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Ernst Mayr's Interactions with JBS Haldane

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Ernst Mayr's Interactions with JBS Haldane HPLS DOI 10.1007/s40656-016-0098-x NOTES AND COMMENTS Ernst Mayr’s interactions with J. B. S. Haldane 1 2,3 Veena Rao • Vidyanand Nanjundiah Received: 30 October 2015 / Accepted: 8 February 2016 Ó Springer International Publishing AG 2016 Abstract Ernst Mayr and J. B. S. Haldane, major contributors to the ‘modern synthesis’ in evolutionary theory, set an example of how scientific disagreements need not come in the way of friendship. After getting acquainted, they kept dis- cussing issues related to evolution until just before Haldane’s death in 1964. Their dissimilar backgrounds meant that they adopted different approaches. A major disagreement emerged regarding the right way to look at the role of genes in evolution. Mayr felt that the elementary models of population genetics were oversimplifications and therefore inadequate for representing evolutionary pro- cesses, though he was not consistent in his attitude. Haldane, on the other hand, maintained that the mathematical treatment of simple models had an important role to play. The Mayr-Haldane interactions illustrate divergent viewpoints concerning the utility of mathematics in biology. Keywords Population genetics Á Beanbag dispute Á Evolution Á Mathematical models & Veena Rao [email protected] Vidyanand Nanjundiah [email protected] 1 National Institute of Advanced Studies, Bangalore 560012, India 2 Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University, Marais Street, Stellenbosch 7600, South Africa 3 Centre for Human Genetics, Electronic City (Phase I), Bangalore 560100, India 123 V. Rao, V. Nanjundiah 1 Introduction Population genetics is a mathematical approach that aims at explaining biological evolution in terms of how evolutionary forces affect the distribution of genes and genotypes in populations. Natural selection, drift, some other evolutionary process, or combination of processes, provide its theoretical underpinnings. How gene and genotype frequencies vary in space (within populations) and time (over generations) has been a major concern of population genetics.1 The most elementary formulation, which continues to be taught to this day, involves a single locus, (usually) two alleles at each locus, a genetic system that operates according to Mendelian principles, a deterministic genotype-phenotype relationship and a fixed fitness associated with each phenotype. If allelic combinations at different loci influence the phenotype, and therefore fitness, but do so independently of one another, it is mathematically trivial to extend the one-locus two-allele formulation to several loci and two or more alleles at each locus.2 Simple as such models are, they have provided useful insights into several phenomena of evolutionary interest.3 Or have they? Among others, Ernst Mayr, one of the contributors to the Evolutionary Synthesis, famously thought not.4 In his view the models were not just simple, they were simplistic. He used the adjective ‘beanbag’ to lampoon models of Mendelian population genetics in which each gene locus was considered separately and independently: ‘The Mendelian was apt to compare the genetic contents of a population to a bag full of colored beans’.5 Mayr’s derisory characterisation was vigorously rebutted by his friend J. B. S. Haldane, a fellow contributor to the 1 See for example the standard texts by Li (1955) or Futuyma (2013). 2 Trivial in principle, that is. In practice, the combinatorial complexity increases rapidly with the number of loci; and, once recombination is considered, it becomes increasingly difficult to arrive at analytical solutions. 3 The classical books by Fisher (1930/1958/1999) and Haldane (1932/1990) are full of examples. Among them, one might cite the results that in the absence of natural selection, variation would be lost very slowly in large populations and relatively rapidly in small populations, that recurrent mutation can allow genes with deleterious effects to persist in stable equilibria and that ‘‘a selective advantage of the heterozygote over both homozygotes will preserve both of a pair of allelomorphs indefinitely’’ (Haldane 1953). Haldane (1953) goes on to say: ‘‘Such ideas as these pass rapidly from being mathematical theorems to being common sense. Other ideas with a superficial appeal to common sense, for example that dominants must oust recessives, appear to require mathematical disproof to prevent their spread’’, the last being a comment on what led to Hardy’s formulation of the celebrated Hardy–Weinberg principle (see Crow 1999). 4 Nor—eventually—did W. H. Provine, historian of population genetics. In contrast to the favourable stand he had taken previously, his opinion as expressed in the 2001 re-issue of The Origins of Theoretical Population Genetics was ‘‘Now I see these theoretical models of the early 1930s, still widely used today, as an impediment to understanding evolutionary biology…’’ (Provine 1971/2001). Regarding ‘‘Evolu- tionary—or ‘‘Modern’’—Synthesis’’, see Provine (1980). The appropriateness of the term, and whether a new synthesis is necessary, or even under way today, has been debated. 