In conservation and breeding, large populations are important for evolutionary viability and selection progress. On the other hand, practical and economic reasons may exist for population subdivision. These populations (islands) may be tied together to form effectively a single population (archipelago) by migration rates of acceptable magnitude. The acceptability of migration rates is judged by the maximum difference (1 â€“ k) in inbreeding between a subpopulation, of size N, and a conceptual aggregate random mating population of size Nn, with n equal to the number of subpopulations. For small migration rates (m) and large subpopulation sizes this maximum difference (1 â€“ k) is equal to 1114M(n + 1)/(n â€“ 1) + 11, where M = mN, the number of migrants in each subpopulation. For large n this result is equivalent to the standard result of the limit inbreeding coefficient of a subpopulation (single island) with migration from a very large noninbred population, 11(4M+ 1). The recommendations for the limitation of inbreeding are, therefore, equivalent to the single island situation for a large number of subpopulations, while a small number of subpopulations (n) requires less migration than a large number. For large migration rates and small subpopulation sizes exact results are available. The general conclusion is that these situations require less migration for a given maximum difference (1 â€“ k) than small rates and large population sizes. The rules for different male and female migration rates are the same as for migration from a large unrelated population (single island situation). Indeed, adjustment with a factor of (n â€“ 1)1(n + 1) allows most conclusions on number of migrants and maximum difference (1 â€“ k) in inbreeding coefficients to carry over from the single island to the archipelagic situation.
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