(Neo)n-Darwinism

Physica 22D (1986) 13-30 North-Holland, Amsterdam

(NEO)"-DARWINISM *

I.J. GOOD Virginia Polytechnic Institute and State Universit.v, Blacksburg, VA 24061, USA

I. Darwinism and neo-neo-Darwinism

According to the theory of evolution, life on earth has changed from one form into another, starting with microscopic simple forms. The concept of progress is not a necessary aspect of the theory, but over the very long haul there has been an increase in the complexity of organisms and in the complexity of groups of organisms. Under any interpretation of complexity, it must be related to brevity of description. No precise definition is available though one possibility "in principle" would be by means of the shortest specification, in a given efficient mathematical language, of all the DNA in the world. A somewhat more practical measure would be the number of extant species or higher taxa, or the sum of the logarithms of the number of branches at each node of the taxonomic tree of living organisms down to some level, or by some other measure of diversity. (For measures of diversity see, for example, Patil and Taillie [1]; Grassle et al. [2].)

Presumably the complexity has not increased regularly and must have decreased whenever there was a major world catastrophe because each

* This lecture arose out of an invitation to write a foreword to a second printing of the Wistar symposium, Moorhead and Kaplan [71]. Ulam, for whom the present conference is in memoriam, contributed to the Wistar symposium and encour- aged the second printing. Unfortunately, after I had written the foreword, the publishing firm collapsed.

catastrophe has eliminated many species and provided new niches for new species to develop. There is evidence that such major catastrophes have occurred regularly about every 26 million years during the last 150 million years (Angler [3]). Thus the complexity has presumably been a saw-toothed function of time.

The evolution of life from inanimate matter is more speculative than the evolution from primeval life, and was not the main topic of the Wistar symposium. Various attempts have been made to explain the mechanism of evolution, the most familiar class of explanations, up to the time of that symposium, being known as the neo- Darwinian theory. Some of the mathematical sym- posiasts claimed that these explanations are inadequate. They asked whether a few billion years or even a trillion years, which is much more than the age of the universe, is enough time; and they argued that rico-Darwinism needs to be replaced by something entirely different. Allowing for molecular biology, and other developments in the last thirty years, perhaps current theory should already be described as neo-neo-Darwinism.

The theory of natural selection is usually attri- buted to Charles Darwin and Alfred Russel Wallace, who presented their ideas on July 1, 1858 at a meeting of the Linnean Society. In a historical sketch at the beginning of the second edition of The Origin of Species [4] (1860), Darwin states that the concept had been anticipated by W.C.

14 l.J. Good/ ( Neo)".Darwinism

Wells in 1813, by Patrick Matthew in 1831, and even to a slight extent by Aristotle. But it is reasonable to name the theory after Darwin because of the detailed observations and arguments in his books.

Darwin noted, as others had done, that for thousands of years organisms have been seen to resemble their parents and other close relatives, even if separated from their parents at birth. He said parents must bequeath hereditary materials and these materials must influence the development of the offspring. Some organisms in a specific environment will tend to have characteristics giving them a propensity to have more or fewer descendants than others of the same species and some of the variation in these characteristics is heritable. In this way favorable changes in the hereditary materials will tend to spread over many generations at the expense of the unfavorable changes. "Favorable" and "unfavorable" are usually understood largely in relation to the expected number of descendants after some lapse of time, so there is an element of recursion in the statement. Darwin was influenced by Malthus [51 (1826) who had emphasized both the possibility of ex- ponential growth of biological populations when resources of food and space remain plentiful and the struggle for existence when they are scarce. Darwin presented some evidence that a succession of small changes could lead ultimately to a change into a new species. Moreover this mechanism was assumed by Darwin to be the primary origin of species. This, in a nutshell, is the Darwinian theory of natural selection. It is a partial explanation of evolution. Some philosophical light can be shed on what is meant by a partial explanation in terms of a concept that I call explicatioity and which I shall discuss below.

Darwin introduced his thesis with a discussion of artificial selection, especially of pigeons bred in captivity. A Martian might regard such selection as a special case of natural selection, not artificial selection, because the Martian might think of homo sapiens as just one species interacting ecologically with the others. Artificial selection is regarded as a

special case of natural selection by the philosopher Rosenberg [6].

Thomas H. Huxley in 1861 gave six lectures on evolution [7] which were issued as a small best-selling book published by a Mr. Hardwicke who did not give Huxley any of the profits. Huxley's brief arguments were highly influential in convincing many people, too busy to read Darwin at first hand, that Darwinism was essentially true, and in particular that man had evolved from primitive creatures*. In his sixth lecture Huxley presented four main arguments here numbered 1 to 4. In the following summary the first paragraph under each number corresponds to Huxley's argument.

1) The fact that animals and plants can be convincingly classified in the form of a taxonomic "tree".

This is readily explained by evolution, whereas there is no reason, known to ordinary humans, why God (as understood by English gentlefolk of the nineteenth century) should have created species having a dendroform classification**.

2) The existence of rudimentary organs, of no obvious use, which correspond to fully developed organs in closely related species.

As Darwin had emphasized, the existence of such imperfections is to be expected from the theory of natural selection but not from a theory of special creation. Huxley mentioned several striking examples of this second point and Stephen Jay Gould [8] made the point in terms of the panda's thumb in a recent book of that title. This thumb is useful but poorly "designed," so to speak, and it fairly clearly evolved from a bone in the wrist of an earlier species. An example of a rudimentary organ that Darwinists sometimes men-

*In the oral presentation "man" was replaced by "woman", but the referee prefers the male chauvinistic form.

**Huxley was of course appealing to human reasoning so that God's reasons were not relevant to Huxley's argument. Most humans who use reasoning can use only human tea- sorting. But there might be some mystics who, like some prophets in the Old Testament, can obtain God's opinion at first hand. Then again there are presumably people who only think they can do this.

LJ. Good/ (Neo)"-Darwinism 15

tion is the human appendix. The difficulty with this example is that the appendix might after all have some value sufficient to compensate for the risk of getting appendicitis. Natural selection is "opportunistic", and, if a use can be found for a rudimentary organ, that organ is apt to be gradu- ally improved for that use. The development of language is presumably an example o f this opportunism. For the original purpose of the mouth was to eat not to talk; to take in negative entropy, not to put it out (el. Good [9]). When the opportunism of natural selection is especially suc- cessful the result looks as if it had been con- sciously designed. Efficient designs are expected to be produced by a supreme being, and also by natural selection, given enough time. Thus efficient "designs", by themselves, lend a little support to creationism, and each suboptimal design gives much support to natural selection. To add up these positive and negative weights requires a judgement or a detailed mathematical theory that is not yet available as far as I know.

3) The fact that fossils of extinct species appear [nearly always] to fit well into a taxonomic tree of life.

