COUNTERING INBREEDING WITH MIGRATION .2. MIGRATION FROM RELATED POPULATIONS

In conservation and breeding, large populations are important for evol utionary viability and selection progress. On the other hand, practica l and economic reasons may exist for population subdivision. These pop ulations (islands) may be tied together to form effectively a single p opulation (archipelago) by migration rates of acceptable magnitude. Th e acceptability of migration rates is judged by the maximum difference (1 - k) in inbreeding between a subpopulation, of size Ri, and a conc eptual 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 - k) is equal to 1/{4M( n + 1)/(n - 1) + 1}, where M = mN, the number of migrants in each subp opulation 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, 1/(4M + 1). T he recommendations for the limitation of inbreeding are, therefore, eq uivalent to the single island situation for a large number of subpopul ations, while a small number of subpopulations (n) requires less migra tion than a large number. For large migration rates and small subpopul ation sizes exact results are available. The general conclusion is tha t these situations require less migration for a given maximum differen ce (1 - k) than small rates and large population sizes. The rules for different male and female migration rates are the same as for migratio n from a large unrelated population (single island situation). Indeed, adjustment with a factor of (n - 1)/(n + 1) allows most conclusions o n number of migrants and maximum difference (1 - k) in inbreeding coef ficients to carry over from the single island to the archipelagic situ ation.