Rate of decrease of genetic variability in a subdivided population

SUMMARY The asymptotic rate of decline of heterozygosity in a linearly subdivided population, in which migration occurs only between adjacent colonies, is investigated. If we denote the number of colonies in the population by n, the number of diploid individuals in a single colony by N and the migration rate between adjacent colonies by m, the rate is approximately equal to (mlT2)/(2n2) when (mlT2)/(2n2) < 1/(2Nn). Thus for these cases the rate is proportional to migration rate but independent of colony size. When the inequality is reversed, the rate is approximately equal to 1/(2nN). Thus it is equal to the rate in a panmictic population of nN diploid individuals. Two methods of approximations for the eigenvector associated with the dominant eigenvalue are also discussed.