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Sabin Lessard 《Journal of mathematical biology》2009,59(5):659-696
Diffusion approximations are ascertained from a two-time-scale argument in the case of a group-structured diploid population
with scaled viability parameters depending on the individual genotype and the group type at a single multi-allelic locus under
recurrent mutation, and applied to the case of random pairwise interactions within groups. The main step consists in proving
global and uniform convergence of the distribution of the group types in an infinite population in the absence of selection
and mutation, using a coalescent approach. An inclusive fitness formulation with coefficient of relatedness between a focal
individual J affecting the reproductive success of an individual I, defined as the expected fraction of genes in I that are identical by descent to one or more genes in J in a neutral infinite population, given that J is allozygous or autozygous, yields the correct selection drift functions. These are analogous to the selection drift functions
obtained with pure viability selection in a population with inbreeding. They give the changes of the allele frequencies in
an infinite population without mutation that correspond to the replicator equation with fitness matrix expressed as a linear
combination of a symmetric matrix for allozygous individuals and a rank-one matrix for autozygous individuals. In the case
of no inbreeding, the mean inclusive fitness is a strict Lyapunov function with respect to this deterministic dynamics. Connections
are made between dispersal with exact replacement (proportional dispersal), uniform dispersal, and local extinction and recolonization.
The timing of dispersal (before or after selection, before or after mating) is shown to have an effect on group competition
and the effective population size.
In memory of Sam Karlin. 相似文献