an:03937776
Zbl 0585.45001
Lui, Roger
A nonlinear integral operator arising from a model in population genetics. III. Heterozygote inferior case
EN
SIAM J. Math. Anal. 16, 1180-1205 (1985).
00150043
1985
j
45G10 92D10 45M05
heterozygote inferior case; asymptotic behavior; recursion; discrete time population genetics model
[For parts I and II see ibid. 13, 913--937, 938--953 (1982; Zbl 0508.45006, Zbl 0508.45007)]. The author continues his series of papers concerning the asymptotic behavior of the solutions to the recursion \(u_{n+1}=Q[u_ n]\) for \(n\geq 0\). Here \(Q[u](x)=\int k(x-y)g(u(y))\,dy\), \(K(x)\geq 0\), \(\int K(x)\,dx=1\). This model proposed by \textit{H. F. Weinberger} [Lect. Notes Math. 648, 47--96 (1978; Zbl 0383.35034)] to describe the spread of advantageous genes, is similar to the model of \textit{R. A. Fisher} [The advance of advantageous genes, Ann. Eugenics 7, 355--369 (1937; JFM 63.1111.04)]. The gene fraction is given by \(g(u)=\frac{su^ 2+u}{1+su^ 2+\sigma (1-u)^ 2}\).
L. A. Sakhnovich
Zbl 0508.45007; Zbl 0508.45006; Zbl 0383.35034; JFM 63.1111.04