4) The fact that fossils found in the newest rocks "in any part of the world, are always, and without exception, found to be closely allied with those [animals] which now live in that part of the world".

Of Huxley's four arguments this is the strongest one in support of the temporal evolution of species, rather than all appearing a few days after the universe began*. (el. Diamond [10]) This argument, when applied to rocks that are not so new, has since been strengthened by being combined with the theory of continental drift.

These four arguments do not rule out the theory known as "Lamarckism" or "the inheritance of acquired characteristics", characteristics that were acquired by individual organisms, whether or not

*In the spoken version the expression was "a few days after God pressed the Big Bang Button". This provoked laughter, but readers of learned periodicals are not supposed to laugh.

by their own efforts. This is an oversimplification of a theory that was proposed by Pierre Antoine de Monet Chevalier de Larnarck in the first fifteen years of the nineteenth century. According to Darwin, Larnarck was largely anticipated by Darwin's grandfather, Erasmus Darwin, b y Goethe, and by Geoffroy Saint-Hilaire, all in 1794 and 1795. Charles Darwin did not by any means claim that there was no validity in Lamarckism, indeed he positively accepted the concept of the inheritance of acquired characteristics: see, in particular, Darwin [11] (1868).

Lamarckism is not entirely false, for viral dis- eases can in a sense be "inherited": viral DNA can attach itself or even become inserted into the chromosome of the host cell. Nor is Lamarckism entirely true. To quote some familiar counter- examples (e.g. Asimov [12], p. 44), the rite of circumcision has been carried out for some hundred generations yet Jewish males are born with foreskins. Then there was an experiment on mice in which their tails were cut off for many generations yet they continued to be born with tails. This is analogous to the circumcision example but in the opposite direction so to speak. Simpson et al. ([13] 1958, p. 442) mention that many such experiments have been done but Lamarckians did not believe in inheritance of mutilations. Simpson et al. also quote two better counter-examples, namely protective coloration, and neuter castes in social insects, both of which can be explained by Darwinism but much less convincingly by Lamarckism. The existence of neuter insects did present a problem for Darwin and he explained it by means of kin selection (Darwin [4] (1860), chap. 8).

In fact there is little evidence that the inheritance of acquired characteristics is the main factor in evolution despite the temporary power of the fanatical and ignorant Lysenko (Judson [14], pp. 370-373). There is strong evidence against, for modern knowledge of heredity shows that infor- marion goes from the chromosomes to the cytoplasm of a cell but not from the cytoplasm to the chromosomes (Weismann's doctrine), apart from

16 LJ. Good/ (Neo)"-Darwinism

viruses and virus-like chromosomal fragments (though it is not yet clear how pervasive this channel of flow is). Recent evidence, however, assigns a special role to certain intracellular organelles- namely mitochondria in animals and plastids in plants. These are essential to life and are transmitted oia cytoplasmic, non-chromosomal, inheritance. They may originally have been "acquired" via infection by bacteria and by unicellular algae respectively. But the main con- troller is almost certainly the chromosome.

While explaining the origin of species, most early Darwinists, unlike Darwin himself, had nothing to say about genetic mechanism, a subject that was scientifically started by Gregor Mendel in 1866. Mendel showed that, at least in some re- spects, inheritance was "particulate" or "atomic", as indeed Darwin believed (Darwin [15], undated, p. 584), rather than continuously graduated, and that genes, the "factors" (as Mendel called them), could be dominant or recessive. In the light of information theory it is difficult to see how organisms or inanimate matter could have adequate stability without atomism of some kind, because, if everything were continuous, "noise" would cause degradation. For example, in communication systems it is necessary to regenerate binary pulses from time to time. The ancient Greek atomist speculators, Leucippus and :Democritus, must have had a good intuition. It seems that some science can be done in an arm- chair.

It was not until 1900 that Mendel's fundamental theory was rediscovered perhaps independently by three biologists. From 1866 to 1900 most biologists did not notice the importance of Mendel's work, especially as he did not do much genetic research after 1866. As an abbot, he found his time too much filled with monastic administration and finances, but he is said to have often muttered "My time will come!" He died in 1884.

In the second decade of the twentieth century the work of T.H. Morgan and his school estab- lished the chromosome theory, thus giving Mendelism a sound material basis.

In the period of about 1915 to 1935, the mathematical theory of genetics and evolution was developed, especially by R.A. Fisher [16, 17], J.B.S. Haldane [18, 19], Sewall Wright [20, 21], and S.S. Chetverikov [22]. The neo-Darwinist theories can be roughly defined as natural selection plus the workings of genetics as understood by about 1935, and they have become successively more explanatory and predictive with the increased understanding of genetics and molecular biology (for example, Dobzhansky [23], Huxley [24], Mayr [25], Simpson [26], Wallace [27], Maynard Smith [28]).

Since 1944 there have been great advances in the knowledge of genetics at the molecular level, two key references being Avery et al. [29] and Watson and Crick [30]. For a useful survey up to the early sixties see Michie [31]. A chromosome is a molecule of DNA and contains a double strand of nucleotides. There are four nucleotides in the "alphabet" abbreviated A, C, G and T. Non-over- lapping triples of consecutive nucleotides "code" for amino acids (via RNA) for example, CAG leads to alanine. These triples are called codons. There are 4 3 = 64 possible codons but only about twenty amino acids so a single amino acid cart correspond to more than one codon. Such codons can be regarded as "synonyms", like distinct words with the same meaning. That is, two codons can be synonyms, but not chemically identical, A chain of amino acids is called a polypeptide and its beginning and end are also determined by codons that can tfierefore be regarded as "punctuation". A protein molecule consists primarily of one or more polypeptides*.

DNA does not always replicate itself exactly and this leads to mutations in organisms. This is one of the mechanisms of evolution. (See mutation, inoersion and translocation in the glossary.)

The understanding of the chemistry of the genetic material has led to a new argument that evolution has occurred and to a method for dis-

*This paragraph is a condensation of a fuller discussion of about 800 words in a longer version of this paper available from the author.

LJ. Good/ (Neo)".Darwinism 17

coveting evolutionary trees (Dayhoff, Park and McLaughlin [33] 1972). The method depends on the degrees of similarity of polypeptide chains in distinct species. For example, the a chain in human hemoglobin contains 141 amino acids and is the same as in the chimpanzee. It differs from that of the gorilla in only one place, from the pig in 13 places, and from the carp in 50 places (Dayhoff [32], p. D-53). Such facts are understandable if evolution is assumed but less so if we assume that the world is a laboratory and that the DNA sequences of distinct species were produced on a "DNA-typewriter" by an ultraintelhgent entity or by a god that is not omniscient and relies on experiment. A theory that all new species are created by an ultraintelligent entity that is not omniscient and omnipotent will here be called "neo-creationism". The precise meaning of this term depends of course on the meaning of "species". Other aspects of some forms of creationism, such as the notion that the universe is only a few thousand years old, will be ignored in this presentation.