5 Mayr (1963, p. 263). The implied negative assessment was leavened with occasional positive statements. Earlier he had granted that beanbag genetics had made useful contributions, had been a ‘‘necessary step in the development of our thinking’’ and had ‘‘restored the prestige of natural selection’’ (Mayr 1959). But on the whole he seems to have thought that its contribution to evolutionary theory was questionable. 123 Ernst Mayr’s interactions with J. B. S. Haldane Synthesis, in a celebrated paper that he wrote just before he died.6 The beanbag genetics dispute has been discussed by several authors7; its crux had to do with whether elementary population genetics provided interesting insights into under- standing how evolution worked. Most recently, as part of a commentary in this journal dealing with Mayr’s recollections of his encounters with Haldane, Sarkar (2013; henceforth ‘‘SS’’) raises doubts regarding some statements made by us in the course of a discussion of the beanbag genetics dispute and its ramifications (Rao and Nanjundiah 2010/2011; henceforth ‘‘VR/VN’’). The doubts are sought to be supported by the inclusion in SS of the text of a typed manuscript that contains Mayr’s recollections of Haldane. The manuscript is stated to have been given by Mayr to Sarkar in 1992, 28 years after Haldane’s death.8 The extensive Haldane-Mayr exchanges constitute important material for students of the Evolutionary Synthesis. The present note extends what is contained in VR/VN regarding their interactions and reiterates the point that Mayr’s stance was inconsistent and at times unclear. We begin by addressing the three issues flagged in SS as important (p. 272 of SS). In order, they touch on (1) a mix-up involving the concept of ‘cost of natural selection’ (and ‘genetic load’), (2) the year of Fisher’s death and (3) a misattribution. (1) The alleged mix-up appears on page 249 of VR/VN. It goes ‘‘Haldane had advanced the notion that there would be a ‘cost’ of natural selection, also referred to as a ‘genetic load’ (H. J. Muller developed the concept independently).’’, and refers to Haldane’s 1957 paper (Haldane 1957). VR/ VN are said to have confused the substitutional load with the mutational load, and not to have noted either Haldane’s original formulation of the mutational load argument in 1937 or Muller’s independent development of it in 1950. Haldane (1957) does deal with the substitutional load and the statement pertaining to his and Muller’s formulations of the mutational load concept is valid. But the confusion is apparent, not real. The intention in VR/VN was neither to trace the history of the term ‘genetic load’ nor to distinguish between mutational and substitutional loads.9 Rather it was to draw attention, solely within the context, to the nature of the objection raised by Mayr to Haldane’s application of the concept of genetic (substitutional) load; an objection that, to be sure, was made with reference to Haldane’s 1957 paper. We were implicitly pointing out that irrespective of the source of the ‘load’, the essence of the argument remains unchanged. Namely, if each deleterious allele independently lowers the reproductive fitness of the individual that carries it, the difference in fitness between the maximally fit individual(s) and everyone else can cause the long-term geometric mean fitness of the population to become less than one. As a result, the population can go 6 Haldane (1964). 7 A list is provided in Rao and Nanjundiah (2010/2011), p. 236; also see Sarkar (2005, 2007, 2013). 8 According to SS ‘‘There is no explicit indication of why or when it was written’’. 9 For that matter, we have not tried to distinguish between them and other sources of genetic load either, e.g. the load due to recombination or segregation. 123 V. Rao, V. Nanjundiah extinct—unless individuals of maximal fitness have a sufficiently large number of offspring; in the worst-case, an intolerably large number. That constitutes the ‘load’.10 Mayr asserted that Haldane had overestimated the load, because it could be significantly smaller, in fact easily tolerable, if alleles at different loci did not act independently.11 The reasoning is as valid for mutational load as it is for substitutional load. (2) SS states that the year of Fisher’s death is given wrongly in VR/VN. That was a regrettable lapse caused by overlooking a misprint, and we appreciate it being drawn to our attention.12 (3) SS refers to a misattribution in VR/VN. Sarkar (2005) contains the sentence ‘‘He [meaning Mayr] once told me that the only contribution that the mathematical theory had made was to show that evolution by natural selection could take place in the time available for it during the history of life on Earth.’’ Going by ‘‘once’’, VR/VN took it that the words following ‘‘told me that’’ were Mayr’s.
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