Commentary: The objection is sustained: a defence of the defense of beanbag genetics
Centre for Ecological Sciences, Indian Institute of Science, Bangalore 560 012, India. E-mail: renee{at}ces.iisc.ernet.in
Accepted 18 February 2008
Darwin couched his theory of evolution by means of natural selection in verbal arguments. According to this theory, if the variation observed between individuals was heritable, and if it contributed differentially to the survivorship and reproductive success of individuals, the process of natural selection would ensure greater representation of individuals bearing favourable traits chosen from the existing variation in subsequent generations. This concept is powerful, whether verbally or mathematically articulated. Ernst Mayr was Darwin's champion in the 20th century, defending Darwin and Darwinism vigorously throughout his long and industrious career that spanned 80 years.1 However, as outlined in Borges,1 even among the Darwinists, the 1950s was a time of conflict between experimental biologists and naturalist-systematists such as Mayr on one hand and theoreticians on the other. The so-called evolutionary synthesis of the 1930s and 1940s that amalgamated Darwin's theory with genetics was largely attributed to the theoretical work of Ronald Fisher, Sewall Wright and JBS Haldane. In 1959, in a plenary address at the Cold Spring Harbor Symposium on the occasion of the centenary celebration of The Origin of Species, Mayr2 made disparaging remarks about the type of theoretical population genetics being done by Fisher, Wright and Haldane, and called their body of work the equivalent of beanbag genetics. He implied that the type of models that they developed, which often dealt with single genes, was too simplistic to reflect the real world that he and other naturalist-systematists and experimentalists such as Theodosius Dobzhansky were investigating. He appeared to throw down the gauntlet to the trinity of Fisher, Wright and Haldane, and challenged them to account for the value of their work; in other words, he appeared to be declaring that their recognition as the major architects of the evolutionary synthesis was unwarranted. This address stimulated Haldane to write his celebrated response: ‘In defense of beanbag genetics’,3 the paper that is being commented upon here.
Before examining Haldane's defence, it is necessary to consider the motivation behind Mayr's statements. Various possibilities have been suggested. First, the statements may have stemmed from Mayr's illiteracy in genetics;4 most of Mayr's knowledge of genetics had been acquired from reading Dobzhansky, or from discussion with such individuals as Dobzhansky's student Bruce Wallace;5 thus Mayr's knowledge of the work of theoretical population geneticists was sketchy and largely derivative. Furthermore, Dobzhansky himself, the source of much of Mayr's genetics, did not understand enough theoretical genetics and took Wright's formulations at face value without truly comprehending the mathematics (see evidence presented in Borges1). Second, Mayr is believed to have criticized models that dealt with independently inherited genes at single loci (the beanbag view) because he was more concerned with the ‘unity of the genotype’ in which there was epistasis or interactions between genes. Thus Mayr's beanbag view could have been a symptom of the conflict between reductionist and holistic views of evolution. However, according to De Winter,6 fundamental misconceptions led to Mayr's caricature of the important work of the population geneticists. For example, Fisher's formulation of a gene-wise theory of selection was reductionist only in that it assumed that genes were inherited independently, while it did not assume that they were either expressed or functioned independently. This fundamental misconception led to Mayr's pejorative remarks and disparaging views of beanbag genetics.6
The third reason for Mayr's critical remarks may have been his need to secure for the naturalist-systematists (such as himself) and the experimental biologists (such as Dobzhansky) an important place in the history of the evolutionary synthesis. Perhaps undue emphasis was being given to the work of the theoreticians and not enough to the contributions of others to the synthesis.7 If Darwin could have made such an impact with a verbal argument, why could not others making verbal arguments also acquire important stature in the history of evolutionary biology? Mayr did indeed verbalize valuable ideas such as one that is now recognized as the founder principle in population biology,5 and therefore may have assumed that mathematical formulations were unnecessary for important insights into evolutionary processes. The fourth reason could be that Mayr revelled in being polemical and, by making outrageous statements, he believed that he was stimulating investigation and advancing the field by provoking responses in clarification (see evidence for this reviewed in Borges1).
Whatever the real reason behind Mayr's challenge, Haldane's spirited defence was the result. In this response, Haldane declares that he would have to pick up the challenge, because as Fisher was not alive at the time, he could not defend himself, while Wright was the gentlest of people, and so unlikely to defend himself. However, although Fisher had passed away, it appeared that he had already anticipated such a challenge to the legitimacy of his work, for I found these words in Fisher's Preface to The Genetical Theory of Natural Selection published in 1930:8
‘The types of mind which result from training in mathematics and in biology certainly differ profoundly; but the difference does not seem to lie in the intellectual faculty ... What is profoundly susceptible of training is the imagination, and mathematicians and biologists seem to differ enormously in the manner in which their imaginations are employed ... Perhaps I can best make clear that the mathematician's imagination also has been trained to some advantage, by quoting a remark dropped casually by Eddington in a recent book—‘We need scarcely add that the contemplation in natural science of a wider domain than the actual leads to a far better understanding of the actual.’ (p. 267, The Nature of the Physical World.) For a mathematician the statement is almost a truism. From a biologist, speaking of his own subject, it would suggest an extraordinarily wide outlook. No practical biologist interested in sexual reproduction would be led to work out the detailed consequences experienced by organisms having three or more sexes; yet what else should he do if he wishes to understand why the sexes are, in fact, always two?’
