When a character is determined by the coexistence of a number of genes, whether dominant or recessive, selection proceeds some what more slowly, but on the same general lines as above. Thus if a character is produced by m recessive genes, and carries a dis advantage measured by k, the proportion y„ of the population carrying it after n generations is given by eliminating s between where the values of a, depend on initial conditions.
Linkage between two selected genes is irrelevant, provided that the probability of crossing over between them is greater than k. An autotetraploid population mating at random is acted on by selection more slowly than a diploid.
It will be clear that in order to obtain any idea of the effect of selection on a relatively rare character in a population in which inbreeding is not intense, it is necessary to know its mode of in heritance. If it is a recessive, or determined by a number of dominant genes, selection, whether favourable or the reverse, will only cause slow changes in the number of individuals which mani fest it. On the other hand selection acts rapidly on rare dominants, and on all characters in a highly inbred population.
If a character while valuable to the community of which an individual is a member diminishes the probable number of off spring left by that individual (as is the case with some social in stincts) it will not spread through the population unless this con sists of small endogamous groups. If, however, as in social insects, most of the individuals are neuters, a socially valuable character, even though tending to shorten their lives, will, in general, spread. Similarly, except in insect societies, a socially disadvantageous character increasing the probable number of offspring left by its bearers will spread through the species.
Fisher investigated the equilibrium which would be reached in a population in which very numerous Mendelian differences existed, under the influence of mutation, random survival and selection. When a gene has great selective value it will rapidly spread all through a population if ever present in appreciable numbers. Thus genetic differences (and hence variation in natural populations), must mainly be due to genes of little sur vival value, or to those which are most beneficial in the hetero zygous condition. If u represents, as above, the ratio of dominant
to recessive genes in any character, then for a large number of different characters the distribution of z, u, is given by the expression di= I sech lzdz, f being the frequency for a 2'7r given value of z, no selection occurs, but mutation is balanced by random extinction. This is a symmetrical function of z, the most frequent value of u being unity. Even in the absence of mutation, the variability of a population is only diminished with extreme slowness by random extinction. In the more important case where the genes are dominants acted upon by selection, a balance is struck between the increase of variance by mutation and its diminution by selection and to a less extent by random z d extinction. Here dfcc , where k is a small quantity depending on the size of the population and the inten sity of selection. This is an asymmetrical function of z and the most frequent value of u is large, i.e., the variation in the popula tion is mainly due to more recessives. The observed values of correlations between relatives for continuously varying charac ters can be predicted with great accuracy if these characters are due to numerous genes whose distribution in the population is determined according to this law. Thus, while Haldane's work relates to the hitherto almost unobserved process of evolution, that of Fisher explains observed facts concerning heredity.
Roy. Soc., ed. 42, p. 321, 1922. (J. B. S. H.) Charles Darwin, after propounding the revolutionary and far reaching theory of natural selection (q.v.) to account for the evolu tionary origin of adaptive characters, set himself to see whether the conception was all-embracing. He came to the conclusion that the bulk of the large group of secondary sexual characters, such as the deer's antlers, the peacock's train, the lark's song, etc., could not be accounted for by the operation of natural selection, but that another type of selective mechanism, which he called sexual selection, here came into operation.