesis before this time corre-

sponds to correcting for the selection effect thatbiogenesis had to have occurred for us to behere

A gambler chosen at random from the groupthat has won within N days found that he hadwon on the first day (n 5 1) This correspondsto finding that biogenesis has occurred rapidlyon Earth that is within Dtbiogenesis

If we set N 5 1 [see Fig 4 +(11 q)] we areconditioning on rapid biogenesis We are con-sidering a group all of whose members havehad rapid biogenesis In this case a randommember having rapid biogenesis can tell usnothing about the probability q To infer some-thing about q we must have N 1

Nonobservability of recent biogenesis

If our conclusions from the daily lottery are toapply to biogenesis on terrestrial planets we need

LINEWEAVER AND DAVIS298

FIG 4 The effect on the likelihood of varying thesomewhat arbitrary number of days that the gamblershave to have won by to be in the group In contrast toFig 1 all the likelihoods of q here are based on the in-formation that a gambler (chosen at random from thegroup whose members have won within N days) has wonon the first day These likelihoods are plotted and labeledldquo+(1N q)rdquo with NIcirc124 In the biogenesis lottery(just as in the daily lottery) N defines the group and is ameasure of the duration biogenesis could have taken[Dt(N) 5 N 3 Dtbiogenesis) For example if N 5 1 we can-not say anything about q since the likelihood +(11 q) isflat (we have conditioned on ldquorapidrdquo biogenesis) Whileif N 5 ` we can put the strongest constraint on q If n 51 (when it could have been much larger 1 n N) wehave more information about q and the likelihood forlarge q is higher (see Appendix Eq A3) The ratio of theprobabilities in the histograms in Fig 3 corresponds tothe ratio of the +(14 q) likelihoods here 3926 5+(14 q 5 030)+(14 q 5 003)5 0690465 15 Thatis with n 5 1 and N 5 4 values of q lt030 are 50 morelikely to be the case than q lt003 [in Fig 3 Dt(N) 5 4 325 Myr] Notice that for 2 N ` the 95 lower limitfor q varies only between 007 and 023

FIG 5 Likelihood of qN In Figs 1 and 4 the likelihoodof q is shown where q is the probability of winning onany one day Here we show likelihoods of qN the un-known probability of winning on or before the Nth dayThis figure shows the effect of varying N The informa-tion used to compute these likelihoods is that a gamblerchosen at random from the group whose members havewon within N days has won on the first day (see Ap-pendix Eqs A6ndashA8) Translated this becomes a planetchosen at random from the group of planets that has hadbiogenesis within Dt(N) 5 N 3 Dtbiogenesis has had bio-genesis within Dtbiogenesis As in Fig 4 if N 5 1 we cansay nothing meaningful about q1 (5 q) However even ifN 5 2 we can make a stronger statement about q2 thanwe could about q q2 013 at the 95 confidence levelThe 95 lower limit on qN increases dramatically as N in-creases constraining qN to be close to 1 The ability to ex-tract a useful constraint even if N is low reduces the in-fluence of the selection effects discussed in the text

to correct for the fact that the evolution of an ob-server takes some time How long it takes ob-serving equipment or complex life or multicel-lular eukaryotes to evolve is difficult to say OnEarth it took 4 Gyr A limited pace of evolutionhas prevented us from looking back at our ownhistory and seeing that biogenesis happened lastyear or even more recently than 2 Gyr ago (weconsider a plausible range for the requisite timeelapsed since biogenesis to be between 2 and 10billion years or Dtevolve 5 416

22 Gyr)This selection effect for nonrecent biogenesis is

selecting for biogenesis to happen a few billionyears before the present regardless of whether ithappened rapidly It is not a selection effect forrapid biogenesis since the longer it took us toevolve to a point when we could measure the ageof the Earth the older the Earth became Simi-larly if biogenesis took 1 Gyr longer than it ac-tually did we would currently find the age of theEarth to be 5566 Gyr (5 4566 1 1) old ldquoWhy isthe Earth 4566 billion years oldrdquo ldquoBecause ittook that long to find it outrdquo The generalizationof this plausible assumption to the ensemble ofterrestrial planets is necessary if the likelihoodsand constraints in Figs 1 4 and 5 are to be ap-plicable to the group of terrestrial planets

Potential problems

Any effect that makes rapid biogenesis a pre-requisite for life would undermine our inferencesfor q For example although it is usually assumedthat the heavy bombardment inhibited biogene-sis energetic impacts may have set up largechemical and thermal disequilibria that playsome crucial role in biogenesis We know so lit-tle about the details of the chemical evolution thatled to life that heat pulses and rapid cooling af-ter large impacts may be part of the preconditionsfor biogenesis If true the time scale of biogene-sis would be linked to the time scale of the ex-ponential decay of bombardment and biogenesiswould (if it occurred at all) be necessarily rapidmost extant life in the Universe would have rapidbiogenesis and little could be inferred about theabsolute value of q from our sample of 1

In a panspermia scenario the rapid appearanceof life on Earth is explained not by rapid terres-trial biogenesis as assumed here but by the ubiq-uity of the ldquoseeds of liferdquo (eg Hoyle and Wick-ramasinghe 1999) An analysis in the context of

a panspermia scenario would be subject to thesame observational constraints as terrestrial bio-genesis and would therefore lead to the same in-ferred probability for the appearance of life onother terrestrial planets

Another potential problem Suppose the auto-catalytic chemical cycles leading to life are expo-nentially sensitive to some still unknown pecu-liarity of the initial conditions on Earth In thiscase to have the same q as the Earth our groupof terrestrial planets may have to be almost in-distinguishable rare clones of Earth That is con-ditioning on planets identical to Earth (ldquosame qrdquo)would be conditioning on rapid biogenesis (N 51) and would prevent us from inferring muchabout q from the observations of rapid biogene-sis on Earth [see +(11 q) in Fig 4]

This is an example of the more general issue ofthe status of the rapidity of biogenesis on EarthDid it have to be rapid If we assume it couldhave been otherwise then we can infer somethingabout q If it had to be that way we cannot Themiddle ground might be the most plausible op-tion Biogenesis did not necessarily have to hap-pen as rapidly as it did but (to be consistent withour existence) it may have had to happen within1 or 2 billion years of the Earthrsquos formation

If this is true we need to look carefully at theinfluence of varying the somewhat arbitrary andcounterfactual duration [Dt(N) 5 N 3 Dtbiogenesis]that biogenesis could have taken on Earth Whatvalues of Dt(N) are plausible and how do theyaffect the results This is done in Fig 4 whichquantifies the degree of variability one can as-sume for the duration of biogenesis and still haveinteresting constraints on q The lower N is theless variability is assumed For example if N 5 2[see +(12 q)] we are assuming that biogenesiscould only have taken as long as 2 3 Dtbiogenesismdashenough variability to be able to say somethingabout q but small enough to maintain the nonob-servability of recent biogenesis

Figure 5 allows us to generalize our inferencesabout q (the probability of biogenesis within Dtbiogenesis) to inferences about qN [the probabil-ity of biogenesis within an arbitrary time Dt(N)]Specifically it shows that we only need to be ableto assume that biogenesis could have been twiceas long as Dtbiogenesis to have interesting con-straints q2 013 at the 95 confidence level [see+(12 qN)] This is the result reported in the ab-stract

IS LIFE COMMON IN THE UNIVERSE 299

HOW COMMON IS LIFE

Relation of our analysis to the Drake Equation

The Drake Equation was devised to address thequestion of ldquoHow many communicative civiliza-tions are in our Galaxyrdquo (eg Sagan 1973) It hasbeen criticized as ldquoa way of compressing a largeamount of ignorance into a small spacerdquo (Olivercited in Dicke 1998) Despite its shortcomings itcontinues to focus the efforts of the search for ex-traterrestrial intelligence (SETI) community Animportant goal of the SETI community is to turnits subjective probabilities into mathematicalprobabilities We have done that here for one ofthe most important terms

We are interested in a simpler question ldquoHowcommon is life in the Universerdquo Our question issimpler because life is more generic than intelli-gent or technological life We modify the DrakeEquation to address our question and introducea parameter F which is a measure of how com-mon life is in the universe F is the fraction of starsin our galaxy today orbited by planets that havehad independent biogenesis

F 5 NlN p 5 fp fe fl (3)

where Nl is the number of stars in our Galaxy or-bited by planets that have had independent bio-genesis N p is the number of stars in our Galaxyfp is the fraction of stars in our Galaxy with plan-etary systems fe is the fraction of these planetarysystems that have a terrestrial planet suitable forlife in the same way as the Earth that is theyhave approximately the same probability q as theEarth and fl is the fraction of these suitable plan-ets on which biogenesis has occurred

Many recent observations of the frequency andage dependence of circumstellar disks aroundyoung stars in star-forming regions support thewidely accepted idea that planet formation is acommon by-product of star formation and thatthe fraction of stars with planetary systems isclose to unity fp lt 1 (eg Habing et al 1999 Mc-Caughrean et al 2000 Meyer and Beckwith2000)

Equation 3 then becomes

F lt fe fl (4)

If F 1022 then 1 of all stars have (or havehad) life and we conclude that life is ldquocommonrdquo

in the Universe If F 10211 we may be the onlylife in the Galaxy and life is ldquorarerdquo

There has been little agreement on the value offl Hart (1996) wrote ldquoThe value of fl is extremelyspeculativerdquo but argued based on the concate-nation of low probabilities that it must be ex-tremely small and thus life elsewhere is improb-able However Shostak (1998) assumed quite theopposite ldquoOn the basis of the rapidity with whichbiology blossomed on Earth we can optimisti-cally speculate that this fraction ( fl ) is also one(100)rdquo Our analysis is a close statistical look atthis optimistic speculation

The relation between the fraction of suitableplanets on which biogenesis has occurred (ldquoflrdquo inthe Drake Equation) and the q analyzed here is

fl(qN) 5 1 2 (1 2 q)N (5)

fl(qDt(N)) 5 1 2 (1 2 q) (6)

fl(qt) 5 1 2 (1 2 q) (7)

where Eq 5 refers to the daily lottery (see Ap-pendix Eq A5) Eq 6 is the translation to the bio-genesis lottery and we obtain Eq 7 by using t 5Dtfrustrated 1 Dt(N) Equation 7 is plotted in Figs2 and 3 Thus in Eq 7 we have expressed the ldquoflrdquoterm of the Drake Equation as a function of timeof the observables Dtfrustrated and Dtbiogenesis andof the probability q for which we have derivedthe relative likelihood In addition since fl(qN) 5qN (see Eq A5) Fig 5 shows the relative likeli-hood of fl and establishes quantitative but model-dependent (specifically N 1-dependent) con-straints on fl For example for terrestrial planetsolder than 1 Gyr (2 3 Dtbiogenesis) fl 13 atthe 95 confidence level

However to go from fl to an answer to the ques-tion ldquoHow common is liferdquo (ie to go from fl toF in Eq 4 we need to know fe the fraction of theseplanetary systems with a terrestrial planet suitablefor life in the same way as the Earth Our under-standing of planet formation is consistent with theidea that ldquoterrestrialrdquo planet formation is a com-mon feature of star formation (Wetherill 1996 Lis-sauer and Lin 2000) The mass histogram of de-tected extrasolar planets peaks at low masses(dNdM ~ M21) and is also consistent with thisidea (Tabachnik and Tremaine 2001 Zucker andMazeh 2001 Lineweaver and Grether 2002)

Our analysis assumed the existence of a group

1t2

D

D

tb

t

i

f

o

r

g

u

e

s

n

tr

e

a

s

t

i

e

s

d 2

1DtbD

io

t(

g

N

en

)

esis 2

LINEWEAVER AND DAVIS300

of terrestrial planets with approximately thesame but unknown (q [ [01]) probability of bio-genesis It is reasonable to postulate the existenceof such a q group since although we do not knowthe details of the chemical evolution that led tolife we have some ideas about the factors in-volved energy flux temperatures the presenceof water planet orbit residence time in the con-tinuously habitable zone mass of the planet at-mospheric composition bombardment rate at theend of planetary accretion and its dependence onthe masses of the large planets in the planetarysystem metallicity of the prestellar molecularcloud crust composition vulcanism basic chem-istry hydration pH and presence of particularclay minerals amino acids and other molecularbuilding blocks for life (Lahav 1999) Since all ormany of these physical variables determine theprobability of biogenesis and since the Earthdoes not seem to be special with respect to anyof them (ie the Earth probably does not occupya thinly populated region of this multidimen-sional parameter space) the assumption that theprobability of biogenesis on these planets wouldbe approximately the same as on Earth is plausi-ble This is equivalent to assuming that q is aldquoslowlyrdquo varying function of environment Iftrue fe and F are not vanishingly small This canbe contrasted with the ldquoexponentially sensitiverdquocase discussed in Potential problems

DISCUSSION

Carter (1983) has pointed out that the time scalefor the evolution of intelligence on the Earth (5Gyr) is comparable to the main sequence lifetimeof the Sun (10 Gyr) Under the assumption thatthese two time scales are independent he arguedthat this would be unlikely to be observed unlessthe average time scale for the evolution of intel-ligence on a terrestrial planet is much longer thanthe main sequence lifetime of the host star [seeLivio (1999) for an objection to the idea that thesetwo time scales are independent] Carterrsquos argu-ment is strengthened by recent models of the ter-restrial biosphere indicating that the gradual in-crease of solar luminosity will make Earthuninhabitable in a billion years or somdashseveral billion years before the Sun leaves the main se-quence (Caldeira and Kasting 1992 Rampinoand Caldeira 1994)

Our analysis is similar in style to Carterrsquos how-

ever we are concerned with the appearance ofthe earliest life forms not the appearance of in-telligent life Subject to the caveats raised in Po-tential problems and by Livio (1999) the implica-tions of our analysis and Carterrsquos are consistentand complementary The appearance of life onterrestrial planets may be common but the ap-pearance of intelligent life may be rare

SUMMARY

Our existence on Earth does not mean that theprobability of biogenesis on a terrestrial planetq is large because if q were infinitesimallysmall and there were only one life-harboringplanet in the Universe we would of necessityfind ourselves on that planet However such ascenario would imply either that Earth has aunique chemistry or that terrestrial biogenesishas taken a long time to occur Neither is sup-ported by the evidence we have Since little canbe said about the probability q of terrestrialbiogenesis from our existence we assume max-imum ignorance 0 q 1 We then use theobservation of rapid terrestrial biogenesis toconstrain q (Fig 4)

We convert the constraints on q into constraintson the fl term of the Drake Equation (the frac-tion of suitable planets that have life) For ter-restrial planets older than 1 Gyr we find thatfl is most probably close to unity and 13 atthe 95 confidence level

If terrestrial planets are common and they haveapproximately the same probability of biogen-esis as the Earth our inference of high q (orhigh qN) indicates that a substantial fraction ofterrestrial planets have life and thus life is com-mon in the UniverseHowever there are assumptions and selection

effects that complicate this result

Although we correct the analysis for the factthat biogenesis is a prerequisite for our exis-tence our result depends on the plausible as-sumption that rapid biogenesis is not such aprerequisite

Although we have evidence that the fraction ofplanets that are ldquoterrestrialrdquo in a broad astro-nomical sense (rocky planet in the continu-ously habitable zone) is large this may be dif-ferent from the fraction of planets that areldquoterrestrialrdquo in a more detailed chemical sense

IS LIFE COMMON IN THE UNIVERSE 301

Although we can make reasonable estimates ofwhat the crusts and atmospheres are made ofwithout detailed knowledge of the steps ofchemical evolution we cannot be sure that as-tronomically terrestrial planets have the sameq as Earth That is the fraction of planets be-longing to the Earthrsquos q group is uncertainThus although we have been able to quantifythe fl term of the Drake Equation using rapidbiogenesis our knowledge of the fe term is stillonly qualitative and inhibits our ability to drawstronger conclusions about how common lifeis in the Universe

APPENDIX LIKELIHOODCOMPUTATIONS

Let the unknown but constant probability ofwinning a daily lottery be q Given the informa-tion that a gambler who buys one ticket each dayfor n days lost on the first n 2 1 days and wonon the nth day we can compute the likelihoodfunction for q (probability of the data given themodel q)

L(n q) 5 (1 2 q)n21q (A1)

This is equal to the fraction of all gamblers whofirst experienced (n21) losses and then wonGiven only the information that the gambler wonat least once on or before the nth day the likeli-hood function for q is

L(n q) 5 1 2 (1 2 q)n (A2)

