OPTIMAL CONTROL OF GENETIC DIVERSITY IN THE MORAN MODEL WITH POPULATION GROWTH

Abstract

In the Moran model of drift and selection of a mutant allele with population growth, instead of examining the consequences of pre-specified selection and population growth, the coexistence of the wild allele and the mutant allele becomes the maximization of the expected sojourn time in a given set. The process is controlled by the additional mortality of the mutant and by population growth. This makes it possible to retroactively assign fitness values as functions of the constraints, thus guiding a conservation policy or the achievement of a wishful proportion of mutants. This also gives the optimal conditions that have allowed an observed coexistence.