Rates of decay for the survival probability of a mutant gene.
If qk is the extinction probability of a slightly supercritical branching process with offspring distribution [pkr:r = 0, 1, 2, ...], then it is shown that if supk sigma r r3pkr less than infinity, inf sigma 2k greater than 0, and mk----1, then 1-qk approximately 2(mk - 1)sigma -2k, where mk = sigma r rpkr, sigma 2k = k sigma r r2pkr - m2k. This provides a simple set of sufficient conditions for the validity of a conjecture of Ewens (1969) for the survival probability of a slightly advantageous mutant gene.
Athreya
K B
KB
Iowa State University, Ames 50011.
D005787:Gene Frequency / Q000235:genetics; D005796:Genes / Q000235:genetics; D008433:Mathematics; D008957:Models, Genetic; D009154:Mutation / Q000235:genetics*; D011336:Probability; D012641:Selection, Genetic