This is equal to the fraction of all gamblers whohave won at least once on or before the nth dayGiven the information that a group of gamblershave won at least once on or before the Nth dayand that a gambler chosen at random from thisgroup won at least once on or before the nth day(n N) the likelihood of q is

L(n N q) 5 5 (A3)

Out of all the gamblers who have won on or be-fore the Nth day this is the fraction who havewon on or before the nth day Notice that as N Rn the likelihood of low q increases and that if N 5n the likelihood is the same for all q (see Fig 4)As N R ` we have L(n N q) R L(n q)

1 2 (1 2 q)n1 2 (1 2 q)N

L(n q)L(N q)

which yields the tightest constraints on q A nor-malized likelihood + (or probability density) isdefined such that ograve10 +(q)dq 5 1 Thus the renor-malization conversion is

+(x) 5(A4)

The normalized likelihoods for Eqs A1ndashA3 areplotted in Fig 1 for the cases n 5 3 and N 5 12The 95 confidence levels cited are Bayesiancredible intervals based on a uniform prior for q

Although q is the probability of winning thelottery in 1 day we would like to generalize andask what is the probability qN of winning the lot-tery within N days In the analogous biogenesislottery q is the probability of biogenesis on a ter-restrial planet with the same unknown probabil-ity of biogenesis as the Earth The time windowfor biogenesis constrained by observations onEarth Dtbiogenesis corresponds to 1 day for thegambler However we would like to compute thelikelihood of biogenesis after an arbitrary periodof time Dt(N) 5 N 3 Dtbiogenesis Let qN be theprobability of winning on or before the Nth day

qN 5 1 2 (1 2 q)N 5 L(N q) (A5)

(see Eqs A2 and A3) We would like to know thelikelihood of qN rather than limit ourselves to thelikelihood of q (5q1) Suppose the information is the same that was available to computeL(n N q) That information is A randomly cho-sen gambler from the group of gamblers who havewon after N days won on or before the nth dayWe want L(n N qN) The relationship betweenthe likelihood of qN and the likelihood of q is

+(n N qN) dqN 5 +(n N q) dq (A6)

which with dqNdq 5 N(1 2 q)N21 (from Eq A5)becomes

+(n N qN)

5 (A7)

5 (A8)

which is plotted in Fig 5 and has as expected rel-atively larger likelihoods for larger values of qN

+(n N q)N(1 2 q)N21

+(n N q)

dqNdq

+(x)

E1

0L(x)dx

LINEWEAVER AND DAVIS302

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

conditions were probably an effective and recur-ring autoclave for sterilizing the earliest life formsor more generally frustrating the evolution of lifeA steadily decreasing heavy bombardment con-tinued until 38 Gyr ago

Estimates of the time of the most recent steril-izing impact range between 444 and 37 Gyr ago(Maher and Stevenson 1988 Oberbeck andFogleman 1989 Sleep et al 1989 Halliday 2001)These estimates span the time from the solidifi-cation of the Moonrsquos crust to the end of the lateheavy bombardment Thus life was frustrated forat least the first 01 Gyr and possibly as long asthe first 09 Gyr of the Earthrsquos existence We takeour preferred value as the middle of this rangeDtfrustrated lt 05 6 04 Gyr The range of these es-timates reflects the large uncertainties due tosmall number statistics for the largest impactorsand the uncertainty of the energy required to ster-ilize the Earth completely We do not know wherebiogenesis happened or the extent to which it wasprotected from the effects of impacts Tidal poolshave little protection hydrothermal vents havesome protection while autotrophic thermophilesin subsurface rock under several kilometers ofcrust were probably in effective bomb shelters

The roots of the universal tree of life point toa thermophilic origin (or at least a thermophiliccommon ancestor) for all life on Earth (Pace 1991Stetter 1996) This suggests a hot biogenesis inhydrothermal vents or possibly subsurface rockandor selection for thermophilia by periodictemperature pulses from large impacts If weknew that life evolved on the surface of the Earthand was therefore more susceptible to impactsterilizations life would have been frustratedlonger and our preferred value would be moreprecise Dtfrustrated lt 07 6 02 Gyr

If we accept the carbon isotopic evidence forlife 385 billion years ago (Mojzsis et al 1996)then life has been on Earth at least that long (ieDtlife is at least 385 Gyr) In addition because ofthe Earthrsquos tectonic history this time is also theearliest time we could reasonably hope to find bi-ological evidence from rocks on Earthmdasheven iflife existed earlier With this selection effect inmind (which we know exists at some level) ourpreferred value for the time life has existed onEarth is Dtlife lt 40104

202 GyrIt is possible that biogenesis occurred several

times on Earth For example during the periodDtfrustrated life could have evolved and been ster-ilized multiple times We do not know if this hap-

pened Similar potential sterilizations and bio-geneses could have occurred during the periodDtlife but we do not know For the purposes ofthis analysis we can ignore this complication Weare only interested in the shortest period withinwhich the observations can constrain biogenesisto have occurred Thus Dtbiogenesis is our best ob-servational constraint on any epoch of biogene-sis and this happens to be on the period betweenthe most recent sterilizing impact that is olderthan the oldest evidence we have for life on Earth

Since our preferred values yield Dtfrustrated 1Dtlife lt DtEarth there is little time left for biogen-esis to have occurred This is the basis for thestatement that biogenesis occurred rapidly Sub-stituting our three preferred values DtEarth Dtfrustrated and Dtlife into Eq 1 and solving for Dtbiogenesis yields

Dtbiogenesis 5 01105201 Gyr (2)

Thus we take 600 Myr as a crude estimate ofthe upper limit for the time it took life to appearon Earth Assuming biogenesis took place on thesurface of the Earth Oberbeck and Fogleman(1989) found this maximum time to be 25 MyrMaher and Stevenson (1988) assumed that bio-genesis took somewhere between 01 and 10 Myrdepending on environment while Sleep et al(2001) found a similar range for evolutionarilysignificant periods of clement surface conditionsIndependently biologists specializing in thechemistry of the origin of life have estimated thatthe time required for biogenesis is potentiallyquite short (Miller 1982) and could be 8 Myr(Lazcano and Miller 1994) Thus several lines ofevidence indicate that biogenesis was geologi-cally rapid If biogenesis occurred in the fissuresaround a hydrothermal vent or in subsurfacerocks it was well protected and we can only con-strain biogenesis to have taken less than 600Myr If biogenesis occurred on the surface itprobably took less than 25 Myr In this analy-sis we consider 600 and 25 Myr to represent thehigh and low ends of a plausible range for Dtbiogenesis (Figs 2 and 3 respectively)

These observational constraints on DtfrustratedDtbiogenesis and Dtlife are important because theyquantify how rapidly biogenesis occurred onEarth and enable us to put limits on the proba-bility that biogenesis occurred on other planetsFor example consider a group of terrestrial plan-ets with approximately the same probability of

LINEWEAVER AND DAVIS296

biogenesis ldquoqrdquo as Earth Suppose q 5 030 Attheir formation none of these planets had life Astime passed life arose on more and more of themThe thick line in Fig 2 shows the increasing per-centage of these planets with life as time passesAfter Dtbiogenesis 30 will have life (that is howq 5 030 is defined) After 4566 Gyr 93 willhave life (7 still will not) Of that 93 32 willlike the Earth have had biogenesis within Dtbiogenesis The histogram on the far right of Fig2 represents these numbers Suppose q is only003 Then only 20 will have life after 4566 Gyrand only 14 of those will have had biogenesislike the Earth within Dtbiogenesis Assuming Earthis a random member of the planets with life thesingle observation that biogenesis occurredwithin Dtbiogenesis on Earth indicates that largervalues of q are more likely than small values Thisis the basic idea behind our analysis It is illus-trated in Figs 1 4 and 5 which also show quan-titative constraints on q under the various as-sumptions discussed in the next section

The histograms in Figs 2 and 3 also show thatif q is large the fraction of gamblers or terrestrialplanets who have won after a certain time is large

Suppose the gambler did not know how manygamblers had won by the 12th day but only thathe is a random member of the group that had wonFrom the fact that he won quickly he can infer thatq is large This tells the gambler that after a fewdays a large fraction of lottery ticket buyers are inthe winnersrsquo group He is not alone For the bio-genesis lottery finding large q means that after afew times Dtbiogenesis a large fraction of the terres-trial planets with probability of biogenesis similarto the Earth have (or have had) life

SELECTION EFFECTS

Daily lottery R biogenesis lottery

In the first section we drew parallels betweena daily lottery and a biogenesis lottery Explicitlythese parallels are

The first day of the lottery corresponds to theend of Dtfrustrated the time when conditions be-come clement enough for biogenesis

All the gamblers had the same (but unknown)

IS LIFE COMMON IN THE UNIVERSE 297

FIG 3 Zoomed-in version of Fig 2 with two differences (1) The window for biogenesis shown here is at the shortend of the range permitted by observations Dtbiogenesis 5 25 Myr (2) In Fig 2 by normalizing the histograms to 4566Gyr we have assumed that Earth is a random member of a group of planets at least 4566 Gyr old upon which bio-genesis could have happened anytime up to 4566 after formation including 1 million years ago This ignores thenonobservability-of-recent-biogenesis selection effect Here to minimize the influence of this selection effect we onlyallow biogenesis to occur anytime earlier than 377 Gyr ago [ie within ldquoDt(N 5 4)rdquo] The influence of this normal-ization time Dt(N) is illustrated in Fig 4

chance of winning the lottery each time theybought a ticket (q is the probability of winningper day) This corresponds to a group of ter-restrial planets with approximately the same(but unknown) chance of biogenesis as theEarth (q is the probability of biogenesis withina period of time called here Dtbiogenesis)

We selected a gambler at random from thosewho had won on or before the Nth day Thuswe conditioned on winning before a certaintime This corresponds to assuming that theEarth is a random member of the group of ter-restrial planets that has had biogenesis on orbefore the end of Dt(N) 5 N 3 Dtbiogenesis Con-ditioning on biogenesis before this time corre-

sponds to correcting for the selection effect thatbiogenesis had to have occurred for us to behere

A gambler chosen at random from the groupthat has won within N days found that he hadwon on the first day (n 5 1) This correspondsto finding that biogenesis has occurred rapidlyon Earth that is within Dtbiogenesis

If we set N 5 1 [see Fig 4 +(11 q)] we areconditioning on rapid biogenesis We are con-sidering a group all of whose members havehad rapid biogenesis In this case a randommember having rapid biogenesis can tell usnothing about the probability q To infer some-thing about q we must have N 1

Nonobservability of recent biogenesis

If our conclusions from the daily lottery are toapply to biogenesis on terrestrial planets we need

LINEWEAVER AND DAVIS298

FIG 4 The effect on the likelihood of varying thesomewhat arbitrary number of days that the gamblershave to have won by to be in the group In contrast toFig 1 all the likelihoods of q here are based on the in-formation that a gambler (chosen at random from thegroup whose members have won within N days) has wonon the first day These likelihoods are plotted and labeledldquo+(1N q)rdquo with NIcirc124 In the biogenesis lottery(just as in the daily lottery) N defines the group and is ameasure of the duration biogenesis could have taken[Dt(N) 5 N 3 Dtbiogenesis) For example if N 5 1 we can-not say anything about q since the likelihood +(11 q) isflat (we have conditioned on ldquorapidrdquo biogenesis) Whileif N 5 ` we can put the strongest constraint on q If n 51 (when it could have been much larger 1 n N) wehave more information about q and the likelihood forlarge q is higher (see Appendix Eq A3) The ratio of theprobabilities in the histograms in Fig 3 corresponds tothe ratio of the +(14 q) likelihoods here 3926 5+(14 q 5 030)+(14 q 5 003)5 0690465 15 Thatis with n 5 1 and N 5 4 values of q lt030 are 50 morelikely to be the case than q lt003 [in Fig 3 Dt(N) 5 4 325 Myr] Notice that for 2 N ` the 95 lower limitfor q varies only between 007 and 023

FIG 5 Likelihood of qN In Figs 1 and 4 the likelihoodof q is shown where q is the probability of winning onany one day Here we show likelihoods of qN the un-known probability of winning on or before the Nth dayThis figure shows the effect of varying N The informa-tion used to compute these likelihoods is that a gamblerchosen at random from the group whose members havewon within N days has won on the first day (see Ap-pendix Eqs A6ndashA8) Translated this becomes a planetchosen at random from the group of planets that has hadbiogenesis within Dt(N) 5 N 3 Dtbiogenesis has had bio-genesis within Dtbiogenesis As in Fig 4 if N 5 1 we cansay nothing meaningful about q1 (5 q) However even ifN 5 2 we can make a stronger statement about q2 thanwe could about q q2 013 at the 95 confidence levelThe 95 lower limit on qN increases dramatically as N in-creases constraining qN to be close to 1 The ability to ex-tract a useful constraint even if N is low reduces the in-fluence of the selection effects discussed in the text

to correct for the fact that the evolution of an ob-server takes some time How long it takes ob-serving equipment or complex life or multicel-lular eukaryotes to evolve is difficult to say OnEarth it took 4 Gyr A limited pace of evolutionhas prevented us from looking back at our ownhistory and seeing that biogenesis happened lastyear or even more recently than 2 Gyr ago (weconsider a plausible range for the requisite timeelapsed since biogenesis to be between 2 and 10billion years or Dtevolve 5 416

22 Gyr)This selection effect for nonrecent biogenesis is

selecting for biogenesis to happen a few billionyears before the present regardless of whether ithappened rapidly It is not a selection effect forrapid biogenesis since the longer it took us toevolve to a point when we could measure the ageof the Earth the older the Earth became Simi-larly if biogenesis took 1 Gyr longer than it ac-tually did we would currently find the age of theEarth to be 5566 Gyr (5 4566 1 1) old ldquoWhy isthe Earth 4566 billion years oldrdquo ldquoBecause ittook that long to find it outrdquo The generalizationof this plausible assumption to the ensemble ofterrestrial planets is necessary if the likelihoodsand constraints in Figs 1 4 and 5 are to be ap-plicable to the group of terrestrial planets

Potential problems

Any effect that makes rapid biogenesis a pre-requisite for life would undermine our inferencesfor q For example although it is usually assumedthat the heavy bombardment inhibited biogene-sis energetic impacts may have set up largechemical and thermal disequilibria that playsome crucial role in biogenesis We know so lit-tle about the details of the chemical evolution thatled to life that heat pulses and rapid cooling af-ter large impacts may be part of the preconditionsfor biogenesis If true the time scale of biogene-sis would be linked to the time scale of the ex-ponential decay of bombardment and biogenesiswould (if it occurred at all) be necessarily rapidmost extant life in the Universe would have rapidbiogenesis and little could be inferred about theabsolute value of q from our sample of 1

In a panspermia scenario the rapid appearanceof life on Earth is explained not by rapid terres-trial biogenesis as assumed here but by the ubiq-uity of the ldquoseeds of liferdquo (eg Hoyle and Wick-ramasinghe 1999) An analysis in the context of

a panspermia scenario would be subject to thesame observational constraints as terrestrial bio-genesis and would therefore lead to the same in-ferred probability for the appearance of life onother terrestrial planets

Another potential problem Suppose the auto-catalytic chemical cycles leading to life are expo-nentially sensitive to some still unknown pecu-liarity of the initial conditions on Earth In thiscase to have the same q as the Earth our groupof terrestrial planets may have to be almost in-distinguishable rare clones of Earth That is con-ditioning on planets identical to Earth (ldquosame qrdquo)would be conditioning on rapid biogenesis (N 51) and would prevent us from inferring muchabout q from the observations of rapid biogene-sis on Earth [see +(11 q) in Fig 4]

This is an example of the more general issue ofthe status of the rapidity of biogenesis on EarthDid it have to be rapid If we assume it couldhave been otherwise then we can infer somethingabout q If it had to be that way we cannot Themiddle ground might be the most plausible op-tion Biogenesis did not necessarily have to hap-pen as rapidly as it did but (to be consistent withour existence) it may have had to happen within1 or 2 billion years of the Earthrsquos formation

If this is true we need to look carefully at theinfluence of varying the somewhat arbitrary andcounterfactual duration [Dt(N) 5 N 3 Dtbiogenesis]that biogenesis could have taken on Earth Whatvalues of Dt(N) are plausible and how do theyaffect the results This is done in Fig 4 whichquantifies the degree of variability one can as-sume for the duration of biogenesis and still haveinteresting constraints on q The lower N is theless variability is assumed For example if N 5 2[see +(12 q)] we are assuming that biogenesiscould only have taken as long as 2 3 Dtbiogenesismdashenough variability to be able to say somethingabout q but small enough to maintain the nonob-servability of recent biogenesis

