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252–256 (1997).

5. Edwards, G., Dora, K. A., Gardener, M. J., Garland, C. J. &

Weston, A. H. Nature 396, 269–272 (1998).

6. Rees, D. D., Palmer, R. M. J., Hodson, H. F. & Moncada, S. Br. J.

Pharmacol. 96, 418–424 (1989).

7. Haddy, F. J. in Mechanisms of Vasodilatation (eds Vanhoutte,

P. M. & Leusen, I.) 200–205 (Karger, Basel, 1978).

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(1980).

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(1989).

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12.Howlett, R. Nature 395, 625–626 (1998).

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216 NATURE | VOL 396 | 19 NOVEMBER 1998 | www.nature.com

Biogeography

Competition exposed by knight?Peter R. Grant

“To do science is to search for repeat-ed patterns, not simply to accumu-late facts” — so ran the famous

opening sentence of Robert MacArthur’sGeographical Ecology1. There is no betterexemplar than Jared Diamond’s attempt,three years later, to extract pattern andmeaning from a mass of biogeographicaldata on bird species on islands around NewGuinea2. The data and Diamond’s inter-pretation of them have been controversial,but they have now been re-evaluated bySanderson, Moulton and Selfridge, writingin Oecologia3.

One pattern that stood out in Diamond’sanalysis was a lack of co-occurrence of cer-tain bird species, which nonetheless haveinterdigitating geographical distributions— that is, the species occur throughout thearchipelago. He interpreted this pattern asevidence of diffusely acting competitiveexclusion, by which he meant species wereexcluded from certain islands by the com-bined competitive influence of a set of oth-ers; he therefore built competition into a setof rules that appeared to have governed theassembly of communities of bird species onislands. This touched off a long and some-times acrimonious debate about the statisti-cal evidence for competition in nature4–6.Sanderson et al.3 report how they have over-come statistical limitations of previousanalyses. Their results provide support forDiamond’s original interpretations, whileleaving some intriguing issues open.

Three questions have been asked of Dia-mond’s work. Was the pattern identified cor-rectly? If so, was the causal process inferredcorrectly? And how general are the rules? Thefirst is pivotal. Connor and Simberloff4

addressed it by employing a statisticalmethod that yields a distribution of speciesoccurrences expected by chance. Ten timesthey randomly reassigned the 56 Vanuatu(New Hebrides) bird species to the 28 islandsin the archipelago, while preservingunchanged the observed number of speciesper island and the number of islands perspecies. The small number of reassignments,constrained by the nature of the data, wereused to generate a ‘null’ distribution ofspecies occurring together on no islands(so-called checkerboards), one island, twoislands, three islands and so on. Connor and

Simberloff then compared the observeddistribution with the computed one, foundclose agreement with a x2 test, and conclud-ed there was no evidence for any systematicstructuring process such as interspecificcompetition.

The debate has focused on how the nullmodel should be constructed5,6. If competi-tion between species has indeed structuredcommunities, the random scrambling ofspecies occurrences might defeat thepurpose of statistically detecting it7,8, so it iscrucial to construct the null model in a satis-factory way5,7–9. The random scramblingtechnique has been avoided altogether bySanderson and colleagues3. To appreciatetheir alternative it is helpful to think in termsof a matrix, with the names of islands at thetop of the columns and individual specieslisted at the left margin of the rows. In thematrix itself a species does (1) or does not (0)occur on a particular island.

To produce a genuinely null modelSanderson et al. used a recursive algorithm,commonly used in computer science, knownas the knight’s tour. As in chess, the knightmoves in an L pattern. The goal of the tour isto touch each cell of a matrix once and onlyonce. When thwarted in forward moves itbacktracks, reorients and moves forwardagain. Starting with a truly null matrix of 0s,and operating by random placement ofspecies and the knight’s rule of movement,they sequentially filled the matrix withspecies (1s) until all observed column androw totals were obtained. No less than 5,000unique matrices were generated by this pro-cedure, giving a distribution of frequenciesof species co-occurrences to compare withthe actual ones.

The result? Species pairs never occurringtogether are as frequent as expected bychance, but those occurring together twiceand only twice are improbably rare; they falloutside the computed 99% confidence lim-its. Improbable rarity supports the competi-tion hypothesis2 because it implies certaincombinations of species can coexist onlyunder rare circumstances. But otherhypotheses invoking predation, parasitism,hybridization, habitat requirements, differ-ent colonization routes, time lags in the dis-persal of species throughout the archipelagoand so forth are not excluded.

