Finite island model for organelle and nuclear genes in plants

Abstract

Recurrence equations for genetic diversities and differentiation were developed for hermaphrodite plant species in an island model of population structure. This was made possible by the definitions of diversities at all hierarchical levels from gamete to total population and by the definition of migration rates specific to plants for both nuclear and cytoplasmic genomes. Mating system was also incorporated. Numerical computations were used to compare equilibrium values of differentiation obtained with our equations with those predicted by classical formulas. We show that the differences (sometimes high) result from the interpretations of the definition of gene diversity in a population of finite size. We interpret it as the probability that two genes sampled with replacement are different alleles (instead of without replacement). The effects of several parameters (ploidy level, mode of inheritance, outcrossing rate, population size) on genetic subdivision were evaluated. Contrary to the situation in animals, plant migration is intrinsically asymmetrical because a gene transmitted to the next generation through the male gamete may migrate in the pollen grain and in the seed, whereas a gene transmitted through the female gamete can migrate only in the seed. As a consequence, mode of inheritance (in the case of cytoplasmic genes) and outcrossing rate have strong impacts on subdivision, especially when pollen migration is larger than seed migration (a likely situation in many plant species). Parameters estimated in a survey of oak populations (Quercus robur L.) were used to examine whether our understanding of a real situation could be improved by the model. In particular, the rate of return to equilibrium was studied after a perturbation, i.e. a temporary decrease of population sizes (a bottle-neck). © 1993 The Genetical Society of Great Britain.