The Distribution of Gene Frequencies in Populations.

The effects of the various evolutionary factors-mutation, cross breeding,. selection and inbreeding-can be reduced to common terms by considering the rates of change which they tend to bring about in the relative frequencies of alleles.' In the absence of such factors, there is constancy of gene frequencies from the symmetry of the Mendelian mechanism. The frequency (q) of a given gene changes at the rate Aq = uq per generation under recurrent mutation of the gene to alleles at the rate u. Mutation in the opposite direction at the average rate v per generation changes the gene frequency at the rate, Aq = v(l q). If a certain gene has the frequency q in a local population but q1 in the species as a whole, exchange of the proportion m of the local population with an equal number of random individuals from the whole species leads to change of gene frequencies in the former at the rate Aq = -m(q q,). Cross breeding is, however, most likely to be with neighboring populations which differ but little in value of q. In this case the coefficient m is only a small fraction of the actual amount of exchange. There may be other complications such as selective immigration or emigration, but the above simple form will suffice here to illustrate cross breeding or migration pressure. The simplest kind of selection is that in which the heterozygote is exactly half way between the two homozygotes in the extent per individual to which it contributes to the next generation. The selective value of zygotes (relative to a certain standard) will be designated w and the mean value for a population, w.