When there is the same amino acid in the same location on the a chain, in two species, it is natural to assume, if evolution is true, that the closer the relationship of the species the larger the fraction of corresponding codons that are chemically identical and not merely "synonymous". This might also tend to happen if the ultraintelligent entity makes clever use of subroutines when writing DNA programs. This criterion, of identical codons where synonymous ones would do, is one guide to the production of taxonomic trees. This last remark would be valid even under the form of neo-creationism just mentioned, and one day the ultraintelligent entity might reveal the truth to us. Under a standard form of creationism (with an omnipotent and omniscient God as the creator of species), there is no reason known to humans why identical rather than merely synonymous codons should be used for similar purposes in similar species. Thus the tendency to synonymous codons gives some brownie points (evidential weights) to natural selection and to neo-creationism over

standard creationism, when human reasoning is used. As always God may know better.

Darwin believed that the change from one species to another was always gradual, but this is by no means always the case, at least under current interpretations of "species". An example is based on "polyploidy" where cells have a multiple set of chromosomes. Bruce Wallace ([34], p. 618) says "Polyploidy is a well-known and well-understood mechanism by which 'instant speciation' occurs in plants" and, in Wallace ([27], p. 36)that instant speciation stands "in direct contradiction to Pope Plus XII's statement that 'the process by which one species gives birth to another remains entirely impenetrable'." Wallace cites work sug- gesting that the amount of DNA has frequently doubled during the course of evolution. He mentions the interesting example provided by the genetic map of the bacterium Escherichia coli (Zipkas and Riley [35]). It has a chromosome with the topology of a circle and there are many examples of related genes on this chromosome that are about 180 ° or 90 ° apart. This can be neatly explained by assuming that the chromosome arose in the course of evolution by two duplications from an earlier simpler chromosome. Partially tetra- ploid mice have been produced (Yu and Markert [36]), but the evolutionary significance for mammals is undemonstrated.

There is often functional association between genes that are close on a chromosome. For example, if a gene A has the ability to turn on or turn off the effect of gene B, in which case A is called an "operator gene" and A and B jointly are called an "operon", then A and B are often close together on a chromosome. The concept of operons was discovered in E. cob by Jacob and Monod [37] (see also Monod et al. [38]), though partially anticipated by Barbara McClintock in the fifties (see, for example, McClintock [39]). The concept of operons helps to explain why cells in different parts of the body of a higher organism produce different organs,although they all have essentially the same DNA. The concept also leads to a partial explanation or why the same DNA produces a

18 LJ. Good/ (Neo)n-Darwinism

caterpillar and a butterfly. Without reference to operons there would have to be interaction or communication between some adjacent cells to explain differentiation. As a conjecture, perhaps this interaction is analogous to infection by "retroviruses", that is, involving insertion of RNA that can produce DNA, the reverse of the familiar procedure of production of RNA by DNA. (For retroviruses, see, for example, Jacob [40], p. 138.)

A reasonable speculation for why synergistic genes are sometimes close on the same chromosome is that it is functional for them to act as a composite unit, supergene, or gene complex. Ford ([41], p. 110) suggested (though an alternative explanation was proposed by Turner; see Wallace [34], pp. 532-535), that if synergistic genes were far apart at some time, in the course of evolution they might get closer together by natural selection combined with "inversion" and "translocation". The fact that supergenes exist is analogous to the fact that new creative concepts can arise by combining two known concepts in a useful manner, a process named "bisociation" by Arthur Koestler. (See also Good [42] and the references therein where the relevance to artificial intelligence is mentioned.) Gadgets for combining ideas were designed by Ramon Lull in the thirteenth century (Gardner [43], pp. 1-27).

The advances in molecular biology have con- verted neo-Darwinism into (neo)"-Darwinism where n > 2, though it is artificial to give n any special value, like talking about fifth-generation computers. Also it is somewhat misleading to attach only Darwin's name to the theories that have emerged from his work.

Discussions of evolution are partly biological and partly philosophical. Let's get philosophical.

2. What is a good scientific explanation?

It is possible to argue the case for or against neo-Darwinism in more than one way. Kitcher [44] bases the ease mainly on the "problem-solv- ing" ability of neo-Darwinism, and the lack of this ability in ereationism whose scientific credentials

he claims to demolish. His arguments are strong but will not be repeated here. Kitcher cites the creationist literature of course, but does not mention Thompson [45] who believes that Krishna created all species of organisms. For other recent defenses of neo-Darwinism see Ebert et al. [46] and Ruse [47].

I am going to discuss the relevance of a concept that I call explicativity. It is based on what the referee calls "the unsupportable mire of theory as 'truth'." Therefore, to reply to Pontius Pilate so to speak, I must begin by defining what I mean by a true theory, though "approximately true" would be a more cautious description. I adopt the pragmatic interpretation: a theory is (approximately) true if its observable implications are (approximately) true. See also Good [72].

The philosophy of science is more tricky than is sometimes supposed. For example, I believe that even Rosenberg [6] made a slip when he assumed that a good explanation of an event E is obviously corroborated by the event (Good [48]). (To avoid extra notation I shall allow E to denote an event, a proposition asserting that the event obtains, or a description. Often, E is treated as evidence for or against some hypothesis or theory. No confusion need arise.) Under some interpretations of explanation and corroboration it may be possible to defend Rosenberg's assumption, but I shall argue that it is not obviously true. Suppose, for example, that all but two mutually exclusive hypotheses or theories, H 1 and H2, have been somehow eliminated in advance, so that i f H 1 is corroborated then H 2 is to some extent undermined. (! regard a hypothesis as a proposition or conjunction of propositions. A hypothesis implies various conditional probabilities for some class of events.) This occurs, under a reasonable interpretation of corroboration, if P (E I H1) > P(E I H 2) (where P(A I B) denotes the epistemic probability of A given B), that is, if H 1 makes E more probable than H 2 does*. But after collecting obseroations it is easy to

*Epistemic probabilities are either logical or personal probabilities and are often judged only approximately. In/.his paper


invent complicated and far-fetched hypotheses that are, in this sense, better corroborated by the observations made so far than more reasonable explanations. For example, let E denote a description of all known species of animals, and let H R denote the hypothesis that Ronald Reagan went back in a time machine and created precisely those species; that is, HR contains the same description of the species as is given by E. (I am supposing that HR is formulated by someone who knows what species exists, otherwise that person would need amazing paranormal powers.) We could call that supply-side creationism**. Then P(E I HR) = 1, so H R is better corroborated than is the theory of natural selection. But even Reagan would not regard HR as the better explanation. The prior probability of H R (prior to taking into account the fact that the various species exist), negligible anyway, becomes smaller and smaller as more and more species are brought into the definition of H R. As each new species is allowed for, we can see by Bayes's theorem* that the corroboration cannot do more than compensate for the corresponding loss in the prior probability of H R. So corroboration is not enough. The argument applies equally well if Reagan is replaced by Krishna.