100 YEARS AGOA few particulars of Mr. Nikola Tesla’snew method of electric powertransmission are given in the currentnumber of the Electrical Review. Fromthe article it appears that the inventionconsists in transmitting electrical powerwithout the employment of metallic lineconductors, by taking advantage of theconductivity of the rarefied air existing inthe upper regions of the earth’satmosphere. … Heretofore, it has beenpossible, by means of the apparatus atcommand, to produce only moderateelectrical pressures, and even these withconsiderable risks and difficulties. MrTesla, however, claims that he hasdevised means whereby he is enabled togenerate, with safety and ease, electricalpressures measured by hundreds ofthousands, and even by millions of volts.

I think perhaps it may be worth notingthat apple-blossom was gathered in theneighbourhood of Exeter last week. Stillmore remarkable is the fact that asecond crop of apples has made fairprogress … [S]ome “Red Quaranders”have been gathered, nearly the size ofwalnuts. Two of these, now somewhatshrivelled, are enclosed.From Nature 17 November 1898.

50 YEARS AGOIt is becoming more and more clear tomost people connected with BritishIndustry that the way out of the presenteconomic crisis will not be by theintroduction of new machines. … Amongthe ways which have been and are beingincreasingly used to add to overallefficiency is what industry has come tocall ‘education and training’. Simple asthis may sound, it is surprising that, evenin ‘enlightened’ firms, the process ofproviding a man with specific training todo a job is often regarded as somethingwhich hinders rather than helpsproduction. Engineers, of course, have tobe trained; so have chemists. They mayeven need a four-year preliminary coursebefore their training starts. But the semi-skilled and unskilled workers can pick uptheir jobs by being put alongside Joe andTom. In the Services men are given theirtraining before being assigned to a unit;in industry many men and women haveto learn their jobs by picking up all thatcannot be concealed from them.From Nature 20 November 1948.

Nature © Macmillan Publishers Ltd 1998

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Null models are used to assess departuresfrom randomness in other fields such aspalaeobiology10 and the reconstruction ofphylogeny11, so this new analytical proce-dure will be useful beyond community ecol-ogy. Some interlocking statistical and bio-logical concerns remain, however, centredon the problem of interdependencies.

For example, in the Vanuatu analysispairs occurring nine and only nine times,like the twos, are improbably rare, but pairsoccurring ten and only ten times areimprobably common. These opposite direc-tions in deviation of ‘neighbours’ in the fre-quency distribution (and there are others)hint at further structure in the data, struc-ture that may be statistical12,13 or biological.The source of that structure might lie in thefull set of 56 bird species being analysedtogether, rather than just guilds of potentialcompetitors, and in the artificiality (andconvenience) of holding the number ofislands per species constant, for which thereis no biological theory; in contrast thereis good biogeographical theory14 to justifyholding the number of species per islandconstant in the null modelling.

This raises the issue of how a biologicallyrealistic null model can be constructed forcommunities of species in an archipelagowhen the source area and set of species can-not be specified; and of how sequential colo-nization and local adaptation, geographyand history15, can be adequately built intothe null model. In fact, how much biology

should be incorporated into the null model? Here we have echoes of a major issue in

population genetics — whether variation ismaintained by random drift or selection. Weare left, as Diamond2 was, with a challengingproblem, that of determining the relativeinfluences of chance and necessity (system-atic forces, such as competition) in theassembly of biological communities throughtime.Peter R. Grant is in the Department of Ecology andEvolutionary Biology, Princeton University,Princeton, New Jersey, 08544-1003, USA.e-mail: prgrant@princeton.edu1. MacArthur, R. H. Geographical Ecology (Princeton Univ. Press,

1972).

2. Diamond, J. in Ecology and Evolution of Communities (eds

Cody, M. L. & Diamond, J. M.) (Harvard Univ. Press, 1975).

3. Sanderson, J. G., Moulton, M. P. & Selfridge, R. G. Oecologia

116, 275–283 (1998).

4. Connor, E. F. & Simberloff, D. Ecology 60, 1132–1140 (1979).

5. Wiens, J. A. The Ecology of Bird Communities, Vol. 1

(Cambridge Univ. Press, 1989).

