Optimization of Mean Fitness of a Population via Artificial Selection

Abstract

The proposed control-theoretical model of artificial selection is based on the classical Fisher model of natural selection. Artificial selection is realized by changing the fitness of certain genotypes in a Mendelian population. Time-dependent fitness parameters are considered as control functions (artificial selection strategies). Under certain conditions on the model parameters the mean fitness of the population attains a maximum at the equilibrium of the selection dynamics. Thus the problem of optimization of the mean fitness via artificial selection is an optimal control problem. Using a sufficient condition for local controllability of nonlinear systems with invariant manifold, the existence of optimal artificial selection strategy is obtained.