Haldane and the Emergence of Modern Evolutionary Theory 53a one locus model with random mating, Jennings extended his analysis to some
simple cases of this type; his results were presented by Warren [1917]. Thus, these
analyses of selection remained quite rudimentary though they were sufficient to
convince Warren that natural selection acting upon Mendelian factors was quite
sufficient to explain the type of adaptation that was the result of evolutionary
change.
The rudimentary state of the analysis of selection was due for rapid change with
the advent of Fisher, Wright, and Haldane. In 1918, Fisher published a long paper,
“The correlation between relatives on the supposition of Mendelian inheritance.”
In it, he systematically carried out a program that Pearson [1904] had perfunctorily
abandoned, namely, that of connecting biometry to Mendelism. Giving a far more
general analysis than Yule [1906], he showed that all the correlation coefficients
measured by Pearson and his collaborators could be systematically and correctly
predicted from a Mendelian basis.^8 He also showed that phenotypic traits which
depended on a large number of Mendelian factors, each with a tiny effect, would
have a normal distribution. This was precisely one of the generalizations that
the biometricians had made from their observations. Finally, Fisher showed that
the so-called “Law of Ancestral Heredity”, by which the biometricians expressed
the contribution of each preceding generation to a particular trait, could also be
derived from a variety of Mendelian models. If there still were any lingering doubt
that biometry and Mendelism were compatible, Fisher’s paper removed them. In
effect, Fisher had reduced biometrical theory to Mendelism.^9
In 1922, Fisher turned to the question whether natural selection and mutation
sufficed to explain the observed distributions of alleles (at a single locus) in a
population. He focused on the factors that maintained variability, being skeptical
of the suggestion by A. L. Hagedoorn and A. C. Hagedoorn-Vorstheuvel la Brand
[1921] that random survival, rather than selection or mutation, was the critical
factor in allele frequency changes. First, Fisher showed that, in the absence of
mutation and ignoring stochastic factors, a stable equilibrium between two alleles
is only reached if selection favors the heterozygote over the two homozygotes. This
was the first explanation of such polymorphism on the basis of what came to be
known as “heterosis”. Next, he calculated that, if the frequency of any allele is
very small, selection cannot prevent random extinction. He then assumed that
the alleles had achieved an equilibrium distribution. He calculated the shape of
this distribution if fortuitous extinction or various types of selection were balanced
by mutation. A low mutation rate sufficed to counteract extinction and maintain
genetic variability. With selection, a large mutation rate was necessary if the
variation in the population is to be maintained at the equilibrium levels.
Fisher also showed that strongly selected alleles would be rapidly fixed, leaving
as variable only alleles that were subject to weak selection. However, almost all
(^8) Many of these results had already been obtained by Weinberg [1909a,b; 1910], but in an age
when genetics was almost entirely the domain of the Anglophone world, Weinberg’s efforts were
ignored.
(^9) Sarkar [1998; 2004] discusses this reduction in detail.