A closely related point is that, in a technical sense in statistical inference, "likelihood" is not enough, a fact well known to "neo-Bayesians" (see the glossary).

Among the criteria used for choosing between scientific theories are the abilities to explain, to predict, and to discover. The theory of natural selection is strongest at explanation though it does have value for prediction and discovery. One example of a prediction arises from what I said

I write as if they had precise numerical values for the sake of brevity. One can instead use "upper and lower probabilities", but this would confuse the structure of the arguments with little logical gain.

**This name provoked considerable laughter at the conference though the economic analogy is of course imperfect. The idea is that Reagan is supposed to be supplying the species.

tSee under "Bayesian" in the glossary.

before about identical and synonymous codons in closely related species. That is, neo-neo-Darwinism predicts that synonymous codons that perform similar functions in two closely related species will probably be identical and not merely synonymous (when these codons have not yet been examined). Another class of predictions is implicit in T.H. Huxley's fourth argument, the one about fossils. As Kitcher ([44], p. 80) says "Paleontological prediction [concerning what will be dug up in the future] is possible because scientists sometimes have enough evidence to apply the problem-solv- ing strategies of evolutionary theory to puzzles about the past."

Let us consider what is meant by a good explanatory theory or hypothesis H when we wish to explain some evidence E. To quite an extent the answer can be captured in a formula but I cannot here do justice to the philosophy of explanation. The formula, which depends largely on a Bayesian philosophy, is only semi-quantitative or even just qualitative in some applications because its terms can often be judged only very approximately, but it summarizes many words. It follows from some very reasonable postulates which are listed in the appendix, together with other comments. The formula, to be explained in more detail soon, is

H) = log [P(EIH)/P(E)] + y log P(H)

(1)

Here ~(E : H) is called the explicatioity of H with respect to E and is intended to measure, before E was observed, the extent to which a reasonable degree of belief in E is increased by allowing for a hypothesis H. The main weakness of the formula is that it does not allow directly for the complexity of H other than by its prior probability P(H). The parameter y is a measure of the undesirability of clutter, that is, of adjoining irrelevancies to H. The precise value of ,/ is not very important and the reader can take , /= ½ for definiteness. Of course P(E) denotes the (epistemic) probability of E before we know that E obtains. When there are just two mutually exclusive and exhaustive hypotheses,


H 1 and H 2, w e have P(E)=P(Hx)P(EIH1)+ P(H2)P(EIH2). I mention that as an exercise for those who wish to revise their knowledge of elementary probability.

Let's interpret (1) informally. The first term on the right measures the degree to which the probability of E is increased (in ratio) when H is assumed, the probabilities being estimated as if the truth value of E had not been determined. If the first term is large then E is made more believ- able if H is assumed. The second term 7 log P(H) handicaps hypotheses of low initial probability, that is, far-fetched hypotheses. Usually P(H) depends very much on personal judgement. For example, the initial probability of natural selection seems to me many times larger than neo-creationism, when neither theory contains descriptions of species. Natural selection also gains from the first term. Consider, for example, the features of the circular E. coli genetic map. There is no known reason why an omniscient being should have done anything in particular such as placing related genes about 90 ° and 180 ° apart, as in fact occurs, but there is a sensible conjecture in terms of genetic principles, as mentioned before.

To compare two hypotheses Hx and H2, of roughly equal complexities, we can write

Ha) - H2) = log [P(EIHx)/P(E I H2) ]

+ 7 log[P(Hx)/P(H2)], (2)

when it is assumed that one or other of them is (approximately) true. The approximate numerical values of the two terms on the right here are somewhat less difficult to judge than in formula (1) though the judgement is still not easy. It is often less difficult to judge ratios of small probabilities than to judge the individual small probabilities themselves. For applications in the hard sciences the first term on the right can sometimes be estimated accurately, and it can be large. It has been called the weight of eoidence provided by E in favor of H x as compared with H 2. The second

term is more difficult to judge but is often small compared with the total weight of evidence so it is not important to judge it accurately. The prior probabilities of the hypotheses should be judged as if we did not know whether E had occurred.

Let us try to apply the formula with H 1 -- natural selection and H 2 --special creation in the form that a being created each distinct species. (Here H 2 is not supposed to contain descriptions of the species.) For this application, E is a conjunction of a large number of observations or propositions, E--- Ex&E2&E3&... ; for example, E97 might be a description of elephants. (The various components of E are not necessarily only descriptions of species.) The probabilities P(E971H1) and P(E97[H2) are both extremely small, but the ratio might be regarded by some people as close to 1, and it is only the ratio that concerns us. Now let El63 mean that a frozen mammoth was found. Then I judge that

P(E97&E1631Hx)/P(E97&Ex,aIH2) >> 1,

because natural selection "predicts" that living species resemble other, often extinct, species, but God knows why an omniscient being should prefer this phenomenon. Since we are not gods we have to use human judgements of the probability ratios. Some readers might prefer to write the inequality in the form

P(EaTIExr~&Ht) P(E971Et63&H2) P(E971H1 ) >> P(E971H2 )

because the two sides here are Keynes's measures of association. The inequality asserts that there is a kind of correlation between elephants and mam- moths that is much more to be expected (by humans) given H 1 than given H~'.

The argument is weaker against neo-creationism than against creationism because an ultraintelli-

*I have expressed the argument in this second form for the benefit of those, such as the referee, who regard the function of a theory as the specification of correlations.


gent entity need by no means be omniscient and might enjoy experimental programming. But it is hard for humans to understand why either kind of entity should bother to carry out such experiments over a period of billions of years. In short, P(E I H2) /P(EIH1) is very small unless the entity is an experimentalist and is not omniscient.

As another example, let E 7 describe precisely the structure of the Panda's thumb. Then, although P(ETInatural selection) is very small, P(ETIneo-creationism ) is smaller, and P(Evlcrea- tionism) is much smaller in ratio.

A remarkable and relevant fact is that all animals and plants depend on DNA, and use essentially the same code, and the identity of the a unit of hemoglobin of man and chimpanzee cannot be a coincidence. If E 8 is defined as either of these two facts, again P(EslHa)/P(EalH2) seems to me to be considerably greater than unity unless tidy-mindedness or laziness is conjoined to H 2.

When using formula (2), with H 1 =natura l selection and H 2 = special creation, we can consider T.H. Huxley's four arguments. Natural selection will gain enormously from the first term on the right but the second term will depend both on scientific judgement and on theological views. It will vary from one person to another even if all believe in God. Some fundamentalists will regard this term as minus infinity and therefore won't need to take the first term into account! Others will call this dogmatism.

In principle, when evaluating a theory of evolution, E should denote all that is known about life, otherwise there is a danger of using a biased sample. It is difficult to avoid bias.

