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Haldane and Modern Evolutionary Genetics

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Haldane and Modern Evolutionary Genetics Journal of Genetics, Vol. 96, No. 5, November 2017, pp. 773–782 © Indian Academy of Sciences https://doi.org/10.1007/s12041-017-0833-4 HALDANE AT 125 Haldane and modern evolutionary genetics BRIAN CHARLESWORTH* Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, Charlotte Auerbach Rd., Edinburgh EH9 3FL, UK *E-mail: [email protected]. Published online 24 November 2017 Keywords. allele frequency; evolutionary genetics; Haldane’s rule; mutation; natural selection. Introduction of evolution which is well worth reading today. The After- word by Egbert Leigh to the 1990 Princeton University J. B. S. Haldane is renowned as one of the three ‘Found- Press edition of The causes of evolution provides an exten- ing Fathers’ of population genetics, mainly because of his sive discussion of Haldane’s work on population genetics series of papers on mathematical models of selection that up to 1932, and includes corrections of some mathematical were published in the 1920s and early 1930s. He also made errors (Haldane 1990). many other important contributions to genetics and to To some extent, this early work was anticipated by the other fields, especially biochemistry and physiology. The mathematician Harry Norton of Trinity College Cam- other two Founding Fathers also did important work out- bridge, who presented numerical results on the time taken side population genetics—R. A. Fisher in statistics and for the spread of a selectively advantageous mutation in an human genetics, and S. Wright in mammalian and develop- appendix to the book by R. C. Punnett on mimicry (Pun- mental genetics. Like Fisher, but unlike Wright, Haldane nett 1915), but never published the underlying derivations. was unusual among biologists in having had a sound train- Haldane was also a member of Trinity for some time in the ing in mathematics. He was one of the most erudite figures 1920s, and is said to have been stimulated to work on pop- of the twentieth century, and did not hesitate to display ulation genetics by conversations with Norton (Provine his wide knowledge in his numerous popular essays. He 1971). Norton’s then unpublished work on the theory of was also famous for his colourful and irascible personal- selection in an age-structured population (Norton 1928) ity as well as for his Marxism, which represented a (very was mentioned in Haldane’s 1927 paper on the same sub- understandable) revolt against the British upper classes ject (Haldane 1927a). Fisher had also previously treated into which he was born. In this essay, I will focus on his the theory of selection on a single autosomal locus in his main contributions to population genetics and evolution- 1922 paper, where the maintenance of variability by het- ary biology. This is not an exhaustive survey of Haldane’s erozygote superiority in fitness was described for the first work in this area; rather, I will examine topics that are still time (Fisher 1922). Since Haldane did not cite Fisher in his influential in contemporary research. I will discuss some first two papers, it seems clear that his work was indepen- more personal aspects at the end of this article. dent of Fisher’s—in contrast to Fisher, he always provided detailed citations of the literature in his papers. Haldane’s papers, again in contrast to Fisher’s, often included lengthy Gene frequency change caused by selection algebraic derivations. According to John Maynard Smith, Fisher was once heard to refer to ‘Allthat algebra that Jack Haldane pioneered the theoretical study of natural selec- seems to find necessary’. tion acting on Mendelian variants in a series of papers His first paper (Haldane 1924a) has been enormously starting in 1924. He summarized the main results in the influential. This described formulae for the time taken appendix to his 1932 book The causes of evolution (Hal- for selection to change the frequency of an advanta- dane 1932), a wonderfully clear account of genetic aspects geous allelic variantat a single locus, in large populations 773 774 Brian Charlesworth reproducing with discrete generations under a variety of The exception is the case of a completely recessive muta- genetic systems. These included asexual (haploid) inheri- tion in a randomly mating population. The extremely tance, random mating with autosomal diploid inheritance low frequency of homozygotes for a rare advantageous (including dominance or recessivity of the effect of the allele means that selection is ineffective. Haldane pointed mutation on fitness), and sex-linkage. This paper was out that this implies that mutations with beneficial effects followed by one dealing with the effects of partial inbreed- on their heterozygous carriers are much more likely con- ing, assortative mating and selective fertilization (Haldane tribute to evolution than completely recessive mutations, 1924b), and another concerning selection at a single locus consistent with the fact that the allele causing melanism with arbitrary dominance as