An interacting system in population genetics. II
J. Math. Kyoto Univ., 20 (4):
723--733 (1980)Abstract
Introduction
In th e previous paper 1 0 we studied a n interacting system in population
genetics, which is called a continuous time stepping stone m o d e l. L e t u s review
o u r m o d e l. L e t S b e a countable s e t . Each element i o f S is called a colony.
Assuming that there a re two alleles A a n d B at each colony, we denote by x
(1—x ) th e gene frequency o f th e A-allele (resp. the B-allele) f o r th e colony iE S.
We consider a time evolution o f gene frequencies, which is caused by migration
among colonies and random sampling drift.
L e t X -= 0 1 ' be the space of systems of gene frequencies, which is equipped
with th e product topology. L e t C(X ) be the Banach space o f all continuous func-
tions equipped with the suprem um norm and C (X ) be th e s e t o f all C -functions
depending only o n finite number o f coordinates o f X.
L e t u s consider th e following infinite dimensional differential operator A,