Figure 5 allows us to generalize our inferencesabout q (the probability of biogenesis within Dtbiogenesis) to inferences about qN [the probabil-ity of biogenesis within an arbitrary time Dt(N)]Specifically it shows that we only need to be ableto assume that biogenesis could have been twiceas long as Dtbiogenesis to have interesting con-straints q2 013 at the 95 confidence level [see+(12 qN)] This is the result reported in the ab-stract

IS LIFE COMMON IN THE UNIVERSE 299

HOW COMMON IS LIFE

Relation of our analysis to the Drake Equation

The Drake Equation was devised to address thequestion of ldquoHow many communicative civiliza-tions are in our Galaxyrdquo (eg Sagan 1973) It hasbeen criticized as ldquoa way of compressing a largeamount of ignorance into a small spacerdquo (Olivercited in Dicke 1998) Despite its shortcomings itcontinues to focus the efforts of the search for ex-traterrestrial intelligence (SETI) community Animportant goal of the SETI community is to turnits subjective probabilities into mathematicalprobabilities We have done that here for one ofthe most important terms

We are interested in a simpler question ldquoHowcommon is life in the Universerdquo Our question issimpler because life is more generic than intelli-gent or technological life We modify the DrakeEquation to address our question and introducea parameter F which is a measure of how com-mon life is in the universe F is the fraction of starsin our galaxy today orbited by planets that havehad independent biogenesis

F 5 NlN p 5 fp fe fl (3)

where Nl is the number of stars in our Galaxy or-bited by planets that have had independent bio-genesis N p is the number of stars in our Galaxyfp is the fraction of stars in our Galaxy with plan-etary systems fe is the fraction of these planetarysystems that have a terrestrial planet suitable forlife in the same way as the Earth that is theyhave approximately the same probability q as theEarth and fl is the fraction of these suitable plan-ets on which biogenesis has occurred

Many recent observations of the frequency andage dependence of circumstellar disks aroundyoung stars in star-forming regions support thewidely accepted idea that planet formation is acommon by-product of star formation and thatthe fraction of stars with planetary systems isclose to unity fp lt 1 (eg Habing et al 1999 Mc-Caughrean et al 2000 Meyer and Beckwith2000)

Equation 3 then becomes

F lt fe fl (4)

If F 1022 then 1 of all stars have (or havehad) life and we conclude that life is ldquocommonrdquo

in the Universe If F 10211 we may be the onlylife in the Galaxy and life is ldquorarerdquo

There has been little agreement on the value offl Hart (1996) wrote ldquoThe value of fl is extremelyspeculativerdquo but argued based on the concate-nation of low probabilities that it must be ex-tremely small and thus life elsewhere is improb-able However Shostak (1998) assumed quite theopposite ldquoOn the basis of the rapidity with whichbiology blossomed on Earth we can optimisti-cally speculate that this fraction ( fl ) is also one(100)rdquo Our analysis is a close statistical look atthis optimistic speculation

The relation between the fraction of suitableplanets on which biogenesis has occurred (ldquoflrdquo inthe Drake Equation) and the q analyzed here is

fl(qN) 5 1 2 (1 2 q)N (5)

fl(qDt(N)) 5 1 2 (1 2 q) (6)

fl(qt) 5 1 2 (1 2 q) (7)

where Eq 5 refers to the daily lottery (see Ap-pendix Eq A5) Eq 6 is the translation to the bio-genesis lottery and we obtain Eq 7 by using t 5Dtfrustrated 1 Dt(N) Equation 7 is plotted in Figs2 and 3 Thus in Eq 7 we have expressed the ldquoflrdquoterm of the Drake Equation as a function of timeof the observables Dtfrustrated and Dtbiogenesis andof the probability q for which we have derivedthe relative likelihood In addition since fl(qN) 5qN (see Eq A5) Fig 5 shows the relative likeli-hood of fl and establishes quantitative but model-dependent (specifically N 1-dependent) con-straints on fl For example for terrestrial planetsolder than 1 Gyr (2 3 Dtbiogenesis) fl 13 atthe 95 confidence level

However to go from fl to an answer to the ques-tion ldquoHow common is liferdquo (ie to go from fl toF in Eq 4 we need to know fe the fraction of theseplanetary systems with a terrestrial planet suitablefor life in the same way as the Earth Our under-standing of planet formation is consistent with theidea that ldquoterrestrialrdquo planet formation is a com-mon feature of star formation (Wetherill 1996 Lis-sauer and Lin 2000) The mass histogram of de-tected extrasolar planets peaks at low masses(dNdM ~ M21) and is also consistent with thisidea (Tabachnik and Tremaine 2001 Zucker andMazeh 2001 Lineweaver and Grether 2002)

Our analysis assumed the existence of a group

1t2

D

D

tb

t

i

f

o

r

g

u

e

s

n

tr

e

a

s

t

i

e

s

d 2

1DtbD

io

t(

g

N

en

)

esis 2

LINEWEAVER AND DAVIS300

of terrestrial planets with approximately thesame but unknown (q [ [01]) probability of bio-genesis It is reasonable to postulate the existenceof such a q group since although we do not knowthe details of the chemical evolution that led tolife we have some ideas about the factors in-volved energy flux temperatures the presenceof water planet orbit residence time in the con-tinuously habitable zone mass of the planet at-mospheric composition bombardment rate at theend of planetary accretion and its dependence onthe masses of the large planets in the planetarysystem metallicity of the prestellar molecularcloud crust composition vulcanism basic chem-istry hydration pH and presence of particularclay minerals amino acids and other molecularbuilding blocks for life (Lahav 1999) Since all ormany of these physical variables determine theprobability of biogenesis and since the Earthdoes not seem to be special with respect to anyof them (ie the Earth probably does not occupya thinly populated region of this multidimen-sional parameter space) the assumption that theprobability of biogenesis on these planets wouldbe approximately the same as on Earth is plausi-ble This is equivalent to assuming that q is aldquoslowlyrdquo varying function of environment Iftrue fe and F are not vanishingly small This canbe contrasted with the ldquoexponentially sensitiverdquocase discussed in Potential problems

DISCUSSION

Carter (1983) has pointed out that the time scalefor the evolution of intelligence on the Earth (5Gyr) is comparable to the main sequence lifetimeof the Sun (10 Gyr) Under the assumption thatthese two time scales are independent he arguedthat this would be unlikely to be observed unlessthe average time scale for the evolution of intel-ligence on a terrestrial planet is much longer thanthe main sequence lifetime of the host star [seeLivio (1999) for an objection to the idea that thesetwo time scales are independent] Carterrsquos argu-ment is strengthened by recent models of the ter-restrial biosphere indicating that the gradual in-crease of solar luminosity will make Earthuninhabitable in a billion years or somdashseveral billion years before the Sun leaves the main se-quence (Caldeira and Kasting 1992 Rampinoand Caldeira 1994)

Our analysis is similar in style to Carterrsquos how-

ever we are concerned with the appearance ofthe earliest life forms not the appearance of in-telligent life Subject to the caveats raised in Po-tential problems and by Livio (1999) the implica-tions of our analysis and Carterrsquos are consistentand complementary The appearance of life onterrestrial planets may be common but the ap-pearance of intelligent life may be rare

SUMMARY

Our existence on Earth does not mean that theprobability of biogenesis on a terrestrial planetq is large because if q were infinitesimallysmall and there were only one life-harboringplanet in the Universe we would of necessityfind ourselves on that planet However such ascenario would imply either that Earth has aunique chemistry or that terrestrial biogenesishas taken a long time to occur Neither is sup-ported by the evidence we have Since little canbe said about the probability q of terrestrialbiogenesis from our existence we assume max-imum ignorance 0 q 1 We then use theobservation of rapid terrestrial biogenesis toconstrain q (Fig 4)

We convert the constraints on q into constraintson the fl term of the Drake Equation (the frac-tion of suitable planets that have life) For ter-restrial planets older than 1 Gyr we find thatfl is most probably close to unity and 13 atthe 95 confidence level

If terrestrial planets are common and they haveapproximately the same probability of biogen-esis as the Earth our inference of high q (orhigh qN) indicates that a substantial fraction ofterrestrial planets have life and thus life is com-mon in the UniverseHowever there are assumptions and selection

effects that complicate this result

Although we correct the analysis for the factthat biogenesis is a prerequisite for our exis-tence our result depends on the plausible as-sumption that rapid biogenesis is not such aprerequisite

Although we have evidence that the fraction ofplanets that are ldquoterrestrialrdquo in a broad astro-nomical sense (rocky planet in the continu-ously habitable zone) is large this may be dif-ferent from the fraction of planets that areldquoterrestrialrdquo in a more detailed chemical sense

IS LIFE COMMON IN THE UNIVERSE 301

Although we can make reasonable estimates ofwhat the crusts and atmospheres are made ofwithout detailed knowledge of the steps ofchemical evolution we cannot be sure that as-tronomically terrestrial planets have the sameq as Earth That is the fraction of planets be-longing to the Earthrsquos q group is uncertainThus although we have been able to quantifythe fl term of the Drake Equation using rapidbiogenesis our knowledge of the fe term is stillonly qualitative and inhibits our ability to drawstronger conclusions about how common lifeis in the Universe

APPENDIX LIKELIHOODCOMPUTATIONS

Let the unknown but constant probability ofwinning a daily lottery be q Given the informa-tion that a gambler who buys one ticket each dayfor n days lost on the first n 2 1 days and wonon the nth day we can compute the likelihoodfunction for q (probability of the data given themodel q)

L(n q) 5 (1 2 q)n21q (A1)

This is equal to the fraction of all gamblers whofirst experienced (n21) losses and then wonGiven only the information that the gambler wonat least once on or before the nth day the likeli-hood function for q is

L(n q) 5 1 2 (1 2 q)n (A2)

This is equal to the fraction of all gamblers whohave won at least once on or before the nth dayGiven the information that a group of gamblershave won at least once on or before the Nth dayand that a gambler chosen at random from thisgroup won at least once on or before the nth day(n N) the likelihood of q is

L(n N q) 5 5 (A3)

Out of all the gamblers who have won on or be-fore the Nth day this is the fraction who havewon on or before the nth day Notice that as N Rn the likelihood of low q increases and that if N 5n the likelihood is the same for all q (see Fig 4)As N R ` we have L(n N q) R L(n q)

1 2 (1 2 q)n1 2 (1 2 q)N

L(n q)L(N q)

which yields the tightest constraints on q A nor-malized likelihood + (or probability density) isdefined such that ograve10 +(q)dq 5 1 Thus the renor-malization conversion is

+(x) 5(A4)

The normalized likelihoods for Eqs A1ndashA3 areplotted in Fig 1 for the cases n 5 3 and N 5 12The 95 confidence levels cited are Bayesiancredible intervals based on a uniform prior for q

Although q is the probability of winning thelottery in 1 day we would like to generalize andask what is the probability qN of winning the lot-tery within N days In the analogous biogenesislottery q is the probability of biogenesis on a ter-restrial planet with the same unknown probabil-ity of biogenesis as the Earth The time windowfor biogenesis constrained by observations onEarth Dtbiogenesis corresponds to 1 day for thegambler However we would like to compute thelikelihood of biogenesis after an arbitrary periodof time Dt(N) 5 N 3 Dtbiogenesis Let qN be theprobability of winning on or before the Nth day

qN 5 1 2 (1 2 q)N 5 L(N q) (A5)

(see Eqs A2 and A3) We would like to know thelikelihood of qN rather than limit ourselves to thelikelihood of q (5q1) Suppose the information is the same that was available to computeL(n N q) That information is A randomly cho-sen gambler from the group of gamblers who havewon after N days won on or before the nth dayWe want L(n N qN) The relationship betweenthe likelihood of qN and the likelihood of q is

+(n N qN) dqN 5 +(n N q) dq (A6)

which with dqNdq 5 N(1 2 q)N21 (from Eq A5)becomes

+(n N qN)

5 (A7)

5 (A8)

which is plotted in Fig 5 and has as expected rel-atively larger likelihoods for larger values of qN

+(n N q)N(1 2 q)N21

+(n N q)

dqNdq

+(x)

E1

0L(x)dx

LINEWEAVER AND DAVIS302

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

biogenesis ldquoqrdquo as Earth Suppose q 5 030 Attheir formation none of these planets had life Astime passed life arose on more and more of themThe thick line in Fig 2 shows the increasing per-centage of these planets with life as time passesAfter Dtbiogenesis 30 will have life (that is howq 5 030 is defined) After 4566 Gyr 93 willhave life (7 still will not) Of that 93 32 willlike the Earth have had biogenesis within Dtbiogenesis The histogram on the far right of Fig2 represents these numbers Suppose q is only003 Then only 20 will have life after 4566 Gyrand only 14 of those will have had biogenesislike the Earth within Dtbiogenesis Assuming Earthis a random member of the planets with life thesingle observation that biogenesis occurredwithin Dtbiogenesis on Earth indicates that largervalues of q are more likely than small values Thisis the basic idea behind our analysis It is illus-trated in Figs 1 4 and 5 which also show quan-titative constraints on q under the various as-sumptions discussed in the next section

The histograms in Figs 2 and 3 also show thatif q is large the fraction of gamblers or terrestrialplanets who have won after a certain time is large

Suppose the gambler did not know how manygamblers had won by the 12th day but only thathe is a random member of the group that had wonFrom the fact that he won quickly he can infer thatq is large This tells the gambler that after a fewdays a large fraction of lottery ticket buyers are inthe winnersrsquo group He is not alone For the bio-genesis lottery finding large q means that after afew times Dtbiogenesis a large fraction of the terres-trial planets with probability of biogenesis similarto the Earth have (or have had) life

SELECTION EFFECTS

Daily lottery R biogenesis lottery

In the first section we drew parallels betweena daily lottery and a biogenesis lottery Explicitlythese parallels are

The first day of the lottery corresponds to theend of Dtfrustrated the time when conditions be-come clement enough for biogenesis

All the gamblers had the same (but unknown)

IS LIFE COMMON IN THE UNIVERSE 297

FIG 3 Zoomed-in version of Fig 2 with two differences (1) The window for biogenesis shown here is at the shortend of the range permitted by observations Dtbiogenesis 5 25 Myr (2) In Fig 2 by normalizing the histograms to 4566Gyr we have assumed that Earth is a random member of a group of planets at least 4566 Gyr old upon which bio-genesis could have happened anytime up to 4566 after formation including 1 million years ago This ignores thenonobservability-of-recent-biogenesis selection effect Here to minimize the influence of this selection effect we onlyallow biogenesis to occur anytime earlier than 377 Gyr ago [ie within ldquoDt(N 5 4)rdquo] The influence of this normal-ization time Dt(N) is illustrated in Fig 4

chance of winning the lottery each time theybought a ticket (q is the probability of winningper day) This corresponds to a group of ter-restrial planets with approximately the same(but unknown) chance of biogenesis as theEarth (q is the probability of biogenesis withina period of time called here Dtbiogenesis)

We selected a gambler at random from thosewho had won on or before the Nth day Thuswe conditioned on winning before a certaintime This corresponds to assuming that theEarth is a random member of the group of ter-restrial planets that has had biogenesis on orbefore the end of Dt(N) 5 N 3 Dtbiogenesis Con-ditioning on biogenesis before this time corre-

sponds to correcting for the selection effect thatbiogenesis had to have occurred for us to behere

A gambler chosen at random from the groupthat has won within N days found that he hadwon on the first day (n 5 1) This correspondsto finding that biogenesis has occurred rapidlyon Earth that is within Dtbiogenesis

If we set N 5 1 [see Fig 4 +(11 q)] we areconditioning on rapid biogenesis We are con-sidering a group all of whose members havehad rapid biogenesis In this case a randommember having rapid biogenesis can tell usnothing about the probability q To infer some-thing about q we must have N 1

Nonobservability of recent biogenesis

If our conclusions from the daily lottery are toapply to biogenesis on terrestrial planets we need