Here is Fisher declaring that mathematical exploration of the realm of possibilities is what gives better insight to our understanding of the natural world, and pointing out to the dichotomy between biologists and mathematicians, a divide that must surely have contributed to Mayr's remarks. Haldane also provides several examples of this divide in his defence, which in the spirit of Fisher's words, appears to be more of a defence of theoretical biology or even of theory in science, rather than a defence of just theoretical population genetics. Lewontin9 believes, however, that evaluating the contribution of the theoretical work of the trio (Fisher–Wright–Haldane) to the evolutionary synthesis that occurred in the 1930s and 1940s is difficult because of the confusion between the history and the sociology of science at that time. According to Lewontin9 there was a genuine disconnect between the biologists and the theoreticians, and many important insights into evolutionary processes that were possible from the theory were simply unavailable to the biologists because of their mathematical illiteracy; the evolutionary synthesis proceeded without a true merger of these fields. Leigh10 also feels that the reason why the work of Fisher, for example, was little known among evolutionary biologists, especially in the United States, was the difficult mathematics, and that Mayr, who did not understand most of it, exercised a powerful negative influence over its assimilation into mainstream evolutionary biology. Ewens11 questions whether such complex mathematics was actually required for the problems at hand, since Mayr and Dobzhansky seemed to make do with verbal arguments. However, as Haldane remarks scathingly in his defence, the mathematics was rather simplistic and even elementary to a mathematician. Ewens11 further points out that when Fisher, Haldane and Wright resorted to verbal arguments, their reasoning was prone to flaws, which gives mathematical formulations a definite advantage. It is therefore understandable that Haldane's student, the eminent evolutionary biologist John Maynard Smith, who was largely responsible for bringing game theory into evolutionary biology, was also extremely critical of imprecise arguments that were not accompanied by numerical models, and was thus unabashedly a champion of beanbag genetics. For Maynard Smith, natural history without mathematics was muddled while mathematics without natural history was sterile.12 There have also been questions about whether Haldane's Marxist ideology influenced his science, and whether mathematics itself is intrinsically dialectical.13 Perhaps the reference to the Shiva (destroyer) and the Vaishnava (preserver) approaches in biology that features in Haldane's defence is a symptom of a dialectical perspective.
It is also important to consider why Haldane felt impelled to write this defence. Haldane must have known that Mayr did have a tendency to make broad, sweeping statements, oftentimes those with deliberate provocative intent. Why did Haldane simply not ignore Mayr? Perhaps Mayr was considered too powerful a figure in evolutionary biology, and as founding Editor of the important journal Evolution (the official publication of the Society for the Study of Evolution)1 wielded too much intellectual influence to be ignored. Therefore, Haldane's response was also a political one, to rectify any lasting damage to how theoretical biology was perceived by those charting science policy and by those holding the purse strings of the funds for research.
Mayr is believed to have felt that the only serious contribution that mathematicians had made was in the demonstration that there was sufficient time for life on earth to have evolved by the process of natural selection.14 Since this was largely Haldane's contribution, this could explain why Mayr felt that, of the trio, Haldane was the most important contributor to the synthesis.14 Could this explain why Mayr maintained contact with Haldane, even visiting him in India? Mayr's former excellent relationship with Wright deteriorated completely after Mayr's 1959 address, so much so that Mayr did not even invite Wright to two important conferences that were held on the evolutionary synthesis in 1974 organized by the Committee on the Recent History of Science and Technology of the American Academy of Arts and Sciences.7 Dobzhansky attended these conferences and, echoing Mayr in 1959, raised doubts about the value of theoretical work (cited in Lewontin9):
‘Do you think that the fancy mathematics of Kimura, Lewontin, Crow, and others will also guide ... experimental work in the future? That is, do you believe that this theoretical work has a value independent of experimental work or do you regard this theoretical work as an instrument designed to guide experimental work?’
Needless to say, Lewontin was brusque in his reply and equally disparaging of the implication that the mathematics was merely mental callisthenics. Thus, sceptical attitudes towards theoretical population genetics continued to prevail amongst the experimental biologists and the naturalist-systematist architects of the synthesis, with Mayr remaining unrelenting until the end of his life.14
Mayr felt that the beanbag represented the atomization of the genome, with individual genes being viewed as the target of natural selection, and he strongly objected to this view over one in which a cohesive genome or genotype with its corresponding phenotype was the unit of selection. This unit of selection problem (phenotype vs gene as the unit of natural selection) persisted into very recent times as Harvard holism vs British beanbag genetics15 with Stephen Jay Gould at Harvard pitted against Richard Dawkins in Oxford.
Despite all these assaults, the beanbag endures,16 with the formulation of better and more sophisticated theoretical population genetics models that include multiple interacting loci, thus making the transition from the classical models of Fisher, Wright and Haldane to more modern ones.17 Surely as long as evolutionary biologists need to explore the realms of the possible vs the actual, the beanbag will live on.
Conflict of interest: None declared.
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