Kin selection is implicated in partial sib-mating populations with constant viability differences before mating.
The change in the frequency of a rare mutant allele under constant sex-differentiated viability selection in an infinite, partial full-sib mating population is studied. The diplo-diploid and haplo-diploid polygynous models are considered with a Poisson distribution for the number of offspring produced by every mated female. Reproduction is followed by weak selection among the offspring and then mating to form the next generation. It is shown that the rate of change with respect to the frequency of the mutant allele and the intensity of selection can be expressed in terms of costs or benefits of substituting the mutant type for the wild type, which correspond to average excesses in viability in females and males, multiplied by coefficients of relatedness to the individuals affected by such a substitution and reproductive values associated to the sexes of these individuals. This reveals hidden interactions between mated individuals and between males for mating, the former having positive effects on the reproductive success of related individuals and the latter having negative effects. Such interactions are the result of reproductive constraints when a fixed proportion of females must mate with a male sib and all females are fertilized as long as one mate is available. However, they affect the change in allele frequency because there is inbreeding or relatedness between mates and more generally relatedness between interacting individuals. Surprisingly, the effects of these interactions cancel out in a diploid population when the number of offspring is large enough so that the possibility for a female to have no male sib to mate with can be neglected and the viability differences are the same in both sexes.
Lessard
Sabin
S
Département de Mathématiques et de Statistique, Université de Montréal, Montreal, Quebec H3C 3J7, Canada. lessards@dms.umontreal.ca
D000465:Algorithms; D000483:Alleles; D000818:Animals; D005260:Female; D005787:Gene Frequency; D005828:Genetics, Population; D007178:Inbreeding; D008297:Male; D008957:Models, Genetic; D009154:Mutation; D012098:Reproduction / Q000235:genetics; D012641:Selection, Genetic