LINEWEAVER AND DAVIS298

FIG 4 The effect on the likelihood of varying thesomewhat arbitrary number of days that the gamblershave to have won by to be in the group In contrast toFig 1 all the likelihoods of q here are based on the in-formation that a gambler (chosen at random from thegroup whose members have won within N days) has wonon the first day These likelihoods are plotted and labeledldquo+(1N q)rdquo with NIcirc124 In the biogenesis lottery(just as in the daily lottery) N defines the group and is ameasure of the duration biogenesis could have taken[Dt(N) 5 N 3 Dtbiogenesis) For example if N 5 1 we can-not say anything about q since the likelihood +(11 q) isflat (we have conditioned on ldquorapidrdquo biogenesis) Whileif N 5 ` we can put the strongest constraint on q If n 51 (when it could have been much larger 1 n N) wehave more information about q and the likelihood forlarge q is higher (see Appendix Eq A3) The ratio of theprobabilities in the histograms in Fig 3 corresponds tothe ratio of the +(14 q) likelihoods here 3926 5+(14 q 5 030)+(14 q 5 003)5 0690465 15 Thatis with n 5 1 and N 5 4 values of q lt030 are 50 morelikely to be the case than q lt003 [in Fig 3 Dt(N) 5 4 325 Myr] Notice that for 2 N ` the 95 lower limitfor q varies only between 007 and 023

FIG 5 Likelihood of qN In Figs 1 and 4 the likelihoodof q is shown where q is the probability of winning onany one day Here we show likelihoods of qN the un-known probability of winning on or before the Nth dayThis figure shows the effect of varying N The informa-tion used to compute these likelihoods is that a gamblerchosen at random from the group whose members havewon within N days has won on the first day (see Ap-pendix Eqs A6ndashA8) Translated this becomes a planetchosen at random from the group of planets that has hadbiogenesis within Dt(N) 5 N 3 Dtbiogenesis has had bio-genesis within Dtbiogenesis As in Fig 4 if N 5 1 we cansay nothing meaningful about q1 (5 q) However even ifN 5 2 we can make a stronger statement about q2 thanwe could about q q2 013 at the 95 confidence levelThe 95 lower limit on qN increases dramatically as N in-creases constraining qN to be close to 1 The ability to ex-tract a useful constraint even if N is low reduces the in-fluence of the selection effects discussed in the text

to correct for the fact that the evolution of an ob-server takes some time How long it takes ob-serving equipment or complex life or multicel-lular eukaryotes to evolve is difficult to say OnEarth it took 4 Gyr A limited pace of evolutionhas prevented us from looking back at our ownhistory and seeing that biogenesis happened lastyear or even more recently than 2 Gyr ago (weconsider a plausible range for the requisite timeelapsed since biogenesis to be between 2 and 10billion years or Dtevolve 5 416

22 Gyr)This selection effect for nonrecent biogenesis is

selecting for biogenesis to happen a few billionyears before the present regardless of whether ithappened rapidly It is not a selection effect forrapid biogenesis since the longer it took us toevolve to a point when we could measure the ageof the Earth the older the Earth became Simi-larly if biogenesis took 1 Gyr longer than it ac-tually did we would currently find the age of theEarth to be 5566 Gyr (5 4566 1 1) old ldquoWhy isthe Earth 4566 billion years oldrdquo ldquoBecause ittook that long to find it outrdquo The generalizationof this plausible assumption to the ensemble ofterrestrial planets is necessary if the likelihoodsand constraints in Figs 1 4 and 5 are to be ap-plicable to the group of terrestrial planets

Potential problems

Any effect that makes rapid biogenesis a pre-requisite for life would undermine our inferencesfor q For example although it is usually assumedthat the heavy bombardment inhibited biogene-sis energetic impacts may have set up largechemical and thermal disequilibria that playsome crucial role in biogenesis We know so lit-tle about the details of the chemical evolution thatled to life that heat pulses and rapid cooling af-ter large impacts may be part of the preconditionsfor biogenesis If true the time scale of biogene-sis would be linked to the time scale of the ex-ponential decay of bombardment and biogenesiswould (if it occurred at all) be necessarily rapidmost extant life in the Universe would have rapidbiogenesis and little could be inferred about theabsolute value of q from our sample of 1

In a panspermia scenario the rapid appearanceof life on Earth is explained not by rapid terres-trial biogenesis as assumed here but by the ubiq-uity of the ldquoseeds of liferdquo (eg Hoyle and Wick-ramasinghe 1999) An analysis in the context of

a panspermia scenario would be subject to thesame observational constraints as terrestrial bio-genesis and would therefore lead to the same in-ferred probability for the appearance of life onother terrestrial planets

Another potential problem Suppose the auto-catalytic chemical cycles leading to life are expo-nentially sensitive to some still unknown pecu-liarity of the initial conditions on Earth In thiscase to have the same q as the Earth our groupof terrestrial planets may have to be almost in-distinguishable rare clones of Earth That is con-ditioning on planets identical to Earth (ldquosame qrdquo)would be conditioning on rapid biogenesis (N 51) and would prevent us from inferring muchabout q from the observations of rapid biogene-sis on Earth [see +(11 q) in Fig 4]

This is an example of the more general issue ofthe status of the rapidity of biogenesis on EarthDid it have to be rapid If we assume it couldhave been otherwise then we can infer somethingabout q If it had to be that way we cannot Themiddle ground might be the most plausible op-tion Biogenesis did not necessarily have to hap-pen as rapidly as it did but (to be consistent withour existence) it may have had to happen within1 or 2 billion years of the Earthrsquos formation

If this is true we need to look carefully at theinfluence of varying the somewhat arbitrary andcounterfactual duration [Dt(N) 5 N 3 Dtbiogenesis]that biogenesis could have taken on Earth Whatvalues of Dt(N) are plausible and how do theyaffect the results This is done in Fig 4 whichquantifies the degree of variability one can as-sume for the duration of biogenesis and still haveinteresting constraints on q The lower N is theless variability is assumed For example if N 5 2[see +(12 q)] we are assuming that biogenesiscould only have taken as long as 2 3 Dtbiogenesismdashenough variability to be able to say somethingabout q but small enough to maintain the nonob-servability of recent biogenesis

Figure 5 allows us to generalize our inferencesabout q (the probability of biogenesis within Dtbiogenesis) to inferences about qN [the probabil-ity of biogenesis within an arbitrary time Dt(N)]Specifically it shows that we only need to be ableto assume that biogenesis could have been twiceas long as Dtbiogenesis to have interesting con-straints q2 013 at the 95 confidence level [see+(12 qN)] This is the result reported in the ab-stract

IS LIFE COMMON IN THE UNIVERSE 299

HOW COMMON IS LIFE

Relation of our analysis to the Drake Equation

The Drake Equation was devised to address thequestion of ldquoHow many communicative civiliza-tions are in our Galaxyrdquo (eg Sagan 1973) It hasbeen criticized as ldquoa way of compressing a largeamount of ignorance into a small spacerdquo (Olivercited in Dicke 1998) Despite its shortcomings itcontinues to focus the efforts of the search for ex-traterrestrial intelligence (SETI) community Animportant goal of the SETI community is to turnits subjective probabilities into mathematicalprobabilities We have done that here for one ofthe most important terms

We are interested in a simpler question ldquoHowcommon is life in the Universerdquo Our question issimpler because life is more generic than intelli-gent or technological life We modify the DrakeEquation to address our question and introducea parameter F which is a measure of how com-mon life is in the universe F is the fraction of starsin our galaxy today orbited by planets that havehad independent biogenesis

F 5 NlN p 5 fp fe fl (3)

where Nl is the number of stars in our Galaxy or-bited by planets that have had independent bio-genesis N p is the number of stars in our Galaxyfp is the fraction of stars in our Galaxy with plan-etary systems fe is the fraction of these planetarysystems that have a terrestrial planet suitable forlife in the same way as the Earth that is theyhave approximately the same probability q as theEarth and fl is the fraction of these suitable plan-ets on which biogenesis has occurred

Many recent observations of the frequency andage dependence of circumstellar disks aroundyoung stars in star-forming regions support thewidely accepted idea that planet formation is acommon by-product of star formation and thatthe fraction of stars with planetary systems isclose to unity fp lt 1 (eg Habing et al 1999 Mc-Caughrean et al 2000 Meyer and Beckwith2000)

Equation 3 then becomes

F lt fe fl (4)

If F 1022 then 1 of all stars have (or havehad) life and we conclude that life is ldquocommonrdquo

in the Universe If F 10211 we may be the onlylife in the Galaxy and life is ldquorarerdquo

There has been little agreement on the value offl Hart (1996) wrote ldquoThe value of fl is extremelyspeculativerdquo but argued based on the concate-nation of low probabilities that it must be ex-tremely small and thus life elsewhere is improb-able However Shostak (1998) assumed quite theopposite ldquoOn the basis of the rapidity with whichbiology blossomed on Earth we can optimisti-cally speculate that this fraction ( fl ) is also one(100)rdquo Our analysis is a close statistical look atthis optimistic speculation

The relation between the fraction of suitableplanets on which biogenesis has occurred (ldquoflrdquo inthe Drake Equation) and the q analyzed here is

fl(qN) 5 1 2 (1 2 q)N (5)

fl(qDt(N)) 5 1 2 (1 2 q) (6)

fl(qt) 5 1 2 (1 2 q) (7)

where Eq 5 refers to the daily lottery (see Ap-pendix Eq A5) Eq 6 is the translation to the bio-genesis lottery and we obtain Eq 7 by using t 5Dtfrustrated 1 Dt(N) Equation 7 is plotted in Figs2 and 3 Thus in Eq 7 we have expressed the ldquoflrdquoterm of the Drake Equation as a function of timeof the observables Dtfrustrated and Dtbiogenesis andof the probability q for which we have derivedthe relative likelihood In addition since fl(qN) 5qN (see Eq A5) Fig 5 shows the relative likeli-hood of fl and establishes quantitative but model-dependent (specifically N 1-dependent) con-straints on fl For example for terrestrial planetsolder than 1 Gyr (2 3 Dtbiogenesis) fl 13 atthe 95 confidence level

However to go from fl to an answer to the ques-tion ldquoHow common is liferdquo (ie to go from fl toF in Eq 4 we need to know fe the fraction of theseplanetary systems with a terrestrial planet suitablefor life in the same way as the Earth Our under-standing of planet formation is consistent with theidea that ldquoterrestrialrdquo planet formation is a com-mon feature of star formation (Wetherill 1996 Lis-sauer and Lin 2000) The mass histogram of de-tected extrasolar planets peaks at low masses(dNdM ~ M21) and is also consistent with thisidea (Tabachnik and Tremaine 2001 Zucker andMazeh 2001 Lineweaver and Grether 2002)

Our analysis assumed the existence of a group

1t2

D

D

tb

t

i

f

o

r

g

u

e

s

n

tr

e

a

s

t

i

e

s

d 2

1DtbD

io

t(

g

N

en

)

esis 2

LINEWEAVER AND DAVIS300

of terrestrial planets with approximately thesame but unknown (q [ [01]) probability of bio-genesis It is reasonable to postulate the existenceof such a q group since although we do not knowthe details of the chemical evolution that led tolife we have some ideas about the factors in-volved energy flux temperatures the presenceof water planet orbit residence time in the con-tinuously habitable zone mass of the planet at-mospheric composition bombardment rate at theend of planetary accretion and its dependence onthe masses of the large planets in the planetarysystem metallicity of the prestellar molecularcloud crust composition vulcanism basic chem-istry hydration pH and presence of particularclay minerals amino acids and other molecularbuilding blocks for life (Lahav 1999) Since all ormany of these physical variables determine theprobability of biogenesis and since the Earthdoes not seem to be special with respect to anyof them (ie the Earth probably does not occupya thinly populated region of this multidimen-sional parameter space) the assumption that theprobability of biogenesis on these planets wouldbe approximately the same as on Earth is plausi-ble This is equivalent to assuming that q is aldquoslowlyrdquo varying function of environment Iftrue fe and F are not vanishingly small This canbe contrasted with the ldquoexponentially sensitiverdquocase discussed in Potential problems

DISCUSSION

Carter (1983) has pointed out that the time scalefor the evolution of intelligence on the Earth (5Gyr) is comparable to the main sequence lifetimeof the Sun (10 Gyr) Under the assumption thatthese two time scales are independent he arguedthat this would be unlikely to be observed unlessthe average time scale for the evolution of intel-ligence on a terrestrial planet is much longer thanthe main sequence lifetime of the host star [seeLivio (1999) for an objection to the idea that thesetwo time scales are independent] Carterrsquos argu-ment is strengthened by recent models of the ter-restrial biosphere indicating that the gradual in-crease of solar luminosity will make Earthuninhabitable in a billion years or somdashseveral billion years before the Sun leaves the main se-quence (Caldeira and Kasting 1992 Rampinoand Caldeira 1994)

Our analysis is similar in style to Carterrsquos how-

ever we are concerned with the appearance ofthe earliest life forms not the appearance of in-telligent life Subject to the caveats raised in Po-tential problems and by Livio (1999) the implica-tions of our analysis and Carterrsquos are consistentand complementary The appearance of life onterrestrial planets may be common but the ap-pearance of intelligent life may be rare

SUMMARY

Our existence on Earth does not mean that theprobability of biogenesis on a terrestrial planetq is large because if q were infinitesimallysmall and there were only one life-harboringplanet in the Universe we would of necessityfind ourselves on that planet However such ascenario would imply either that Earth has aunique chemistry or that terrestrial biogenesishas taken a long time to occur Neither is sup-ported by the evidence we have Since little canbe said about the probability q of terrestrialbiogenesis from our existence we assume max-imum ignorance 0 q 1 We then use theobservation of rapid terrestrial biogenesis toconstrain q (Fig 4)

We convert the constraints on q into constraintson the fl term of the Drake Equation (the frac-tion of suitable planets that have life) For ter-restrial planets older than 1 Gyr we find thatfl is most probably close to unity and 13 atthe 95 confidence level

If terrestrial planets are common and they haveapproximately the same probability of biogen-esis as the Earth our inference of high q (orhigh qN) indicates that a substantial fraction ofterrestrial planets have life and thus life is com-mon in the UniverseHowever there are assumptions and selection

effects that complicate this result

Although we correct the analysis for the factthat biogenesis is a prerequisite for our exis-tence our result depends on the plausible as-sumption that rapid biogenesis is not such aprerequisite

Although we have evidence that the fraction ofplanets that are ldquoterrestrialrdquo in a broad astro-nomical sense (rocky planet in the continu-ously habitable zone) is large this may be dif-ferent from the fraction of planets that areldquoterrestrialrdquo in a more detailed chemical sense

IS LIFE COMMON IN THE UNIVERSE 301

Although we can make reasonable estimates ofwhat the crusts and atmospheres are made ofwithout detailed knowledge of the steps ofchemical evolution we cannot be sure that as-tronomically terrestrial planets have the sameq as Earth That is the fraction of planets be-longing to the Earthrsquos q group is uncertainThus although we have been able to quantifythe fl term of the Drake Equation using rapidbiogenesis our knowledge of the fe term is stillonly qualitative and inhibits our ability to drawstronger conclusions about how common lifeis in the Universe

APPENDIX LIKELIHOODCOMPUTATIONS

Let the unknown but constant probability ofwinning a daily lottery be q Given the informa-tion that a gambler who buys one ticket each dayfor n days lost on the first n 2 1 days and wonon the nth day we can compute the likelihoodfunction for q (probability of the data given themodel q)

L(n q) 5 (1 2 q)n21q (A1)

This is equal to the fraction of all gamblers whofirst experienced (n21) losses and then wonGiven only the information that the gambler wonat least once on or before the nth day the likeli-hood function for q is

L(n q) 5 1 2 (1 2 q)n (A2)

This is equal to the fraction of all gamblers whohave won at least once on or before the nth dayGiven the information that a group of gamblershave won at least once on or before the Nth dayand that a gambler chosen at random from thisgroup won at least once on or before the nth day(n N) the likelihood of q is

L(n N q) 5 5 (A3)

Out of all the gamblers who have won on or be-fore the Nth day this is the fraction who havewon on or before the nth day Notice that as N Rn the likelihood of low q increases and that if N 5n the likelihood is the same for all q (see Fig 4)As N R ` we have L(n N q) R L(n q)

1 2 (1 2 q)n1 2 (1 2 q)N

L(n q)L(N q)

which yields the tightest constraints on q A nor-malized likelihood + (or probability density) isdefined such that ograve10 +(q)dq 5 1 Thus the renor-malization conversion is

+(x) 5(A4)

The normalized likelihoods for Eqs A1ndashA3 areplotted in Fig 1 for the cases n 5 3 and N 5 12The 95 confidence levels cited are Bayesiancredible intervals based on a uniform prior for q