well as selection on a pheno- is dominant. This principle has come to known as ‘Hal- type generated by a combination of alleles at multiple loci dane’s sieve’ (Turner 1977), and has stood up very well (Haldane 1927a). to later investigations of other cases of recent, human- As Haldane pointed out in the introduction to his first induced evolution, such as insecticide resistance, where paper ‘A satisfactory theory of natural selection must be mutations that affect the phenotype of their heterozygous quantitative. In order to establish the view that natural carriers seem to prevail (Bourguet and Raymond 1998), in selection is capable of accounting for the known facts contrast to the properties of most new mutations. of evolution we must show not only that it can cause a Haldane also pointed out that this sieve does not species to change, but that it can cause it to change at apply to populations that reproduce with some degree of a rate which will account for past and present transmuta- inbreeding, or to sex-linkage when advantageous muta- tions’. At first sight, it might seem that a new advantageous tions are expressed in the heterogametic sex. The latter mutation that is present in only one individual in a large observation was influential in the much later development population would need very many generations to spread of the theory of the ‘Faster-X effect’, in which a faster rate to a high frequency, possibly of the order of the popu- of adaptive evolution is predicted for the X (or Z) chromo- lation size. But Haldane showed that mutations spread some compared with the autosomes (Charlesworth et al. much more quickly, except for completely recessive auto- 1987; Meisel and Connallon 2013). The availability of data somal mutations in a randomly mating population. Since on DNA sequence data on within-species variability and exact solutions to the recursion relations can only be found between-species divergence has now permitted this predic- for some special cases (notably haploidy), Haldane mostly tion to be tested and (in some cases) verified (Meisel and used differential equations as approximations to the recur- Connallon 2013). Similarly, comparisons of inbreeding sion equations; these approximations are accurate when and outbreeding species suggest that recessive or partially selection is sufficiently weak. recessive selectively advantageous mutations are fixed at He showed that, with haploidy or with diploid auto- faster rates in inbreeders than outbreeders (Charlesworth somal inheritance and an dominant favourable allele, the 1992; Ronfort and Glémin 2013). time taken for an allele to spread between a given initial A weakness of this approach to predicting the efficacy and final frequency is only logarithmically dependent on of selection is that a new mutation occurs in the progeny the initial frequency of the allele (Haldane 1924a). It is of only a single individual. It is therefore extremely vulner- inversely proportional to the selection coefficient s,the able to chance loss, even if the population size is large and increase in fitness to carriers of the mutation, when fitness it has a substantial selective advantage; the deterministic is measured relative to the value for the initial popula- equations apply only when the number of individuals car- tion. For these cases, the time taken for an advantageous rying the mutation is sufficiently large that chance loss is allele to spread from a low to a high frequency is a rela- improbable. Fisher (1922) applied the method of branch- tively small multiple (of the order of 10) of 1/s, even if the ing processes to this problem for the case of a very large population size is very large. Selection can therefore trans- population with constant size, assuming a mutation that form the composition of a population over a period that increased fitness relative to wild type by an amount s.Hal- is very short compared with the geological timescale. He dane adopted Fisher’s approach (Haldane 1927b), and used his equation for a dominant autosomal allele to esti- used a Taylor series approximation to show that (with a mate the selective advantage of the famous melanic form Poisson distribution of offspring number), the probabil- of the peppered moth, Biston betularia, which increased ity of ultimate survival of a mutation is approximately 2s greatly in frequency in industrial areas of Britain dur- if selection is so weak that terms in s2 can be neglected. ing the nineteenth century. His estimate of s = 0.33, When the mutation is unconditionally advantageous, this based on observed changes in the frequency of the melanic is also the probability of fixation of the mutation. form, was in quite good agreement with later, direct esti- In 1930, Fisher applied the diffusion equation method to mates based on mark-recapture experiments (Cook 2003). populations of arbitrary size, and obtained the 2s formula These results did much to persuade biologists that nat- for fixation probability as the limiting value as popula- ural selection is a powerful mechanism of evolutionary tion size increases (Fisher 1930a).
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