6. Gotelli, N. J. & Graves, G. R. Null Models in Ecology

(Smithsonian Press, Washington, DC, 1996).

7. Grant, P. R. & Abbott, I. Evolution 34, 332–341 (1980).

8. Colwell, R. K. & Winkler, D. W. in Ecological Communities (eds

Strong, D. R. Jr, Simberloff, D., Abele, L. G. & Thistle, A. B.)

(Princeton Univ. Press, 1984).

9. Harvey, P. H., Colwell, R. K., Silvertown, J. W. & May, R. M.

Annu. Rev. Ecol. Syst. 14, 189–211 (1985).

10.Raup, D. M., Gould, S. J., Schopf, T. J. M. & Simberloff, D. S.

J. Geol. 81, 525–542 (1973).

11.Harvey, P. H., Brown, A. J. L., Maynard Smith, J. M. & Nee, S.

(eds) New Uses for New Phylogenies (Oxford Univ. Press, 1996).

12.Roberts, A. & Stone, L. Oecologia 83, 560–567 (1990).

13.Stone, L. & Roberts, A. Oecologia 91, 419–424 (1992).

14.MacArthur, R. H. & Wilson, E. O. The Theory of Island

Biogeography (Princeton Univ. Press, 1967).

15.Ricklefs, R. E. & Schluter, D. Species Diversity in Ecological

Communities (Univ. Chicago Press, 1996).

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NATURE | VOL 396 | 19 NOVEMBER 1998 | www.nature.com 217

Photonics

An atomic dimmer switchPhilip H. Bucksbaum

On page 239 of this issue1, DoronMeshulach and Yaron Silberbergof the Weizmann Institute show how

atoms can be made to absorb light more orless readily, or not at all, simply by control-ling the phase of light shone at them. Thisjoins a growing list of new ‘coherent control’methods for manipulating the internalquantum dynamics of atoms and moleculesusing the coherence properties of light,rather than its intensity or colour.

All atoms and molecules can absorb light.The absorption usually occurs for light thathas a frequency n at resonance — that iswhere the energy of a single photon in thelight beam, hn, equals the energy differencebetween the ground state and an excitedquantum state of the system. But when anatom is subjected to intense light, such as thatproduced by a laser, nonlinear absorption isalso possible. In nonlinear absorption, twoor more photons pool their energy to excitethe atom, and the sum of the photon energiesequals the excited-state energy difference.The photons must not only have the right

total energy, they must also arrive at thetarget at nearly the same time, so nonlinearoptical effects are usually stronger when thelight is compressed into a short, intensepulse. This is the principle behind severalpractical devices in lasers such as harmonicfrequency converters.

One reason that the arrangement ofphotons is important in a nonlinear processis quantum interference. When a quantumdynamical process can take more than onepath, interference occurs between the differ-ent possible routes. The interference may bedestructive or constructive, slowing or has-

tening the process. An example is the two-photon absorption experiment describedby Meshulach and Silberberg: if the photonsare both present at the same time, then theabsorption may take two paths, correspond-ing to absorption of photon 1 first, followedby photon 2, or the other way around.Coherent control provides a way to adjustthe quantum interferences between thesedifferent paths, affecting the rate of thewhole process.

This is easier to understand if we stoptalking about photons and consider the lightas a classical electromagnetic wave. The lightpulse is a travelling wave with frequency nand electric field amplitude A, so that anatom will experience the light as an oscillat-ing electric field E = Acos(2pnt) where t istime. Figure 1 is a picture of the electric fieldversus time for a typical short laser pulse. Theturn-on and turn-off create a frequencyspread, shown in the spectral density of thispulse given by its Fourier transform (Fig. 2a).

An atom with a resonance at any frequen-cy in this spectrum can be excited by absorb-ing a single photon of light from the pulse.Each frequency present can have differentphases as well as different amplitudes — thatis, the light with frequency n1 might be a sinewave, sin(2pn1t) while the light with n2

might be a cosine wave cos(2pn2t) or anyintermediate phase. In Fig. 1, all the differentfrequencies happen to be cosine waves.

Figure 1 The electric field of a short laser pulse.

Figure 2 Spectral power distributions. a, Thespectrum of the pulse in Fig. 1. b, The two-photon spectrum of the same pulse. c, The two-photon spectrum of a similar pulse, whosespectral components with frequency greaterthan the mean have been reversed in sign. Thetwo-photon nonlinear absorption rate issharpened.