Although q is the probability of winning thelottery in 1 day we would like to generalize andask what is the probability qN of winning the lot-tery within N days In the analogous biogenesislottery q is the probability of biogenesis on a ter-restrial planet with the same unknown probabil-ity of biogenesis as the Earth The time windowfor biogenesis constrained by observations onEarth Dtbiogenesis corresponds to 1 day for thegambler However we would like to compute thelikelihood of biogenesis after an arbitrary periodof time Dt(N) 5 N 3 Dtbiogenesis Let qN be theprobability of winning on or before the Nth day

qN 5 1 2 (1 2 q)N 5 L(N q) (A5)

(see Eqs A2 and A3) We would like to know thelikelihood of qN rather than limit ourselves to thelikelihood of q (5q1) Suppose the information is the same that was available to computeL(n N q) That information is A randomly cho-sen gambler from the group of gamblers who havewon after N days won on or before the nth dayWe want L(n N qN) The relationship betweenthe likelihood of qN and the likelihood of q is

+(n N qN) dqN 5 +(n N q) dq (A6)

which with dqNdq 5 N(1 2 q)N21 (from Eq A5)becomes

+(n N qN)

5 (A7)

5 (A8)

which is plotted in Fig 5 and has as expected rel-atively larger likelihoods for larger values of qN

+(n N q)N(1 2 q)N21

+(n N q)

dqNdq

+(x)

E1

0L(x)dx

LINEWEAVER AND DAVIS302

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

chance of winning the lottery each time theybought a ticket (q is the probability of winningper day) This corresponds to a group of ter-restrial planets with approximately the same(but unknown) chance of biogenesis as theEarth (q is the probability of biogenesis withina period of time called here Dtbiogenesis)

We selected a gambler at random from thosewho had won on or before the Nth day Thuswe conditioned on winning before a certaintime This corresponds to assuming that theEarth is a random member of the group of ter-restrial planets that has had biogenesis on orbefore the end of Dt(N) 5 N 3 Dtbiogenesis Con-ditioning on biogenesis before this time corre-

sponds to correcting for the selection effect thatbiogenesis had to have occurred for us to behere

A gambler chosen at random from the groupthat has won within N days found that he hadwon on the first day (n 5 1) This correspondsto finding that biogenesis has occurred rapidlyon Earth that is within Dtbiogenesis

If we set N 5 1 [see Fig 4 +(11 q)] we areconditioning on rapid biogenesis We are con-sidering a group all of whose members havehad rapid biogenesis In this case a randommember having rapid biogenesis can tell usnothing about the probability q To infer some-thing about q we must have N 1

Nonobservability of recent biogenesis

If our conclusions from the daily lottery are toapply to biogenesis on terrestrial planets we need

LINEWEAVER AND DAVIS298

FIG 4 The effect on the likelihood of varying thesomewhat arbitrary number of days that the gamblershave to have won by to be in the group In contrast toFig 1 all the likelihoods of q here are based on the in-formation that a gambler (chosen at random from thegroup whose members have won within N days) has wonon the first day These likelihoods are plotted and labeledldquo+(1N q)rdquo with NIcirc124 In the biogenesis lottery(just as in the daily lottery) N defines the group and is ameasure of the duration biogenesis could have taken[Dt(N) 5 N 3 Dtbiogenesis) For example if N 5 1 we can-not say anything about q since the likelihood +(11 q) isflat (we have conditioned on ldquorapidrdquo biogenesis) Whileif N 5 ` we can put the strongest constraint on q If n 51 (when it could have been much larger 1 n N) wehave more information about q and the likelihood forlarge q is higher (see Appendix Eq A3) The ratio of theprobabilities in the histograms in Fig 3 corresponds tothe ratio of the +(14 q) likelihoods here 3926 5+(14 q 5 030)+(14 q 5 003)5 0690465 15 Thatis with n 5 1 and N 5 4 values of q lt030 are 50 morelikely to be the case than q lt003 [in Fig 3 Dt(N) 5 4 325 Myr] Notice that for 2 N ` the 95 lower limitfor q varies only between 007 and 023

FIG 5 Likelihood of qN In Figs 1 and 4 the likelihoodof q is shown where q is the probability of winning onany one day Here we show likelihoods of qN the un-known probability of winning on or before the Nth dayThis figure shows the effect of varying N The informa-tion used to compute these likelihoods is that a gamblerchosen at random from the group whose members havewon within N days has won on the first day (see Ap-pendix Eqs A6ndashA8) Translated this becomes a planetchosen at random from the group of planets that has hadbiogenesis within Dt(N) 5 N 3 Dtbiogenesis has had bio-genesis within Dtbiogenesis As in Fig 4 if N 5 1 we cansay nothing meaningful about q1 (5 q) However even ifN 5 2 we can make a stronger statement about q2 thanwe could about q q2 013 at the 95 confidence levelThe 95 lower limit on qN increases dramatically as N in-creases constraining qN to be close to 1 The ability to ex-tract a useful constraint even if N is low reduces the in-fluence of the selection effects discussed in the text

to correct for the fact that the evolution of an ob-server takes some time How long it takes ob-serving equipment or complex life or multicel-lular eukaryotes to evolve is difficult to say OnEarth it took 4 Gyr A limited pace of evolutionhas prevented us from looking back at our ownhistory and seeing that biogenesis happened lastyear or even more recently than 2 Gyr ago (weconsider a plausible range for the requisite timeelapsed since biogenesis to be between 2 and 10billion years or Dtevolve 5 416

22 Gyr)This selection effect for nonrecent biogenesis is

selecting for biogenesis to happen a few billionyears before the present regardless of whether ithappened rapidly It is not a selection effect forrapid biogenesis since the longer it took us toevolve to a point when we could measure the ageof the Earth the older the Earth became Simi-larly if biogenesis took 1 Gyr longer than it ac-tually did we would currently find the age of theEarth to be 5566 Gyr (5 4566 1 1) old ldquoWhy isthe Earth 4566 billion years oldrdquo ldquoBecause ittook that long to find it outrdquo The generalizationof this plausible assumption to the ensemble ofterrestrial planets is necessary if the likelihoodsand constraints in Figs 1 4 and 5 are to be ap-plicable to the group of terrestrial planets

Potential problems

Any effect that makes rapid biogenesis a pre-requisite for life would undermine our inferencesfor q For example although it is usually assumedthat the heavy bombardment inhibited biogene-sis energetic impacts may have set up largechemical and thermal disequilibria that playsome crucial role in biogenesis We know so lit-tle about the details of the chemical evolution thatled to life that heat pulses and rapid cooling af-ter large impacts may be part of the preconditionsfor biogenesis If true the time scale of biogene-sis would be linked to the time scale of the ex-ponential decay of bombardment and biogenesiswould (if it occurred at all) be necessarily rapidmost extant life in the Universe would have rapidbiogenesis and little could be inferred about theabsolute value of q from our sample of 1

In a panspermia scenario the rapid appearanceof life on Earth is explained not by rapid terres-trial biogenesis as assumed here but by the ubiq-uity of the ldquoseeds of liferdquo (eg Hoyle and Wick-ramasinghe 1999) An analysis in the context of

a panspermia scenario would be subject to thesame observational constraints as terrestrial bio-genesis and would therefore lead to the same in-ferred probability for the appearance of life onother terrestrial planets

Another potential problem Suppose the auto-catalytic chemical cycles leading to life are expo-nentially sensitive to some still unknown pecu-liarity of the initial conditions on Earth In thiscase to have the same q as the Earth our groupof terrestrial planets may have to be almost in-distinguishable rare clones of Earth That is con-ditioning on planets identical to Earth (ldquosame qrdquo)would be conditioning on rapid biogenesis (N 51) and would prevent us from inferring muchabout q from the observations of rapid biogene-sis on Earth [see +(11 q) in Fig 4]

This is an example of the more general issue ofthe status of the rapidity of biogenesis on EarthDid it have to be rapid If we assume it couldhave been otherwise then we can infer somethingabout q If it had to be that way we cannot Themiddle ground might be the most plausible op-tion Biogenesis did not necessarily have to hap-pen as rapidly as it did but (to be consistent withour existence) it may have had to happen within1 or 2 billion years of the Earthrsquos formation

If this is true we need to look carefully at theinfluence of varying the somewhat arbitrary andcounterfactual duration [Dt(N) 5 N 3 Dtbiogenesis]that biogenesis could have taken on Earth Whatvalues of Dt(N) are plausible and how do theyaffect the results This is done in Fig 4 whichquantifies the degree of variability one can as-sume for the duration of biogenesis and still haveinteresting constraints on q The lower N is theless variability is assumed For example if N 5 2[see +(12 q)] we are assuming that biogenesiscould only have taken as long as 2 3 Dtbiogenesismdashenough variability to be able to say somethingabout q but small enough to maintain the nonob-servability of recent biogenesis

Figure 5 allows us to generalize our inferencesabout q (the probability of biogenesis within Dtbiogenesis) to inferences about qN [the probabil-ity of biogenesis within an arbitrary time Dt(N)]Specifically it shows that we only need to be ableto assume that biogenesis could have been twiceas long as Dtbiogenesis to have interesting con-straints q2 013 at the 95 confidence level [see+(12 qN)] This is the result reported in the ab-stract

IS LIFE COMMON IN THE UNIVERSE 299

HOW COMMON IS LIFE

Relation of our analysis to the Drake Equation

The Drake Equation was devised to address thequestion of ldquoHow many communicative civiliza-tions are in our Galaxyrdquo (eg Sagan 1973) It hasbeen criticized as ldquoa way of compressing a largeamount of ignorance into a small spacerdquo (Olivercited in Dicke 1998) Despite its shortcomings itcontinues to focus the efforts of the search for ex-traterrestrial intelligence (SETI) community Animportant goal of the SETI community is to turnits subjective probabilities into mathematicalprobabilities We have done that here for one ofthe most important terms

We are interested in a simpler question ldquoHowcommon is life in the Universerdquo Our question issimpler because life is more generic than intelli-gent or technological life We modify the DrakeEquation to address our question and introducea parameter F which is a measure of how com-mon life is in the universe F is the fraction of starsin our galaxy today orbited by planets that havehad independent biogenesis

F 5 NlN p 5 fp fe fl (3)

where Nl is the number of stars in our Galaxy or-bited by planets that have had independent bio-genesis N p is the number of stars in our Galaxyfp is the fraction of stars in our Galaxy with plan-etary systems fe is the fraction of these planetarysystems that have a terrestrial planet suitable forlife in the same way as the Earth that is theyhave approximately the same probability q as theEarth and fl is the fraction of these suitable plan-ets on which biogenesis has occurred

Many recent observations of the frequency andage dependence of circumstellar disks aroundyoung stars in star-forming regions support thewidely accepted idea that planet formation is acommon by-product of star formation and thatthe fraction of stars with planetary systems isclose to unity fp lt 1 (eg Habing et al 1999 Mc-Caughrean et al 2000 Meyer and Beckwith2000)

Equation 3 then becomes

F lt fe fl (4)

If F 1022 then 1 of all stars have (or havehad) life and we conclude that life is ldquocommonrdquo

in the Universe If F 10211 we may be the onlylife in the Galaxy and life is ldquorarerdquo

There has been little agreement on the value offl Hart (1996) wrote ldquoThe value of fl is extremelyspeculativerdquo but argued based on the concate-nation of low probabilities that it must be ex-tremely small and thus life elsewhere is improb-able However Shostak (1998) assumed quite theopposite ldquoOn the basis of the rapidity with whichbiology blossomed on Earth we can optimisti-cally speculate that this fraction ( fl ) is also one(100)rdquo Our analysis is a close statistical look atthis optimistic speculation

The relation between the fraction of suitableplanets on which biogenesis has occurred (ldquoflrdquo inthe Drake Equation) and the q analyzed here is

fl(qN) 5 1 2 (1 2 q)N (5)

fl(qDt(N)) 5 1 2 (1 2 q) (6)

fl(qt) 5 1 2 (1 2 q) (7)

where Eq 5 refers to the daily lottery (see Ap-pendix Eq A5) Eq 6 is the translation to the bio-genesis lottery and we obtain Eq 7 by using t 5Dtfrustrated 1 Dt(N) Equation 7 is plotted in Figs2 and 3 Thus in Eq 7 we have expressed the ldquoflrdquoterm of the Drake Equation as a function of timeof the observables Dtfrustrated and Dtbiogenesis andof the probability q for which we have derivedthe relative likelihood In addition since fl(qN) 5qN (see Eq A5) Fig 5 shows the relative likeli-hood of fl and establishes quantitative but model-dependent (specifically N 1-dependent) con-straints on fl For example for terrestrial planetsolder than 1 Gyr (2 3 Dtbiogenesis) fl 13 atthe 95 confidence level

However to go from fl to an answer to the ques-tion ldquoHow common is liferdquo (ie to go from fl toF in Eq 4 we need to know fe the fraction of theseplanetary systems with a terrestrial planet suitablefor life in the same way as the Earth Our under-standing of planet formation is consistent with theidea that ldquoterrestrialrdquo planet formation is a com-mon feature of star formation (Wetherill 1996 Lis-sauer and Lin 2000) The mass histogram of de-tected extrasolar planets peaks at low masses(dNdM ~ M21) and is also consistent with thisidea (Tabachnik and Tremaine 2001 Zucker andMazeh 2001 Lineweaver and Grether 2002)

Our analysis assumed the existence of a group

1t2

D

D

tb

t

i

f

o

r

g

u

e

s

n

tr

e

a

s

t

i

e

s

d 2

1DtbD

io

t(

g

N

en

)

esis 2

LINEWEAVER AND DAVIS300

of terrestrial planets with approximately thesame but unknown (q [ [01]) probability of bio-genesis It is reasonable to postulate the existenceof such a q group since although we do not knowthe details of the chemical evolution that led tolife we have some ideas about the factors in-volved energy flux temperatures the presenceof water planet orbit residence time in the con-tinuously habitable zone mass of the planet at-mospheric composition bombardment rate at theend of planetary accretion and its dependence onthe masses of the large planets in the planetarysystem metallicity of the prestellar molecularcloud crust composition vulcanism basic chem-istry hydration pH and presence of particularclay minerals amino acids and other molecularbuilding blocks for life (Lahav 1999) Since all ormany of these physical variables determine theprobability of biogenesis and since the Earthdoes not seem to be special with respect to anyof them (ie the Earth probably does not occupya thinly populated region of this multidimen-sional parameter space) the assumption that theprobability of biogenesis on these planets wouldbe approximately the same as on Earth is plausi-ble This is equivalent to assuming that q is aldquoslowlyrdquo varying function of environment Iftrue fe and F are not vanishingly small This canbe contrasted with the ldquoexponentially sensitiverdquocase discussed in Potential problems

DISCUSSION

Carter (1983) has pointed out that the time scalefor the evolution of intelligence on the Earth (5Gyr) is comparable to the main sequence lifetimeof the Sun (10 Gyr) Under the assumption thatthese two time scales are independent he arguedthat this would be unlikely to be observed unlessthe average time scale for the evolution of intel-ligence on a terrestrial planet is much longer thanthe main sequence lifetime of the host star [seeLivio (1999) for an objection to the idea that thesetwo time scales are independent] Carterrsquos argu-ment is strengthened by recent models of the ter-restrial biosphere indicating that the gradual in-crease of solar luminosity will make Earthuninhabitable in a billion years or somdashseveral billion years before the Sun leaves the main se-quence (Caldeira and Kasting 1992 Rampinoand Caldeira 1994)

Our analysis is similar in style to Carterrsquos how-

ever we are concerned with the appearance ofthe earliest life forms not the appearance of in-telligent life Subject to the caveats raised in Po-tential problems and by Livio (1999) the implica-tions of our analysis and Carterrsquos are consistentand complementary The appearance of life onterrestrial planets may be common but the ap-pearance of intelligent life may be rare

SUMMARY

Our existence on Earth does not mean that theprobability of biogenesis on a terrestrial planetq is large because if q were infinitesimallysmall and there were only one life-harboringplanet in the Universe we would of necessityfind ourselves on that planet However such ascenario would imply either that Earth has aunique chemistry or that terrestrial biogenesishas taken a long time to occur Neither is sup-ported by the evidence we have Since little canbe said about the probability q of terrestrialbiogenesis from our existence we assume max-imum ignorance 0 q 1 We then use theobservation of rapid terrestrial biogenesis toconstrain q (Fig 4)

We convert the constraints on q into constraintson the fl term of the Drake Equation (the frac-tion of suitable planets that have life) For ter-restrial planets older than 1 Gyr we find thatfl is most probably close to unity and 13 atthe 95 confidence level

