COUNTERING INBREEDING WITH MIGRATION .1. MIGRATION FROM UNRELATED POPULATIONS

The effect of migration on inbreeding is modelled for small population s with immigrants from a large unrelated population. Different migrati on rates and numbers for the two sexes are assumed, and a general recu rsion equation for inbreeding progress derived, which can be shown to lead to an equilibrium inbreeding coefficient where the effects of gen etic drift and migration balance each other. For small migration rates and large numbers of breeding animals it is shown that migration of o nly the scarcer sex will minimize the equilibrium inbreeding. Migratio n from only one sex will also be an advantage in small populations wit h large migration rates. In small populations with large migration rat es fewer migrants are necessary for a given equilibrium inbreeding coe fficient than in large populations with small migration rates. Finally , an equation is derived for situations where the number of females is so large that their contribution to inbreeding can be ignored. Simple tables are given for the equilibrium inbreeding coefficients where th e number of migrants and herd sizes are taken into consideration. The general impression from these tables is that for equal numbers of the two sexes, the provision of 2-4 migrants to a population should stabil ize inbreeding. In populations with low male to female ratios, where o nly the inbreeding from the male side is important, one or two male mi grants should stabilize the inbreeding.