The criterion of higher explicativity is, I believe, adequate for comparing hypotheses or theories of approximately equal complexities; otherwise the more complex theory needs to be penalized. For some discussion of complexity in relation to explicativity see Good and McMichael [49] and Good [50]. An example of a fabulously complex, and absurd, theory is suppy-side creationism H R formulated with detailed descriptions of millions of species. If H R is formulated in a simple form in

which the descriptions of the species are omitted, then we must avoid committing the fallacy of assuming that P(E I '' whatever will be will be") = 1. It is of course equal to P(E). To say "whatever will be will be" might help one not to worry unnecessarily about the future but, regarded as a proposition, it has no predictive value. A theory H that leaves the probability of E unchanged has negative explicativity for E when P(H) < 1.

3. The difficulties in the theory of natural selection

Darwin [4] (1860) included a chapter entitled "Difficulties of the theory". He considered that the most serious difficulty was to explain the occurrence of two distinct castes of sterile workers in the same ant nest. He finds an explanation but he says "I do not pretend that the facts given in this chapter s t rengthen. . .my theory; but none of the cases of difficulty, to the best of my judgement, annihilate it". One of the challenges in the Wistar Symposium was along similar lines: a theory that explains everything explains nothing. (This could of course be said of creationism, but the delegates at the Wistar symposium didn't bother to sa), it.)

But theories cannot be disposed of so easily because it is usually necessary to add something to a theory H in order to explain a specific observation (as emphasized by Pierre Duhem*: see, for example, Kitcher [44], p. 44 or Alexander [51]). In physics one has to add initial boundary conditions to the general theories. A physical explanation of a specific observation is thus of the form of a logical conjunction (H & J). Whether the addition of J to H is a piece of adhockery depends on the probability of J; more precisely on whether ~/(E: H)<~/[E:(H & J)], and the difference between the two sides is a measure of adhockery. (As mentioned before, 71 should incorporate an extra penalty for complexity but I don't know how

*Duhem argued that theories and hypotheses are not usually tested one at a time in spite of what one might at. first suppose.

22 l.J. Good/ (Neo)".Darwinism

to do this.) In physics, J might be known to be true because of the known design of an experiment. Darwin's explanation of the sterile ants did not refer to an experimental design and he had to supplement the theory of natural selection with some special speculation J. He was aware of his adhockery but judged that it was not devastating, in other words that J was not too improbable.

4. Critical comments concerning the Wistar symposium

The Wistar symposium was summarized by Bernhard [52] but the following critical comments do not repeat much of what he said, and contain some observations not available in 1967. This section of the paper is especially appropriate for a reason mentioned in the second sentence of the first footnote of section 1.

The title of the symposium implied that evolution as such was not about to be questioned; the question was mainly whether neo-Darwinism is an adequate theory. The main "challenges" were formulated by two mathematicians, Murray Eden and Marcel Schtitzenberger. In what follows I shall adopt the historic present tense.

Among several other topics, Eden refers to the a and fl polypeptide chains in human hemoglobin, of lengths 140 and 146 amino acids respectively*. As strings they can be placed together so that 61 amino acids agree and 76 disagree, with nine "gaps". The agreements are sufficient to suggest strongly that the chains had a common precursor a long time ago and that each chain was then derived by a succession of changes, that is, by changes in individual amino acids and by inser- tions and deletions of amino acids. At first sight it seems necessary that there should be a path, in the "space" of all possible polypeptides, leading from a to /3, such that at each point in the path the

*This paragraph is largely covered in Bernhard's summary, but I thought it too important to omit and it leads on to the next paragraph.

polypeptide was biologically useful. Allowing for further information mentioned by Eden, the length of a path (that is, the number of nucleotide changes) can be seen to be at least 120; for example, 60 from the precursor to each of the chains a and /3. Moreover, if the changes were random, the path length would be far greater than 120, so there is a question of whether there has been enough time for all these mutations to occur. There has really been much more than enough time according to Mayr (see Lewin [53]) because distinct mutations occur in different individuals in a population, and these can later be brought together by mating.

In the last 25 years there has been much work done by molecular biologists in comparing protein and DNA sequences between species. (Eden was talking about the development of two polypeptides within a species.) A potentially powerful technique known as DNA-DNA hybridization has been applied by Sibley and Ahlquist on a large scale to the phylogeny of birds and more recently, and still controversially, to humanoids. In a nutshell the technique is to see how well the DNA of one species sticks to the DNA of another. The questions here resemble those for hemoglobin. For reviews see Sibley and Ahlquist [54] and Lewin [55]. Let me now return to the discussion in the Wistar symposium.

Niels Barricelli asserts in the discussion that most mutations are harmful but are recessive, and therefore can be the preliminary to further mutations in later generations. According to Wallace ([34], pp. 395-408) it is now believed that the fraction of beneficial mutations is much larger than was once supposed. A complete mathematical theory should allow also for neutral mutations, that is, those of neither positive nor negative benefit. Also it is now believed that the selective value of most genes depends on the rest of the genotype. Moreover a species is spread out over space and time and a given gene's advantages and disad- vantages can fluctuate from region to region.

Another argument, related to the question of "whether there has been enough time", is put

l.J. Good/ (Neo)n-Darwinism 23

forward by both Eden and Schtitzenberger in the form of an analogy with a printed language. Of all 27 N sequences of N letters and spaces only something like the square root form grammatical and meaningful English (that is, the geometric mean probability of guessing the next letter of a text is not far from ½). This proportion is a negligibly small fraction of the total number if N is not very small. The inference is that random proteins would hardly ever be of value. This is not a good argument because, starting from a meaningful sentence, rather than from a random string, the probability that a few random changes lead to sense may be a s high a s 10 - 6 and is not utterly negligible. Similarly the DNA of humans may have evolved by "misprints" in the DNA of ape-like creatures, not by such creatures randomly hitting the keys of a DNA typewriter without reference to their own DNA. There is a relevant discussion, in terms of word games, by Maynard Smith [56]. He exemplified the game by the sequence WORD, WORE, GORE, GONE, GENE. This paper should not be confused with his better known work on games in relation to evolution (Maynard Smith [57]).

Schiitzenberger further asks for some more precise rules relating changes in phenotypes to changes in amino acid sequences in polypeptides. Similarly Eden says " . . . the discovery of the syn- tactic and semantic rules of the genetic language are the pertinent tasks; a knowledge of the workings of the typewriter may be interesting but will probably furnish little information about the language". Unlike natural linguistic sequences of letters, some or most polypeptide sequences look random in the sense that "digraph" and "trigraph" frequencies can be predicted from the "mono- graph" frequencies (Good [58]), and this suggests that the causal linkage from amino acids to the action of the polypeptides will be difficult to de- cipher, but the problem is being attacked, for example at Birkbeck College in London.