If terrestrial planets are common and they haveapproximately the same probability of biogen-esis as the Earth our inference of high q (orhigh qN) indicates that a substantial fraction ofterrestrial planets have life and thus life is com-mon in the UniverseHowever there are assumptions and selection

effects that complicate this result

Although we correct the analysis for the factthat biogenesis is a prerequisite for our exis-tence our result depends on the plausible as-sumption that rapid biogenesis is not such aprerequisite

Although we have evidence that the fraction ofplanets that are ldquoterrestrialrdquo in a broad astro-nomical sense (rocky planet in the continu-ously habitable zone) is large this may be dif-ferent from the fraction of planets that areldquoterrestrialrdquo in a more detailed chemical sense

IS LIFE COMMON IN THE UNIVERSE 301

Although we can make reasonable estimates ofwhat the crusts and atmospheres are made ofwithout detailed knowledge of the steps ofchemical evolution we cannot be sure that as-tronomically terrestrial planets have the sameq as Earth That is the fraction of planets be-longing to the Earthrsquos q group is uncertainThus although we have been able to quantifythe fl term of the Drake Equation using rapidbiogenesis our knowledge of the fe term is stillonly qualitative and inhibits our ability to drawstronger conclusions about how common lifeis in the Universe

APPENDIX LIKELIHOODCOMPUTATIONS

Let the unknown but constant probability ofwinning a daily lottery be q Given the informa-tion that a gambler who buys one ticket each dayfor n days lost on the first n 2 1 days and wonon the nth day we can compute the likelihoodfunction for q (probability of the data given themodel q)

L(n q) 5 (1 2 q)n21q (A1)

This is equal to the fraction of all gamblers whofirst experienced (n21) losses and then wonGiven only the information that the gambler wonat least once on or before the nth day the likeli-hood function for q is

L(n q) 5 1 2 (1 2 q)n (A2)

This is equal to the fraction of all gamblers whohave won at least once on or before the nth dayGiven the information that a group of gamblershave won at least once on or before the Nth dayand that a gambler chosen at random from thisgroup won at least once on or before the nth day(n N) the likelihood of q is

L(n N q) 5 5 (A3)

Out of all the gamblers who have won on or be-fore the Nth day this is the fraction who havewon on or before the nth day Notice that as N Rn the likelihood of low q increases and that if N 5n the likelihood is the same for all q (see Fig 4)As N R ` we have L(n N q) R L(n q)

1 2 (1 2 q)n1 2 (1 2 q)N

L(n q)L(N q)

which yields the tightest constraints on q A nor-malized likelihood + (or probability density) isdefined such that ograve10 +(q)dq 5 1 Thus the renor-malization conversion is

+(x) 5(A4)

The normalized likelihoods for Eqs A1ndashA3 areplotted in Fig 1 for the cases n 5 3 and N 5 12The 95 confidence levels cited are Bayesiancredible intervals based on a uniform prior for q

Although q is the probability of winning thelottery in 1 day we would like to generalize andask what is the probability qN of winning the lot-tery within N days In the analogous biogenesislottery q is the probability of biogenesis on a ter-restrial planet with the same unknown probabil-ity of biogenesis as the Earth The time windowfor biogenesis constrained by observations onEarth Dtbiogenesis corresponds to 1 day for thegambler However we would like to compute thelikelihood of biogenesis after an arbitrary periodof time Dt(N) 5 N 3 Dtbiogenesis Let qN be theprobability of winning on or before the Nth day

qN 5 1 2 (1 2 q)N 5 L(N q) (A5)

(see Eqs A2 and A3) We would like to know thelikelihood of qN rather than limit ourselves to thelikelihood of q (5q1) Suppose the information is the same that was available to computeL(n N q) That information is A randomly cho-sen gambler from the group of gamblers who havewon after N days won on or before the nth dayWe want L(n N qN) The relationship betweenthe likelihood of qN and the likelihood of q is

+(n N qN) dqN 5 +(n N q) dq (A6)

which with dqNdq 5 N(1 2 q)N21 (from Eq A5)becomes

+(n N qN)

5 (A7)

5 (A8)

which is plotted in Fig 5 and has as expected rel-atively larger likelihoods for larger values of qN

+(n N q)N(1 2 q)N21

+(n N q)

dqNdq

+(x)

E1

0L(x)dx

LINEWEAVER AND DAVIS302

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

to correct for the fact that the evolution of an ob-server takes some time How long it takes ob-serving equipment or complex life or multicel-lular eukaryotes to evolve is difficult to say OnEarth it took 4 Gyr A limited pace of evolutionhas prevented us from looking back at our ownhistory and seeing that biogenesis happened lastyear or even more recently than 2 Gyr ago (weconsider a plausible range for the requisite timeelapsed since biogenesis to be between 2 and 10billion years or Dtevolve 5 416

22 Gyr)This selection effect for nonrecent biogenesis is

selecting for biogenesis to happen a few billionyears before the present regardless of whether ithappened rapidly It is not a selection effect forrapid biogenesis since the longer it took us toevolve to a point when we could measure the ageof the Earth the older the Earth became Simi-larly if biogenesis took 1 Gyr longer than it ac-tually did we would currently find the age of theEarth to be 5566 Gyr (5 4566 1 1) old ldquoWhy isthe Earth 4566 billion years oldrdquo ldquoBecause ittook that long to find it outrdquo The generalizationof this plausible assumption to the ensemble ofterrestrial planets is necessary if the likelihoodsand constraints in Figs 1 4 and 5 are to be ap-plicable to the group of terrestrial planets

Potential problems

Any effect that makes rapid biogenesis a pre-requisite for life would undermine our inferencesfor q For example although it is usually assumedthat the heavy bombardment inhibited biogene-sis energetic impacts may have set up largechemical and thermal disequilibria that playsome crucial role in biogenesis We know so lit-tle about the details of the chemical evolution thatled to life that heat pulses and rapid cooling af-ter large impacts may be part of the preconditionsfor biogenesis If true the time scale of biogene-sis would be linked to the time scale of the ex-ponential decay of bombardment and biogenesiswould (if it occurred at all) be necessarily rapidmost extant life in the Universe would have rapidbiogenesis and little could be inferred about theabsolute value of q from our sample of 1

In a panspermia scenario the rapid appearanceof life on Earth is explained not by rapid terres-trial biogenesis as assumed here but by the ubiq-uity of the ldquoseeds of liferdquo (eg Hoyle and Wick-ramasinghe 1999) An analysis in the context of

a panspermia scenario would be subject to thesame observational constraints as terrestrial bio-genesis and would therefore lead to the same in-ferred probability for the appearance of life onother terrestrial planets

Another potential problem Suppose the auto-catalytic chemical cycles leading to life are expo-nentially sensitive to some still unknown pecu-liarity of the initial conditions on Earth In thiscase to have the same q as the Earth our groupof terrestrial planets may have to be almost in-distinguishable rare clones of Earth That is con-ditioning on planets identical to Earth (ldquosame qrdquo)would be conditioning on rapid biogenesis (N 51) and would prevent us from inferring muchabout q from the observations of rapid biogene-sis on Earth [see +(11 q) in Fig 4]

This is an example of the more general issue ofthe status of the rapidity of biogenesis on EarthDid it have to be rapid If we assume it couldhave been otherwise then we can infer somethingabout q If it had to be that way we cannot Themiddle ground might be the most plausible op-tion Biogenesis did not necessarily have to hap-pen as rapidly as it did but (to be consistent withour existence) it may have had to happen within1 or 2 billion years of the Earthrsquos formation

If this is true we need to look carefully at theinfluence of varying the somewhat arbitrary andcounterfactual duration [Dt(N) 5 N 3 Dtbiogenesis]that biogenesis could have taken on Earth Whatvalues of Dt(N) are plausible and how do theyaffect the results This is done in Fig 4 whichquantifies the degree of variability one can as-sume for the duration of biogenesis and still haveinteresting constraints on q The lower N is theless variability is assumed For example if N 5 2[see +(12 q)] we are assuming that biogenesiscould only have taken as long as 2 3 Dtbiogenesismdashenough variability to be able to say somethingabout q but small enough to maintain the nonob-servability of recent biogenesis

Figure 5 allows us to generalize our inferencesabout q (the probability of biogenesis within Dtbiogenesis) to inferences about qN [the probabil-ity of biogenesis within an arbitrary time Dt(N)]Specifically it shows that we only need to be ableto assume that biogenesis could have been twiceas long as Dtbiogenesis to have interesting con-straints q2 013 at the 95 confidence level [see+(12 qN)] This is the result reported in the ab-stract

IS LIFE COMMON IN THE UNIVERSE 299

HOW COMMON IS LIFE

Relation of our analysis to the Drake Equation

The Drake Equation was devised to address thequestion of ldquoHow many communicative civiliza-tions are in our Galaxyrdquo (eg Sagan 1973) It hasbeen criticized as ldquoa way of compressing a largeamount of ignorance into a small spacerdquo (Olivercited in Dicke 1998) Despite its shortcomings itcontinues to focus the efforts of the search for ex-traterrestrial intelligence (SETI) community Animportant goal of the SETI community is to turnits subjective probabilities into mathematicalprobabilities We have done that here for one ofthe most important terms

We are interested in a simpler question ldquoHowcommon is life in the Universerdquo Our question issimpler because life is more generic than intelli-gent or technological life We modify the DrakeEquation to address our question and introducea parameter F which is a measure of how com-mon life is in the universe F is the fraction of starsin our galaxy today orbited by planets that havehad independent biogenesis

F 5 NlN p 5 fp fe fl (3)

where Nl is the number of stars in our Galaxy or-bited by planets that have had independent bio-genesis N p is the number of stars in our Galaxyfp is the fraction of stars in our Galaxy with plan-etary systems fe is the fraction of these planetarysystems that have a terrestrial planet suitable forlife in the same way as the Earth that is theyhave approximately the same probability q as theEarth and fl is the fraction of these suitable plan-ets on which biogenesis has occurred

Many recent observations of the frequency andage dependence of circumstellar disks aroundyoung stars in star-forming regions support thewidely accepted idea that planet formation is acommon by-product of star formation and thatthe fraction of stars with planetary systems isclose to unity fp lt 1 (eg Habing et al 1999 Mc-Caughrean et al 2000 Meyer and Beckwith2000)

Equation 3 then becomes

F lt fe fl (4)

If F 1022 then 1 of all stars have (or havehad) life and we conclude that life is ldquocommonrdquo

in the Universe If F 10211 we may be the onlylife in the Galaxy and life is ldquorarerdquo

There has been little agreement on the value offl Hart (1996) wrote ldquoThe value of fl is extremelyspeculativerdquo but argued based on the concate-nation of low probabilities that it must be ex-tremely small and thus life elsewhere is improb-able However Shostak (1998) assumed quite theopposite ldquoOn the basis of the rapidity with whichbiology blossomed on Earth we can optimisti-cally speculate that this fraction ( fl ) is also one(100)rdquo Our analysis is a close statistical look atthis optimistic speculation

The relation between the fraction of suitableplanets on which biogenesis has occurred (ldquoflrdquo inthe Drake Equation) and the q analyzed here is

fl(qN) 5 1 2 (1 2 q)N (5)

fl(qDt(N)) 5 1 2 (1 2 q) (6)

fl(qt) 5 1 2 (1 2 q) (7)

where Eq 5 refers to the daily lottery (see Ap-pendix Eq A5) Eq 6 is the translation to the bio-genesis lottery and we obtain Eq 7 by using t 5Dtfrustrated 1 Dt(N) Equation 7 is plotted in Figs2 and 3 Thus in Eq 7 we have expressed the ldquoflrdquoterm of the Drake Equation as a function of timeof the observables Dtfrustrated and Dtbiogenesis andof the probability q for which we have derivedthe relative likelihood In addition since fl(qN) 5qN (see Eq A5) Fig 5 shows the relative likeli-hood of fl and establishes quantitative but model-dependent (specifically N 1-dependent) con-straints on fl For example for terrestrial planetsolder than 1 Gyr (2 3 Dtbiogenesis) fl 13 atthe 95 confidence level

However to go from fl to an answer to the ques-tion ldquoHow common is liferdquo (ie to go from fl toF in Eq 4 we need to know fe the fraction of theseplanetary systems with a terrestrial planet suitablefor life in the same way as the Earth Our under-standing of planet formation is consistent with theidea that ldquoterrestrialrdquo planet formation is a com-mon feature of star formation (Wetherill 1996 Lis-sauer and Lin 2000) The mass histogram of de-tected extrasolar planets peaks at low masses(dNdM ~ M21) and is also consistent with thisidea (Tabachnik and Tremaine 2001 Zucker andMazeh 2001 Lineweaver and Grether 2002)

Our analysis assumed the existence of a group

1t2

D

D

tb

t

i

f

o

r

g

u

e

s

n

tr

e

a

s

t

i

e

s

d 2

1DtbD

io

t(

g

N

en

)

esis 2

LINEWEAVER AND DAVIS300

of terrestrial planets with approximately thesame but unknown (q [ [01]) probability of bio-genesis It is reasonable to postulate the existenceof such a q group since although we do not knowthe details of the chemical evolution that led tolife we have some ideas about the factors in-volved energy flux temperatures the presenceof water planet orbit residence time in the con-tinuously habitable zone mass of the planet at-mospheric composition bombardment rate at theend of planetary accretion and its dependence onthe masses of the large planets in the planetarysystem metallicity of the prestellar molecularcloud crust composition vulcanism basic chem-istry hydration pH and presence of particularclay minerals amino acids and other molecularbuilding blocks for life (Lahav 1999) Since all ormany of these physical variables determine theprobability of biogenesis and since the Earthdoes not seem to be special with respect to anyof them (ie the Earth probably does not occupya thinly populated region of this multidimen-sional parameter space) the assumption that theprobability of biogenesis on these planets wouldbe approximately the same as on Earth is plausi-ble This is equivalent to assuming that q is aldquoslowlyrdquo varying function of environment Iftrue fe and F are not vanishingly small This canbe contrasted with the ldquoexponentially sensitiverdquocase discussed in Potential problems

DISCUSSION

Carter (1983) has pointed out that the time scalefor the evolution of intelligence on the Earth (5Gyr) is comparable to the main sequence lifetimeof the Sun (10 Gyr) Under the assumption thatthese two time scales are independent he arguedthat this would be unlikely to be observed unlessthe average time scale for the evolution of intel-ligence on a terrestrial planet is much longer thanthe main sequence lifetime of the host star [seeLivio (1999) for an objection to the idea that thesetwo time scales are independent] Carterrsquos argu-ment is strengthened by recent models of the ter-restrial biosphere indicating that the gradual in-crease of solar luminosity will make Earthuninhabitable in a billion years or somdashseveral billion years before the Sun leaves the main se-quence (Caldeira and Kasting 1992 Rampinoand Caldeira 1994)

Our analysis is similar in style to Carterrsquos how-

ever we are concerned with the appearance ofthe earliest life forms not the appearance of in-telligent life Subject to the caveats raised in Po-tential problems and by Livio (1999) the implica-tions of our analysis and Carterrsquos are consistentand complementary The appearance of life onterrestrial planets may be common but the ap-pearance of intelligent life may be rare

SUMMARY

Our existence on Earth does not mean that theprobability of biogenesis on a terrestrial planetq is large because if q were infinitesimallysmall and there were only one life-harboringplanet in the Universe we would of necessityfind ourselves on that planet However such ascenario would imply either that Earth has aunique chemistry or that terrestrial biogenesishas taken a long time to occur Neither is sup-ported by the evidence we have Since little canbe said about the probability q of terrestrialbiogenesis from our existence we assume max-imum ignorance 0 q 1 We then use theobservation of rapid terrestrial biogenesis toconstrain q (Fig 4)

We convert the constraints on q into constraintson the fl term of the Drake Equation (the frac-tion of suitable planets that have life) For ter-restrial planets older than 1 Gyr we find thatfl is most probably close to unity and 13 atthe 95 confidence level

If terrestrial planets are common and they haveapproximately the same probability of biogen-esis as the Earth our inference of high q (orhigh qN) indicates that a substantial fraction ofterrestrial planets have life and thus life is com-mon in the UniverseHowever there are assumptions and selection

effects that complicate this result

Although we correct the analysis for the factthat biogenesis is a prerequisite for our exis-tence our result depends on the plausible as-sumption that rapid biogenesis is not such aprerequisite

Although we have evidence that the fraction ofplanets that are ldquoterrestrialrdquo in a broad astro-nomical sense (rocky planet in the continu-ously habitable zone) is large this may be dif-ferent from the fraction of planets that areldquoterrestrialrdquo in a more detailed chemical sense

