The choice of population size for animal breeding programmes depends on cost and management factors and on predictions of response to selection. In the short term these predictions can be based on parameters such as variances, covariances and effects of inbreeding which are estimable in the base population, but in the Jonger term less accessible measures are required, such as the joint distribution of effects and frequencies of both initially present and new mutant genes influencing the trait.
With dominance, inbreeding effects increase linearly with t/N, where t is generation number and N is effective population size. With the additive model of infinitessimal ggne effects, variance and response decline at first in proportion to (t/N) and increase through mutation in proportion to t Vm, where Vft0 and are the initial genetic variance and new variance per generation from mutation, respectively. Eventually response from mutation increases in proportion to NV . The larger the effect of genes on the trait, the earlier mutation in¥luences mean and variance of response.
Population size effects over the range N = 10 to 160 are generally trivial for 5 generations, but can become substantial after 10 generations. The breeder's time horizon has a major influence on choice of population size.

William G Hill

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume XII. Biotechnology, selection experiments, parameter estimation, design of breeding systems, management of genetic resources., , 245–256, 1986
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