Stanislaw Ulam described some computer simulations of the process of natural selection, using of course very small models. Among other things the simulations verify that evolution by natural selec-

tion proceeds much faster by sexual reproduction than by asexual division. For more details see Schrandt and Ulam [59]. This topic had been discussed by Fisher [17] but at a time when even small-scale simulations were impracticable. Ulam again raises the question of "how to formulate... [the] more functional.., properties of genes", and says " . . . the code must contain some elements which deal with rules for construction and organization and, therefore, are different from the, so to say, lowest level of recipes". He is in effect asking for an explanation of self-organizing systems. Just as higher-level computer languages have evolved from machine language, so the "language of the gene" might be of a much higher level than we suppose on the evidence available at present. The discovery of this high-level language, if it exists, would be of enormous importance.

In recent years some progress has been made that answers these questions to some extent. It has been found, for example, that a gene can be represented several times in DNA, and some of the representations can be imperfect without affecting the phenotype. These imperfect representations are then immune to the selective effect and are therefore free to "drift". Similarly, the parts of a gene can evolve at different rates, the essential parts evolving more slowly than the inessential parts. The literature of these effects can be entered via Maynard Smith [28], chap. 2.

The questions cannot be answered fully before we know all about the chemistry of a cell but partial knowledge might be illuminating. Much is known; for example, Watson ([60], p. 99) says " . . . w e already know at least 1/5, and maybe more than 1/3 of all the metabolic reactions that will ever be described in E. coli". This is impressive, for there are thousands of complicated protein molecules in this unicellular bacterium, but it may be several decades before .the questions raised by Eden, Schi~tzenberger, and Ulam are answered to everyone's satisfaction. Even when the workings of a cell are understood, more is needed to describe its evolution. The problems might be analogous to those of prediction in economics. It

24 LJ. Good/ ( Neo)"-Darwinism

is more important to judge what are the salient parameters and not to complicate matters too much by trying to take everything into account.

William Bossert describes problems of mathematical optimization that suggest the possibility of limitations to the power of natural selection by small changes. When trying to maximize a function of several variables it is easy to get stuck near a "ridge" before reaching even a local maximum. By modeling the process of migration in his computer simulation Bossert overcame the stagnation. In the discussion Barricelli describes some similar computer experiments.

Ernst Mayr, in a lucid and informative presentation, turns the title of the symposium around with his "Evolutionary challenges to the mathematical interpretation of evolution". In effect he is telling us what to do until the mathematician arrives. Among the points he emphasizes is the enormous variation, from species to species, in the time taken for a species to change into one or more new species; it can be anything from a few years (leaving aside the instant speciation of polyploidy) to hundreds of millions of years. The implication is that the parameters in a mathematical model should not too readily be given precise values.

Aspects of evolution that Mayr recalls are (i) the importance of population size; (ii) that "Much, if not most, natural selection is concerned with maintenance evolution", that is, with avoiding change (this is reminiscent of the development of sciences and societies); (iii) the occurrence of "switch evolution" where a species moves to a new niche; (iv) speciation. He then discusses, in relation to these four aspects, the relative importance of mutations and "gene flow" (the move- ment of genes from one population to another).

After discussing several other additions that have been made to neo-Darwinism since 1935, Mayr reaches the conclusion that the mathematical modelling of evolution will eventually need to be not very simple if it is to be realistic. But he concedes that one has to begin by considering simple models.

In the discussion Eden agrees with Mayr but adds that a simple algorithm can sometimes produce results that look complicated. I am reminded of the mechanical "tortoises" of Grey Walter ([61], chap. 5) which had very simple structure but be- haved in a seemingly intelligent manner. An example that is somewhat analogous to the small- scale simulations of evolution on computers is Conway's game Life. See, for example, Gardner [62], where the reference to the Garden of Eden is coincidental; and see also Conway's contribution to the present Los Alamos conference.

It is well known that simplicity can lead to complexity: six axioms of quantum mechanics "in principle" contain the whole of chemistry (though the knowledge of the breakdown of "parity" may also be required for explaining the predominance of right-handed chirality of naturally-occurring sugars and of DNA: see, for example, Garay [63]); the axioms of the integers imply theorems of number theory having complex proofs (but simple formulations), and the simple rules of chess or Go lead to enormously complex games. But it is a long step from knowing the axioms of the integers to proving the deeper theorems of number theory or from knowing chemical principles to explaining the historical details of evolution! Perhaps one day the theory of evolution will have the same kind of appeal as pure mathematics, where simplicity emerges beautifully from the complexity that emerges from simplicity*.

George Wald discusses a process that he calls vicarious selection, which resembles group selection. The concept of group selection, which is controversial, is exemplified by a partly-baked remark I made in about 1965 to the distinguished ornithologist David Lack, namely, "Immortal men became extinct by natural selection". Understand- ing at once, and without a smile, he said "I don't believe in that kind of thing". The remark meant that tribes in which the elders live too long, tend to be destroyed in battle because the elders are liable to have too much power. Presumably Lack

*I think this is typical of beauty in most contexts.

LJ. Good/ (Neo)n-Darwinism 25

did not smile because he had spent much effort in arguing against the concept of group selection.

The example of vicarious selection, which could also be called symbiotic selection, discussed by Wald, was the fact that deep in the ocean, where no light penetrates from the sun, the fish are nevertheless visible because they are coated with luminescent bacteria. The fish are thus visible to their mates, friends, and enemies, and on balance the fish are better off as a group for being visible. Vicariously it is also better for the bacteria because the more fish the more substrate for the bacteria. But then it becomes advantageous for other bacteria to remain dark.

In the discussion Mayr says "The question is often asked how one can select for an attribute that is potentially harmful to its bearer. The answer is that it will be favored by selection if it increases the probability of survival of close relatives", and he mentions that the point was discussed by Darwin. This is kin selection. I cited the relevant chapter by Darwin earlier. The topic is treated at length by Dawkins ([64], p. 97 ft.) but with a new point of view and emphasis, due to W.D. Hamilton. The basic idea can be expressed in an over-simplified and tautologous slogan as "the survival of the fittest genes".

In the discussion of Wald's paper John Fentress mentions a prank that he played on his zoologist .friends. (Charles II played a similar prank on Fellows of the newly formed Royal Society. He asked them why the weight of a bowl containing a goldfish in water was less if the goldfish was dead.) Fentress had observed an event E, but he asked his friends to explain E (the negation of E). He obtained impressive explanations of this false observation, but unfortunately he did not record them. Anyone who does not mind using "experimental dissimulation" can repeat the experiment. "Experimental dissimulation" is the psychologist's name for telling lies. Such pranks might produce mirth but they don't refute theories. It is entirely possible for (H & J) to be a good explanation of E while (H & K) is a good explanation of E. Also, 7/[E:(H & J)] and ,/[E:(H & K)] can both be large.