IS LIFE COMMON IN THE UNIVERSE 301

Although we can make reasonable estimates ofwhat the crusts and atmospheres are made ofwithout detailed knowledge of the steps ofchemical evolution we cannot be sure that as-tronomically terrestrial planets have the sameq as Earth That is the fraction of planets be-longing to the Earthrsquos q group is uncertainThus although we have been able to quantifythe fl term of the Drake Equation using rapidbiogenesis our knowledge of the fe term is stillonly qualitative and inhibits our ability to drawstronger conclusions about how common lifeis in the Universe

APPENDIX LIKELIHOODCOMPUTATIONS

Let the unknown but constant probability ofwinning a daily lottery be q Given the informa-tion that a gambler who buys one ticket each dayfor n days lost on the first n 2 1 days and wonon the nth day we can compute the likelihoodfunction for q (probability of the data given themodel q)

L(n q) 5 (1 2 q)n21q (A1)

This is equal to the fraction of all gamblers whofirst experienced (n21) losses and then wonGiven only the information that the gambler wonat least once on or before the nth day the likeli-hood function for q is

L(n q) 5 1 2 (1 2 q)n (A2)

This is equal to the fraction of all gamblers whohave won at least once on or before the nth dayGiven the information that a group of gamblershave won at least once on or before the Nth dayand that a gambler chosen at random from thisgroup won at least once on or before the nth day(n N) the likelihood of q is

L(n N q) 5 5 (A3)

Out of all the gamblers who have won on or be-fore the Nth day this is the fraction who havewon on or before the nth day Notice that as N Rn the likelihood of low q increases and that if N 5n the likelihood is the same for all q (see Fig 4)As N R ` we have L(n N q) R L(n q)

1 2 (1 2 q)n1 2 (1 2 q)N

L(n q)L(N q)

which yields the tightest constraints on q A nor-malized likelihood + (or probability density) isdefined such that ograve10 +(q)dq 5 1 Thus the renor-malization conversion is

+(x) 5(A4)

The normalized likelihoods for Eqs A1ndashA3 areplotted in Fig 1 for the cases n 5 3 and N 5 12The 95 confidence levels cited are Bayesiancredible intervals based on a uniform prior for q

Although q is the probability of winning thelottery in 1 day we would like to generalize andask what is the probability qN of winning the lot-tery within N days In the analogous biogenesislottery q is the probability of biogenesis on a ter-restrial planet with the same unknown probabil-ity of biogenesis as the Earth The time windowfor biogenesis constrained by observations onEarth Dtbiogenesis corresponds to 1 day for thegambler However we would like to compute thelikelihood of biogenesis after an arbitrary periodof time Dt(N) 5 N 3 Dtbiogenesis Let qN be theprobability of winning on or before the Nth day

qN 5 1 2 (1 2 q)N 5 L(N q) (A5)

(see Eqs A2 and A3) We would like to know thelikelihood of qN rather than limit ourselves to thelikelihood of q (5q1) Suppose the information is the same that was available to computeL(n N q) That information is A randomly cho-sen gambler from the group of gamblers who havewon after N days won on or before the nth dayWe want L(n N qN) The relationship betweenthe likelihood of qN and the likelihood of q is

+(n N qN) dqN 5 +(n N q) dq (A6)

which with dqNdq 5 N(1 2 q)N21 (from Eq A5)becomes

+(n N qN)

5 (A7)

5 (A8)

which is plotted in Fig 5 and has as expected rel-atively larger likelihoods for larger values of qN

+(n N q)N(1 2 q)N21

+(n N q)

dqNdq

+(x)

E1

0L(x)dx

LINEWEAVER AND DAVIS302

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

HOW COMMON IS LIFE

Relation of our analysis to the Drake Equation

The Drake Equation was devised to address thequestion of ldquoHow many communicative civiliza-tions are in our Galaxyrdquo (eg Sagan 1973) It hasbeen criticized as ldquoa way of compressing a largeamount of ignorance into a small spacerdquo (Olivercited in Dicke 1998) Despite its shortcomings itcontinues to focus the efforts of the search for ex-traterrestrial intelligence (SETI) community Animportant goal of the SETI community is to turnits subjective probabilities into mathematicalprobabilities We have done that here for one ofthe most important terms

We are interested in a simpler question ldquoHowcommon is life in the Universerdquo Our question issimpler because life is more generic than intelli-gent or technological life We modify the DrakeEquation to address our question and introducea parameter F which is a measure of how com-mon life is in the universe F is the fraction of starsin our galaxy today orbited by planets that havehad independent biogenesis

F 5 NlN p 5 fp fe fl (3)

where Nl is the number of stars in our Galaxy or-bited by planets that have had independent bio-genesis N p is the number of stars in our Galaxyfp is the fraction of stars in our Galaxy with plan-etary systems fe is the fraction of these planetarysystems that have a terrestrial planet suitable forlife in the same way as the Earth that is theyhave approximately the same probability q as theEarth and fl is the fraction of these suitable plan-ets on which biogenesis has occurred

Many recent observations of the frequency andage dependence of circumstellar disks aroundyoung stars in star-forming regions support thewidely accepted idea that planet formation is acommon by-product of star formation and thatthe fraction of stars with planetary systems isclose to unity fp lt 1 (eg Habing et al 1999 Mc-Caughrean et al 2000 Meyer and Beckwith2000)

Equation 3 then becomes

F lt fe fl (4)

If F 1022 then 1 of all stars have (or havehad) life and we conclude that life is ldquocommonrdquo

in the Universe If F 10211 we may be the onlylife in the Galaxy and life is ldquorarerdquo

There has been little agreement on the value offl Hart (1996) wrote ldquoThe value of fl is extremelyspeculativerdquo but argued based on the concate-nation of low probabilities that it must be ex-tremely small and thus life elsewhere is improb-able However Shostak (1998) assumed quite theopposite ldquoOn the basis of the rapidity with whichbiology blossomed on Earth we can optimisti-cally speculate that this fraction ( fl ) is also one(100)rdquo Our analysis is a close statistical look atthis optimistic speculation

The relation between the fraction of suitableplanets on which biogenesis has occurred (ldquoflrdquo inthe Drake Equation) and the q analyzed here is

fl(qN) 5 1 2 (1 2 q)N (5)

fl(qDt(N)) 5 1 2 (1 2 q) (6)

fl(qt) 5 1 2 (1 2 q) (7)

where Eq 5 refers to the daily lottery (see Ap-pendix Eq A5) Eq 6 is the translation to the bio-genesis lottery and we obtain Eq 7 by using t 5Dtfrustrated 1 Dt(N) Equation 7 is plotted in Figs2 and 3 Thus in Eq 7 we have expressed the ldquoflrdquoterm of the Drake Equation as a function of timeof the observables Dtfrustrated and Dtbiogenesis andof the probability q for which we have derivedthe relative likelihood In addition since fl(qN) 5qN (see Eq A5) Fig 5 shows the relative likeli-hood of fl and establishes quantitative but model-dependent (specifically N 1-dependent) con-straints on fl For example for terrestrial planetsolder than 1 Gyr (2 3 Dtbiogenesis) fl 13 atthe 95 confidence level

However to go from fl to an answer to the ques-tion ldquoHow common is liferdquo (ie to go from fl toF in Eq 4 we need to know fe the fraction of theseplanetary systems with a terrestrial planet suitablefor life in the same way as the Earth Our under-standing of planet formation is consistent with theidea that ldquoterrestrialrdquo planet formation is a com-mon feature of star formation (Wetherill 1996 Lis-sauer and Lin 2000) The mass histogram of de-tected extrasolar planets peaks at low masses(dNdM ~ M21) and is also consistent with thisidea (Tabachnik and Tremaine 2001 Zucker andMazeh 2001 Lineweaver and Grether 2002)

Our analysis assumed the existence of a group

1t2

D

D

tb

t

i

f

o

r

g

u

e

s

n

tr

e

a

s

t

i

e

s

d 2

1DtbD

io

t(

g

N

en

)

esis 2

LINEWEAVER AND DAVIS300

of terrestrial planets with approximately thesame but unknown (q [ [01]) probability of bio-genesis It is reasonable to postulate the existenceof such a q group since although we do not knowthe details of the chemical evolution that led tolife we have some ideas about the factors in-volved energy flux temperatures the presenceof water planet orbit residence time in the con-tinuously habitable zone mass of the planet at-mospheric composition bombardment rate at theend of planetary accretion and its dependence onthe masses of the large planets in the planetarysystem metallicity of the prestellar molecularcloud crust composition vulcanism basic chem-istry hydration pH and presence of particularclay minerals amino acids and other molecularbuilding blocks for life (Lahav 1999) Since all ormany of these physical variables determine theprobability of biogenesis and since the Earthdoes not seem to be special with respect to anyof them (ie the Earth probably does not occupya thinly populated region of this multidimen-sional parameter space) the assumption that theprobability of biogenesis on these planets wouldbe approximately the same as on Earth is plausi-ble This is equivalent to assuming that q is aldquoslowlyrdquo varying function of environment Iftrue fe and F are not vanishingly small This canbe contrasted with the ldquoexponentially sensitiverdquocase discussed in Potential problems

DISCUSSION

Carter (1983) has pointed out that the time scalefor the evolution of intelligence on the Earth (5Gyr) is comparable to the main sequence lifetimeof the Sun (10 Gyr) Under the assumption thatthese two time scales are independent he arguedthat this would be unlikely to be observed unlessthe average time scale for the evolution of intel-ligence on a terrestrial planet is much longer thanthe main sequence lifetime of the host star [seeLivio (1999) for an objection to the idea that thesetwo time scales are independent] Carterrsquos argu-ment is strengthened by recent models of the ter-restrial biosphere indicating that the gradual in-crease of solar luminosity will make Earthuninhabitable in a billion years or somdashseveral billion years before the Sun leaves the main se-quence (Caldeira and Kasting 1992 Rampinoand Caldeira 1994)

Our analysis is similar in style to Carterrsquos how-

ever we are concerned with the appearance ofthe earliest life forms not the appearance of in-telligent life Subject to the caveats raised in Po-tential problems and by Livio (1999) the implica-tions of our analysis and Carterrsquos are consistentand complementary The appearance of life onterrestrial planets may be common but the ap-pearance of intelligent life may be rare

SUMMARY

Our existence on Earth does not mean that theprobability of biogenesis on a terrestrial planetq is large because if q were infinitesimallysmall and there were only one life-harboringplanet in the Universe we would of necessityfind ourselves on that planet However such ascenario would imply either that Earth has aunique chemistry or that terrestrial biogenesishas taken a long time to occur Neither is sup-ported by the evidence we have Since little canbe said about the probability q of terrestrialbiogenesis from our existence we assume max-imum ignorance 0 q 1 We then use theobservation of rapid terrestrial biogenesis toconstrain q (Fig 4)

We convert the constraints on q into constraintson the fl term of the Drake Equation (the frac-tion of suitable planets that have life) For ter-restrial planets older than 1 Gyr we find thatfl is most probably close to unity and 13 atthe 95 confidence level

If terrestrial planets are common and they haveapproximately the same probability of biogen-esis as the Earth our inference of high q (orhigh qN) indicates that a substantial fraction ofterrestrial planets have life and thus life is com-mon in the UniverseHowever there are assumptions and selection

effects that complicate this result

Although we correct the analysis for the factthat biogenesis is a prerequisite for our exis-tence our result depends on the plausible as-sumption that rapid biogenesis is not such aprerequisite

Although we have evidence that the fraction ofplanets that are ldquoterrestrialrdquo in a broad astro-nomical sense (rocky planet in the continu-ously habitable zone) is large this may be dif-ferent from the fraction of planets that areldquoterrestrialrdquo in a more detailed chemical sense

IS LIFE COMMON IN THE UNIVERSE 301

Although we can make reasonable estimates ofwhat the crusts and atmospheres are made ofwithout detailed knowledge of the steps ofchemical evolution we cannot be sure that as-tronomically terrestrial planets have the sameq as Earth That is the fraction of planets be-longing to the Earthrsquos q group is uncertainThus although we have been able to quantifythe fl term of the Drake Equation using rapidbiogenesis our knowledge of the fe term is stillonly qualitative and inhibits our ability to drawstronger conclusions about how common lifeis in the Universe

APPENDIX LIKELIHOODCOMPUTATIONS

Let the unknown but constant probability ofwinning a daily lottery be q Given the informa-tion that a gambler who buys one ticket each dayfor n days lost on the first n 2 1 days and wonon the nth day we can compute the likelihoodfunction for q (probability of the data given themodel q)

L(n q) 5 (1 2 q)n21q (A1)

This is equal to the fraction of all gamblers whofirst experienced (n21) losses and then wonGiven only the information that the gambler wonat least once on or before the nth day the likeli-hood function for q is

L(n q) 5 1 2 (1 2 q)n (A2)

This is equal to the fraction of all gamblers whohave won at least once on or before the nth dayGiven the information that a group of gamblershave won at least once on or before the Nth dayand that a gambler chosen at random from thisgroup won at least once on or before the nth day(n N) the likelihood of q is

L(n N q) 5 5 (A3)

Out of all the gamblers who have won on or be-fore the Nth day this is the fraction who havewon on or before the nth day Notice that as N Rn the likelihood of low q increases and that if N 5n the likelihood is the same for all q (see Fig 4)As N R ` we have L(n N q) R L(n q)

1 2 (1 2 q)n1 2 (1 2 q)N

L(n q)L(N q)

which yields the tightest constraints on q A nor-malized likelihood + (or probability density) isdefined such that ograve10 +(q)dq 5 1 Thus the renor-malization conversion is

+(x) 5(A4)

The normalized likelihoods for Eqs A1ndashA3 areplotted in Fig 1 for the cases n 5 3 and N 5 12The 95 confidence levels cited are Bayesiancredible intervals based on a uniform prior for q

Although q is the probability of winning thelottery in 1 day we would like to generalize andask what is the probability qN of winning the lot-tery within N days In the analogous biogenesislottery q is the probability of biogenesis on a ter-restrial planet with the same unknown probabil-ity of biogenesis as the Earth The time windowfor biogenesis constrained by observations onEarth Dtbiogenesis corresponds to 1 day for thegambler However we would like to compute thelikelihood of biogenesis after an arbitrary periodof time Dt(N) 5 N 3 Dtbiogenesis Let qN be theprobability of winning on or before the Nth day

qN 5 1 2 (1 2 q)N 5 L(N q) (A5)

(see Eqs A2 and A3) We would like to know thelikelihood of qN rather than limit ourselves to thelikelihood of q (5q1) Suppose the information is the same that was available to computeL(n N q) That information is A randomly cho-sen gambler from the group of gamblers who havewon after N days won on or before the nth dayWe want L(n N qN) The relationship betweenthe likelihood of qN and the likelihood of q is

+(n N qN) dqN 5 +(n N q) dq (A6)

which with dqNdq 5 N(1 2 q)N21 (from Eq A5)becomes

+(n N qN)

5 (A7)

5 (A8)

which is plotted in Fig 5 and has as expected rel-atively larger likelihoods for larger values of qN

+(n N q)N(1 2 q)N21

+(n N q)

dqNdq

+(x)

E1

0L(x)dx

LINEWEAVER AND DAVIS302

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

of terrestrial planets with approximately thesame but unknown (q [ [01]) probability of bio-genesis It is reasonable to postulate the existenceof such a q group since although we do not knowthe details of the chemical evolution that led tolife we have some ideas about the factors in-volved energy flux temperatures the presenceof water planet orbit residence time in the con-tinuously habitable zone mass of the planet at-mospheric composition bombardment rate at theend of planetary accretion and its dependence onthe masses of the large planets in the planetarysystem metallicity of the prestellar molecularcloud crust composition vulcanism basic chem-istry hydration pH and presence of particularclay minerals amino acids and other molecularbuilding blocks for life (Lahav 1999) Since all ormany of these physical variables determine theprobability of biogenesis and since the Earthdoes not seem to be special with respect to anyof them (ie the Earth probably does not occupya thinly populated region of this multidimen-sional parameter space) the assumption that theprobability of biogenesis on these planets wouldbe approximately the same as on Earth is plausi-ble This is equivalent to assuming that q is aldquoslowlyrdquo varying function of environment Iftrue fe and F are not vanishingly small This canbe contrasted with the ldquoexponentially sensitiverdquocase discussed in Potential problems

