Survival probabilities for some multitype branching processes in genetics.
Consider a positively regular, slightly supercritical branching process with K types. An approximation to the probability of survival of a line descended from a single individual of type i has recently been derived by Hoppe. If K is large, however, this approximation may not be easy to compute. A further approximation that is easily computable is given. The result is used to estimate probabilities of survival of an allele A that is originally present in one male or one female in a large, random mating, age-structured population. Both autosomal and sex-linked loci are considered. Another application of the approximation is also discussed.
Pollak
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Department of Statistics, Iowa State University, Ames, 50011.
D000483:Alleles; D000818:Animals; D005260:Female; D005828:Genetics, Population; D006801:Humans; D008297:Male; D009154:Mutation / Q000235:genetics*; D011336:Probability