Optimization of gene-assisted selection in small-sized populations: comparison of deterministic and stochastic approaches.

Many of the models used to optimize selection processes in livestock make the assumption that the population is of infinite size and are built on deterministic equations. The finite size case should however be considered explicitly when selection involves one identified gene. Indeed, drift can cause the loss of a favorable allele if its initial frequency is low. In this paper, a stochastic approach was developed to simultaneously optimize selection on two traits in a limited size population: a quantitative trait with underlying polygenic variation and a monogenic trait. We outline the interests of considering the limited size of the population in stochastic modeling with a simple example. Such stochastic models raise some technical problems (uncertain convergence to the maximum, computational burden) which could obliterate their usefulness as compared to simpler but approximate deterministic models which can be used when the population size is large. By way of this simple example, we show the feasibility of the optimization of this type of model using a genetic algorithm and demonstrate its interest compared with the corresponding deterministic model which assumes that the population is of infinite size.