On the theory of partially inbreeding finite populations. II. Partial sib mating.
It is assumed that a population has M males in every generation, each of which is permanently mated with c-1 females, and that a proportion beta of matings are between males and their full sisters or half-sisters. Recurrence equations are derived for the inbreeding coefficient of one random individual, coefficients of kinship of random pairs of mates and probabilities of allelic identity when the infinite alleles model holds. If Ft is the inbreeding coefficient at time t and M is large, (1-Ft)/(1-Ft-1)----1-1/(2Ne) as t increases. The effective population number Ne = aM/[1 + (2a-1)FIS], where FIS is the inbreeding coefficient at equilibrium when M is infinite and the constant a depends upon the conditional probabilities of matings between full sibs and the two possible types of half-sibs. When there are M permanent couples, an approximation to the probability that an allele A survives if it is originally present in one AA heterozygote is proportional to FISs1 + (1-FIS)s2, where s1 and s2 are the selective advantages of AA and AA in comparison with AA. The paper concludes with a comparison between the results when there is partial selfing, partial full sib mating (c = 2) and partial sib mating when c is large.
Pollak
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Department of Statistics, Iowa State University, Ames 50011.
D000483:Alleles; D000818:Animals; D003241:Consanguinity; D003433:Crosses, Genetic; D005260:Female; D005828:Genetics, Population; D006801:Humans; D007178:Inbreeding; D008297:Male; D008957:Models, Genetic; D015233:Models, Statistical; D011336:Probability