Schiitzenberger gives the next presentation, and I have already mentioned his views, but it seems worthwhile to quote some of his words because they are central to the Wistar symposium. "Our thesis is that neo-Darwinism cannot explain the main phenomena of evolution on the basis of standard physico-chemistry . . . . Thus if we claim that radically new principles are needed we also believe that these have to be found within physics... At no point does geology need to use such phrases as 'creation of information', 'increase of efficiency', 'self-organization' and the like . . . . Thus, to conclude, we believe that there is a considerable gap in the neo-Darwinian theory of evolution . . . . ". It seems fair to describe Schi~tzenberger as a reductionist. Later he clarifies his position further by denying that he believes in special creation.

In the discussion Richard Lewontin and C.H. Waddington disagree with Schi~tzenberger's analogy between genetic codes and computer programs. Whereas a single random change in a computer program usually makes it entirely meaningless, a single change of a nucleotide [or several changes] will often lead to a protein molecule, though it is fairly likely to be a useless one. If millions of apparently useless proteins litter the population, some of them may later prove useful; indeed the immune system utilizes the similar principle of producing a multitude of distinct anti- bodies so that some of them come in useful. But Schi~tzenberger wants to know some principles for deciding which proteins are useful. In short he requires that something be added to neo- Darwinism so as to increase greatly its explicativity with respect to the observed properties of life. He seems to require that a science does not de- serve the name unless it is a hard science. Perhaps, if he is to be fully satisfied, the epigenesis of some organism will need to be worked out in detail, starting with the DNA, and working through the hierarchical process of the development of a phenotype. Sydney Brenner's project in Cambridge has this objective. Such a massive achievement would provide a firm basis for an entirely new


attack on the problems of evolution. It might eventually enable men to create entirely new species such as ultralntelligent organisms.

Next, Lewontin considers a computerized prob- abilistie model of fluctuating gene frequencies. In the discussion Alex Fraser describes his computer experiments on genetic systems regarded as learn- hag machines.

The symposium concludes with a "summary discussion" led by Waddington, but it is really more than a summary. He again argues that when neo-Darwinism allows for sex it appears that there has been plenty of time for evolution to have occurred.

Waddington says further that "We can't quan- tify the theory of evolution in any sense until we can answer such questions as: How much information is needed to produce a given complexity of structure?" Also he says that rico-Darwinism has left out important parts of Darwinism. Finally he expresses the opinion that, as a c.onsequence of the discussions, we now know a little better in what directions evolutionary theories are incomplete.

The book concludes with some post-conference comments and the preliminary working papers, including papers by Waddington and by Sewall Wright. Waddington mentions several unsolved problems in the theory of evolution. The papers by Fox & Nakashima and by R. Buvet, are the only ones relevazit to theories of the origin of life. The latter is related to the well-known fact, which I call the Fourth Law of Thermodynamics, that open (non-isolated) systems, such as an animal species, can defy the second law for a long time by eating negative entropy.

Acknowledgements

This paper has benefited from extremely val- uable comments concerning a previous draft, from Richard Burian, Donald Michie, and Bruce Wallace. Michie was even friendly enough to in- elude among his many constructive comments

some scathing ones about some of my worst jokes. The work was supported in part by a grant from the National Institutes of Health.

Appendix

The postulates for explicatioity

Consider the following postulates for explicativity (see Good, [65] where applications are made to statistical problems of significance and estima- tion): (i) ~(E : H) depends at most on all probabilities of the form P(AIB ) where A and B are any logical combinations of E and H. Equivalently, ~(E : H) depends at most on P(E), P(H), and P(E & H). (ii) If K and F have nothing to do with H and E than ~/(E & F : H & K) depends only on ~ (E :H) and 71(F:K). (iii) ~(E:HIH) does not depend on E or H (in fact you can reasonably call it zero). (iv) 7/(E:H) increases with P(EIH ) if P(E) and P(H) are fixed. (v) ~(H : H) > 7/(T : T) where T is a tautology. (vi) ~(T : H) < ~/(T: T) (because a tautology needs no explanation).

Then it follows that ~(E:H) must be some monotonic function f ( x ) of the rightside of eq. (1), and we may as well take f ( x ) = x because we then obtain convenient additive properties.

Given any event E it is reasonable to choose the hypothesis ,H of greatest explicativity ~I(E:H). In some applications this rule leads automatically to sensible interval estimates for parameters. Perhaps it will provide a new basis for a theory of statistical inference with a Bayesian flavor.

For a fuller understanding of explicativity, it is essential to take so-called "dynamic probabilities" into account. A dynamic probability is one that changes by pure thought or calculation without new empirical information; for example, the mo- tions of the planets became more probable when Newton showed that the inverse square law implied elliptical orbits around the sun. (For a fuller explanation see Good [66], p. 129, [67], [65], p. 3120


Glossary

A reliable glossary of about 300 genetic terms is provided by Mayr [69]. The present glossary gives some definitions related to the present paper.

Ad hoc. 1. If a theory or hypothesis is refuted by evidence it can often be patched up by making it more complicated. Whether this is justifiable is often a matter of judgement, and the patching is called ad hoc especially when it is not justifiable. J is an ad hoc addition to a hypothesis or theory H, in the light of evidence E, if ~[E:(H & J)]< ~(E:H); in words, if the addition of J to H reduces the explicativity. (Here a term should be added to ~/ to allow for the complexity of the hypothesis or hypotheses.) 2. A procedure in- vented for a specific occasion is sometimes called ad hoc, whether justifiable or not. The~e two senses of ad hoc are not the same.

Adhockery. The activity of being ad hoc. A measure of adhockery, in sense 1, of J with respect to H (when J modifies H) is ~/(E : H) - ~/[E: (H & J)] in the notation under ad hoc (Good [69]). The cute remark "we make no mockery of honest adhockery" applies to sense 2.

Bayesian statistical method. A statistical method that makes formal use of subjective or logical probabilities often regarding the probabilities of hypotheses. A form of Bayes's theorem states that posterior probabilities of hypotheses are propor- tional to their prior probabilities times their likeli- hoods. Such methods were inaugurated by T. Bayes in 1763 and P.S. de Laplace in 1814.

Codon. A triple of adjacent nucleotides that codes for an amino acid.

Digraph. A pair of letters adjacent in some text; for example, the first three digraphs in this sentence are AP, PA, and AI.

Epigenesis. Development of an individual according to genetic principles.

Inversion. Reversal of direction of a chromosome segment. An example of a reversal or "inversion" is a change from the sequence

T T A C G T A G G T A A A T G C A T C C A T

to

T T C C T A C G T T A A A G G A T G C A A T

in which the piece consisting of A C G T A G G and its complement have been turned through 180 degrees.

