Gene Frequency Changes and a Per-Generation Time-Scale for Continuous-Time Populations with Arbitrary Size Variations

One of the most fundamental calculations needed in an examination of the effect of natural selection in a Mendelian population is to find the rate of change in continuous-time of the frequency of any allele under natural selection, and from this to find the number of generations needed for the frequency of an allele to change from one given value to another. In this paper we analyze the presently accepted self-contained continuous-time theory of allele frequency change for large populations caused only by natural selection, which assumes no mutation and no gene frequency changes due to random genetic drift in a monoecious diploid population. We claim that the present theory is incomplete, with severe restrictions on how the population size varies over time, and with no natural generations concept built in. In order to remedy this we propose a new self-contained theory, making throughout the same assumptions described above concerning mutation and random genetic drift, and also assuming a monoecious diploid population.