Identity coefficients in finite populations. I. Evolution of identity coefficients in a random mating diploid dioecious population.

Abstract

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 Neu, where u is the mutation rate. Applications of these results to the evolution of genetic variability within and between inbred lines are discussed.