Likelihood. In modern statistics the expression "likelihood" is usually to be interpreted in the following technical sense. The likelihood of a hypothesis H, in the light of E, is defined as propor- tional to the probability of E given H. Here E denotes an event, or evidence, or experimental results, and the numerical value of P(EIH) is supposed to be known tautologically when E and H are specified. For example, the event E might be the number r of bacterial colonies on a plate; and H,, might assert that P(EIHm) is e-mmr/(1 • 2" 3 "-" r) (the "Poisson distribu- tion"). Then e-ram r can be taken as the likelihood of H m, or of m, given the observation that there were r colonies. Note that the likelihood depends on the statistical model of the physical situation. If this model is taken for granted, there are many statisticians who believe that the likelihood function, as a function of m in the present example, exhausts all the information concerning the value of m, derivable from the observation r. But the hypothesis of maximum likelihood is not necessarily the best because, for one thing, it doesn't take into account prior probabilities.

Mutation. A change in a chromosome; often in a single gene by a deletion, addition, or substitu- tion of one or. more base pairs.

Neo-Bayesian. There are many modem forms of Bayesian statistical methods different from the views of Bayes and Laplace. They are often called neo-Bayesian to emphasize their modem flavor.

Phenotype. The sum of the observable characteristics, functional, structural, behavioral, etc. of an organism.

Polypeptide. A chain of amino acids in which each amino acid is bound to its successor in the chain by a characteristic configuration known as a "peptide link".


Prior probability. The prior probability of a hypothesis is its probability before some specific evidence is taken into account. Temporal prece- dence is not part of the definition.

Probability. This word has several meanings and definitions. The three main kinds of probability are (a) physical or intrinsic probability or propen: sity, such as the probabilities most often used in physics; (b) a degree of belief which might be a subjective or unique rational degree of belief (also known as a logical probability); and (c) tautologi- cal or mathematical probability which is probability whose value is assigned in a mathematical model by definition. For example, when we talk of a "fair coin", tossed fairly, we mean that the probability of heads is exactly ½, by definition. It is usually reasonably clear from the context what kind of probability is intended. A probability is denoted here by P(A[ B), pronounced " the probability of A given B" (or "conditional on B"), where A and B might denote, for example, propositions, events, or hypotheses.

Random sequence. A random sequence of letters is One in which the probabilities that the letters A, B, C; . . . . Z occur at any place have fixed values PA, Pn . . . . . Pz; the probabilities of the digraphs AA, AB, . . . . ZZ are PUA, PAPB . . . . . P~z, and so on. Of course the "alphabet" does not need to have 26 "letters". In some contexts the probabilities PA, PB, .... are assumed to be equal, as in tables of "random numbers" where the number of letters in the "alphabet" happens to be 10. For a symposium on the concept of randomness see Salmon et al. [68].

Translocation. The transference of a segment of a chromosome to another chromosome.

Trigraph. A sequence of three letters adjacent in some text; for example, the first three trigraphs in this seaatence are ASE, SEQ, and EQU.

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[53] Roger Lewin, "Biology in not postage stamp collecting", Science 216 (1982) 718-720.

[54] C.G. Sibley and J.E. Ahlquist, "The phylogeny of the hominoid primates, as indicated by DNA-DNA hybridization", J. of Molecular Evolution 20 (1984) 2-15.

[55] Roger Lewin, "DNA reveals surprises in human family tree", Science 226 (1984), 1179-1182. (Contains a "box" entitled "Some avian puzzles solved".)

[56] John Maynard Smith, "The limitations of molecular evolution", in: The Scientist Speculates, I.J. Good, general ed. (London: Heinemann; New York: Hafnes; paperback, New York: Capricorn Books), pp. 252-256. French edition entitled Quand les Savants Laissent Libre Cours ~ leur Imagination. German edition entitled Phantasie in der Wissenschafr

[57] John Maynard Smith, Evolution and the Theory of Games (Cambridge Univ. Press, Cambridge, 1982).

[58] l.J. Good, "The irregular shapes of polypeptide chains", J. Statist. Comput. and Simul. 15 (1982) 243-247.

[59] R. Schrandt and S. Ulam, "Some elementary attempts at numerical modelling of problems concerning rates of evolutionary processes" Los Alamos Scientific Laboratory of the University of California report LA-4573-MS (1971) p. 9.

[60] James D. Watson, Molecular Biology of the Gene (Benjamin, Menlo Park, CA, 1970).

[61] W. Grey Walter, The Living Brain (Duckworth, London, 1953).

[62] Martin Gardner, "On cellular automata, self-reproduction, the Garden of Eden and the game 'life' ", Sc. Ames. (February) (1971) 112-117.

[63] A.S. Garay, "Broken symmetries in physics and their relevance in chemistry and biology", in: Origins of Opti-

30 LJ. Good/ (Neo)n-Darwinism

cad Activity in Nature, David C. Walker, ed. (New York, Elsevier, 1979) pp. 245-257. Compare I.J. Good, "Broken symmetry in sn~mals", Speculations in Science and Tech- nology 7 (1984) 314.

[64] Richard Dawkins, The Selfish Gene (Oxford Univ. Press, New York, 1976).

[65] I.J. Good, "Explicativity: a mathematical theory of explanation with statistical applications", Proc. Roy. Soc. (London) A 354 (1977) 303-330. (Largely reprinted in Good, 1983 see ref. 67). The ideas originated in Good (1968) see ref. 66.

[66] I.J. Good, "Corroboration, explanation, evolving probability, simplicity, and a sharpened razor", Brit. J. Phil. Sc. 19 (1968), 123-143.

[67] I.J. Good (1977b), "Dynamic probability, computer chess, • and the measurement of knowledge", in: Machine InteUi-

genc¢ 8, ods. E.W. Eleock and D. Michie (Ellis Horwood Ltd. & John Wiley), 139-150. Reprinted in: I.J. Good,

Good Thinking: The Foundations of Probability and its Appfications (Univ. of Minnesota Press, Ann Arbor, 1983).

[68] W.C. Salmon, J.A. Coffa, I.L Good and H.E. Kyburg, Artcles in a Symposium on fundamental problems in the concept of randomness, in: PSA 1972, K.F. Schaifner and R.S. Cohen, eds. (Keldel, Dordrecht, 1974) pp. 99-149.

[69] Ernst Mayr, Populations, Species, and Evolution (Harvard Univ. Press, Cambridge, MA, 1970).

[70] I.J. Good, "A measure of adhockery", C145, in: J. Statist. Comput. & Simul. 16 (1983) 314.

[71] Paul S. Moorhead and Martin M. Kaplan, eds. Mathe- matical Challenges to the Neo-Darwinian Interpretation of Evolution (The Wistar Institute Press, Philadelphia, 1967).

[72] I.J. Good, "A pragmatic theory of truth of theories or hypotheses", C251, in: J. Statist. Comput. & Simul., in press.

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(Neo)n-Darwinism