On the extremum principle of natural with inbreeding

Abstract

The extremum principle in the genetical theory of natural selection has been discussed when the population undergoes inbreeding at a constant value of the inbreeding coefficient with constant fitness of the three genotypes possible with two alleles at a given locus. The Fundamental Theorem of Natural Selection in such a case loses its predictive value in that the mean fitness of the population may decrease. This however can be restored by defining a new fitness function appropriately. It is shown that both the maximum as well as the minimum principles for such a mean fitness hold good in exactly the same manner as for true mean fitness in random mating populations incorporating dominance effects of genes. With no dominance, however, there is no need to invoke new mean fitness function and the optimality principle holds for an arbitrary mating system.