DISCUSSION

Carter (1983) has pointed out that the time scalefor the evolution of intelligence on the Earth (5Gyr) is comparable to the main sequence lifetimeof the Sun (10 Gyr) Under the assumption thatthese two time scales are independent he arguedthat this would be unlikely to be observed unlessthe average time scale for the evolution of intel-ligence on a terrestrial planet is much longer thanthe main sequence lifetime of the host star [seeLivio (1999) for an objection to the idea that thesetwo time scales are independent] Carterrsquos argu-ment is strengthened by recent models of the ter-restrial biosphere indicating that the gradual in-crease of solar luminosity will make Earthuninhabitable in a billion years or somdashseveral billion years before the Sun leaves the main se-quence (Caldeira and Kasting 1992 Rampinoand Caldeira 1994)

Our analysis is similar in style to Carterrsquos how-

ever we are concerned with the appearance ofthe earliest life forms not the appearance of in-telligent life Subject to the caveats raised in Po-tential problems and by Livio (1999) the implica-tions of our analysis and Carterrsquos are consistentand complementary The appearance of life onterrestrial planets may be common but the ap-pearance of intelligent life may be rare

SUMMARY

Our existence on Earth does not mean that theprobability of biogenesis on a terrestrial planetq is large because if q were infinitesimallysmall and there were only one life-harboringplanet in the Universe we would of necessityfind ourselves on that planet However such ascenario would imply either that Earth has aunique chemistry or that terrestrial biogenesishas taken a long time to occur Neither is sup-ported by the evidence we have Since little canbe said about the probability q of terrestrialbiogenesis from our existence we assume max-imum ignorance 0 q 1 We then use theobservation of rapid terrestrial biogenesis toconstrain q (Fig 4)

We convert the constraints on q into constraintson the fl term of the Drake Equation (the frac-tion of suitable planets that have life) For ter-restrial planets older than 1 Gyr we find thatfl is most probably close to unity and 13 atthe 95 confidence level

If terrestrial planets are common and they haveapproximately the same probability of biogen-esis as the Earth our inference of high q (orhigh qN) indicates that a substantial fraction ofterrestrial planets have life and thus life is com-mon in the UniverseHowever there are assumptions and selection

effects that complicate this result

Although we correct the analysis for the factthat biogenesis is a prerequisite for our exis-tence our result depends on the plausible as-sumption that rapid biogenesis is not such aprerequisite

Although we have evidence that the fraction ofplanets that are ldquoterrestrialrdquo in a broad astro-nomical sense (rocky planet in the continu-ously habitable zone) is large this may be dif-ferent from the fraction of planets that areldquoterrestrialrdquo in a more detailed chemical sense

IS LIFE COMMON IN THE UNIVERSE 301

Although we can make reasonable estimates ofwhat the crusts and atmospheres are made ofwithout detailed knowledge of the steps ofchemical evolution we cannot be sure that as-tronomically terrestrial planets have the sameq as Earth That is the fraction of planets be-longing to the Earthrsquos q group is uncertainThus although we have been able to quantifythe fl term of the Drake Equation using rapidbiogenesis our knowledge of the fe term is stillonly qualitative and inhibits our ability to drawstronger conclusions about how common lifeis in the Universe

APPENDIX LIKELIHOODCOMPUTATIONS

Let the unknown but constant probability ofwinning a daily lottery be q Given the informa-tion that a gambler who buys one ticket each dayfor n days lost on the first n 2 1 days and wonon the nth day we can compute the likelihoodfunction for q (probability of the data given themodel q)

L(n q) 5 (1 2 q)n21q (A1)

This is equal to the fraction of all gamblers whofirst experienced (n21) losses and then wonGiven only the information that the gambler wonat least once on or before the nth day the likeli-hood function for q is

L(n q) 5 1 2 (1 2 q)n (A2)

This is equal to the fraction of all gamblers whohave won at least once on or before the nth dayGiven the information that a group of gamblershave won at least once on or before the Nth dayand that a gambler chosen at random from thisgroup won at least once on or before the nth day(n N) the likelihood of q is

L(n N q) 5 5 (A3)

Out of all the gamblers who have won on or be-fore the Nth day this is the fraction who havewon on or before the nth day Notice that as N Rn the likelihood of low q increases and that if N 5n the likelihood is the same for all q (see Fig 4)As N R ` we have L(n N q) R L(n q)

1 2 (1 2 q)n1 2 (1 2 q)N

L(n q)L(N q)

which yields the tightest constraints on q A nor-malized likelihood + (or probability density) isdefined such that ograve10 +(q)dq 5 1 Thus the renor-malization conversion is

+(x) 5(A4)

The normalized likelihoods for Eqs A1ndashA3 areplotted in Fig 1 for the cases n 5 3 and N 5 12The 95 confidence levels cited are Bayesiancredible intervals based on a uniform prior for q

Although q is the probability of winning thelottery in 1 day we would like to generalize andask what is the probability qN of winning the lot-tery within N days In the analogous biogenesislottery q is the probability of biogenesis on a ter-restrial planet with the same unknown probabil-ity of biogenesis as the Earth The time windowfor biogenesis constrained by observations onEarth Dtbiogenesis corresponds to 1 day for thegambler However we would like to compute thelikelihood of biogenesis after an arbitrary periodof time Dt(N) 5 N 3 Dtbiogenesis Let qN be theprobability of winning on or before the Nth day

qN 5 1 2 (1 2 q)N 5 L(N q) (A5)

(see Eqs A2 and A3) We would like to know thelikelihood of qN rather than limit ourselves to thelikelihood of q (5q1) Suppose the information is the same that was available to computeL(n N q) That information is A randomly cho-sen gambler from the group of gamblers who havewon after N days won on or before the nth dayWe want L(n N qN) The relationship betweenthe likelihood of qN and the likelihood of q is

+(n N qN) dqN 5 +(n N q) dq (A6)

which with dqNdq 5 N(1 2 q)N21 (from Eq A5)becomes

+(n N qN)

5 (A7)

5 (A8)

which is plotted in Fig 5 and has as expected rel-atively larger likelihoods for larger values of qN

+(n N q)N(1 2 q)N21

+(n N q)

dqNdq

+(x)

E1

0L(x)dx

LINEWEAVER AND DAVIS302

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

Although we can make reasonable estimates ofwhat the crusts and atmospheres are made ofwithout detailed knowledge of the steps ofchemical evolution we cannot be sure that as-tronomically terrestrial planets have the sameq as Earth That is the fraction of planets be-longing to the Earthrsquos q group is uncertainThus although we have been able to quantifythe fl term of the Drake Equation using rapidbiogenesis our knowledge of the fe term is stillonly qualitative and inhibits our ability to drawstronger conclusions about how common lifeis in the Universe

APPENDIX LIKELIHOODCOMPUTATIONS

Let the unknown but constant probability ofwinning a daily lottery be q Given the informa-tion that a gambler who buys one ticket each dayfor n days lost on the first n 2 1 days and wonon the nth day we can compute the likelihoodfunction for q (probability of the data given themodel q)

L(n q) 5 (1 2 q)n21q (A1)

This is equal to the fraction of all gamblers whofirst experienced (n21) losses and then wonGiven only the information that the gambler wonat least once on or before the nth day the likeli-hood function for q is

L(n q) 5 1 2 (1 2 q)n (A2)

This is equal to the fraction of all gamblers whohave won at least once on or before the nth dayGiven the information that a group of gamblershave won at least once on or before the Nth dayand that a gambler chosen at random from thisgroup won at least once on or before the nth day(n N) the likelihood of q is

L(n N q) 5 5 (A3)

Out of all the gamblers who have won on or be-fore the Nth day this is the fraction who havewon on or before the nth day Notice that as N Rn the likelihood of low q increases and that if N 5n the likelihood is the same for all q (see Fig 4)As N R ` we have L(n N q) R L(n q)

1 2 (1 2 q)n1 2 (1 2 q)N

L(n q)L(N q)

which yields the tightest constraints on q A nor-malized likelihood + (or probability density) isdefined such that ograve10 +(q)dq 5 1 Thus the renor-malization conversion is

+(x) 5(A4)

The normalized likelihoods for Eqs A1ndashA3 areplotted in Fig 1 for the cases n 5 3 and N 5 12The 95 confidence levels cited are Bayesiancredible intervals based on a uniform prior for q

Although q is the probability of winning thelottery in 1 day we would like to generalize andask what is the probability qN of winning the lot-tery within N days In the analogous biogenesislottery q is the probability of biogenesis on a ter-restrial planet with the same unknown probabil-ity of biogenesis as the Earth The time windowfor biogenesis constrained by observations onEarth Dtbiogenesis corresponds to 1 day for thegambler However we would like to compute thelikelihood of biogenesis after an arbitrary periodof time Dt(N) 5 N 3 Dtbiogenesis Let qN be theprobability of winning on or before the Nth day

qN 5 1 2 (1 2 q)N 5 L(N q) (A5)

(see Eqs A2 and A3) We would like to know thelikelihood of qN rather than limit ourselves to thelikelihood of q (5q1) Suppose the information is the same that was available to computeL(n N q) That information is A randomly cho-sen gambler from the group of gamblers who havewon after N days won on or before the nth dayWe want L(n N qN) The relationship betweenthe likelihood of qN and the likelihood of q is

+(n N qN) dqN 5 +(n N q) dq (A6)

which with dqNdq 5 N(1 2 q)N21 (from Eq A5)becomes

+(n N qN)

5 (A7)

5 (A8)

which is plotted in Fig 5 and has as expected rel-atively larger likelihoods for larger values of qN

+(n N q)N(1 2 q)N21

+(n N q)

dqNdq

+(x)

E1

0L(x)dx

LINEWEAVER AND DAVIS302

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

ACKNOWLEDGMENTS

We acknowledge David Nott and Luis Tenoriofor vetting the statistics Paul Davies John Leslieand an anonymous referee for useful commentsand Kathleen Ragan for editing We thank DonPage for gracefully pointing out an error in theplotting of Eq A8 in Fig 5 of a previous versionCHL is supported by an Australian ResearchCouncil Fellowship and acknowledges supportfrom the Australian Centre for AstrobiologyTMD acknowledges an Australian Postgradu-ate Award

ABBREVIATION

SETI search for extraterrestrial intelligence

REFERENCES

Allegravegre CJ Manhegraves G and Goumlpel C (1995) The age ofthe Earth Geochim Cosmochim Acta 59 1445ndash1456

Caldeira K and Kasting JF (1992) The life span of thebiosphere revisited Nature 360 721ndash723

Canup RM and Asphaug E (2001) Origin of the Moonin a giant impact near the end of the Earthrsquos formationNature 412 708ndash712

Carter B (1983) The anthropic principle and its implica-tions for biological evolution Philos Trans R Soc LondA310 347ndash355

Charnley SB Rodgers SD Kuan Y-J and Huang H-C (2002) Biomolecules in the interstellar mediumand comets Adv Space Res (in press) astro-ph0104416

Cronin JR (1989) Origin of organic compounds in car-bonaceous chondrites Adv Space Res 9(2)59ndash64

Dicke SJ (1998) Life on Other Worlds The 20th-Century Ex-traterrestrial Debate Cambridge University Press Cam-bridge pp 217ndash218

Habing HJ Dominik C Jourdain de Muizon MKessler MF Laureijs RJ Leech K Metcalfe LSalama A Siebenmorgen R and Trams N (1999) Dis-appearance of stellar debris disks around main-sequence stars after 400 million years Nature 401456ndash458

Halliday AN (2000) Terrestrial accretion rates and theorigin of the Moon Earth Planet Sci Lett 176 17ndash30

Halliday AN (2001) Earth science in the beginning Nature 409 144ndash145

Hart MH (1996) Atmospheric evolution the DrakeEquation and DNA sparse life in an infinite universeIn Extraterrestrials Where Are They 2nd edit edited byB Zuckerman and MH Hart Cambridge UniversityPress Cambridge pp 215ndash225

Hartmann WK and Davis DR (1975) Satellite-sizedplanetesimals and lunar origin Icarus 24 504ndash515

Hartmann WK Ryder G Dones L and Grinspoon D(2000) The time-dependent intense bombardment of theprimordial EarthMoon system In Origin of the Earthand Moon edited by RM Canup and K Righter Uni-versity of Arizona Press Tucson pp 493ndash512

Hoyle F and Wickramasinghe NC (1999) AstronomicalOrigins of Life Steps Towards Panspermia Kluwer Aca-demic Boston

Kasting JF Whitmire DP and Reynolds RT (1993)Habitable zones around main sequence stars Icarus 101108ndash128

Lahav N (1999) Biogenesis Theories of Lifersquos Origin Ox-ford University Press Oxford

Lazcano A and Miller SL (1994) How long did it takefor life to begin and evolve to cyanobacteria J MolEvol 39 549ndash554

Lineweaver CH (2001) An estimate of the age distribu-tion of terrestrial planets in the universe quantifyingmetallicity as a selection effect Icarus 151 307ndash313

Lineweaver CH and Grether D (2002) The observa-tional case for Jupiter being a typical massive planetAstrobiology 2 325ndash334

Lissauer JJ and Lin DNC (2000) Diversity of planetarysystems formation scenarios and unsolved problemsIn From Extrasolar Planets to Cosmology The VLT Open-ing Symposium edited by J Bergeron and A RenziniSpringer-Verlag Berlin p 377

Livio M (1999) How rare are extraterrestrial civilizationsand when did they emerge Astrophys J 511 429ndash431

Maher KA and Stevenson DJ (1988) Impact frustrationof the origin of life Nature 331 612ndash614

McCaughrean MJ Stapelfeldt KR and Close LM(2000) High-resolution optical and near-infrared imag-ing of young circumstellar disks In Protostars and Plan-ets IV edited by V Mannings AP Boss and SS Rus-sell University of Arizona Press Tucson pp 485ndash507

Meyer MR and Beckwith SVW (2000) Structure andevolution of circumstellar disks around young starsnew views from ISO In ISO Surveys of a Dusty Universeedited by D Lemke M Stickel and K Wilke Springer-Verlag Heidelberg pp 347ndash355

Miller SL (1982) Prebiotic synthesis of organic com-pounds In Mineral Deposits and the Evolution of the Bio-sphere edited by WD Holland and M SchidlowskiSpringer-Verlag Berlin pp 155ndash176

Mojzsis SJ Arrhenius G McKeegan KD HarrisonTM Nutman AP and Friend CRL (1996) Evidencefor life on Earth before 3800 million years ago Nature384 55ndash59

Nealson KH and Conrad PG (1999) Life past presentand future Philos Trans R Soc Lond [Biol] 3541923ndash1939

Oberbeck VR and Fogleman G (1989) Estimates of themaximum time required to originate life Orig Life EvolBiosph 19 549ndash560

Pace NR (1991) Origin of lifemdashfacing up to the physicalsetting Cell 65 531ndash533

Rampino MR and Caldeira K (1994) The Goldilocksproblem climatic evolution and long-term habitability

IS LIFE COMMON IN THE UNIVERSE 303

of terrestrial planets Annu Rev Astron Astrophys 3283ndash114

Sagan C (1973) Communication with Extraterrestrial Intel-ligenceMIT Press Cambridge MA

Shostak S (1998) Sharing the Universe Lansdowne Syd-ney p 180

Sleep NH Zahnle KJ Kasting JF and Morowitz HJ(1989) Annihilation of ecosystems by large asteroid im-pacts on the early Earth Nature 342 139ndash142

Sleep NH Zahnle K and Neuhoff PS (2001) Initia-tion of clement surface conditions on the early EarthProc Natl Acad Sci USA 98 3666ndash3672

Stetter KO (1996) Hyperthermophiles in the history oflife In Evolution of the Hydrothermal Ecosystems on Earth(and Mars) Ciba Foundation Symposium 202 edited byGR Bock and JA Goode John Wiley amp Sons Chi-chester UK pp 1ndash10

Tabachnik S and Tremaine S (2001) Maximum-likeli-hood method for estimating the mass and period dis-

tributions of extra-solar planets Monthly Notices R As-tron Soc 335(1) 151ndash158

Trimble V (1997) Origin of the biologically important el-ements Orig Life Evol Biosph 27 3ndash21

Wetherill GW (1996) The formation and habitability ofextra-solar planets Icarus 119 219ndash238

Zucker S and Mazeh T (2001) Derivation of the massdistribution of extrasolar planets with MAXLIMAmdashamaximum likelihood algorithm Astrophys J 5621038ndash1044

Address reprint requests toDr Charles H Lineweaver

School of PhysicsUniversity of New South WalesSydney NSW 2052 Australia

E-mail charleybatphysunsweduau

LINEWEAVER AND DAVIS304