Search

Properties of identity relation between genes are discussed, and a derivation of recurrent equations of identity coefficients in a random mating, diploid dioecious population is presented. Computations are run by repeated matrix multiplication. Results show that for effective population size (Ne) larger than 16 and no mutation, a given identity coefficient at any time t can be expressed approximately as a function of (1—f), (1—f)3 and (1—f)6, where f is the mean inbreeding coefficient at time t. Tables are presented, for small Ne values and extreme sex ratios, showing the pattern of change in the identity coefficients over time. The pattern of evolution of identity coefficients is also presented and discussed with respect to N eu, where u is the mutation rate. Applications of these results to the evolution of genetic variability within and between inbred lines are discussed.

In a finite population with one locus and two alleles, selection, in the absence of overdominance, increases the probability of ultimate fixation of the favorable allele (fe). For any selection intensity (s) there is an initial gene frequency, X' below which f, is ail increasing function of the degree of dominance (h) and above which it is a decreasing function of h. X' is also an increasing function of the selection intensity. For overdominance (h > l)fi is less than in the case of no selection when the initial gene frequency is above a certain value X". The point X" is a decreasing function of h and an increasing function of the selection intensity. For both dominance and overdominance f, is a strictly increasing function of the initial gene frequency.