IDENTITY BY DESCENT IN ISLAND-MAINLAND POPULATIONS

A new model is presented for the genetic structure among a collection of island populations, with fluctuating population sizes and continuou s overlapping generations, using a stochastic birth, death and immigra tion (BDI) process. Immigrants enter each island from a large mainland population, with constant gene frequencies, according to a Poisson pr ocess. The average probability of identity by descent (IBD) for two ha ploid individuals randomly selected from an island population is f(0) = (phi f(1) + lambda)/(phi + lambda), where f(1) is the probability of IBD for two randomly selected immigrants, lambda is the birth-rate fo r each individual, and phi is the arrival rate of immigrants into each island. The value of f(0) is independent of the death process, time a nd N. The expected level of genetic differentiation among island popul ations is F-ST = (1 - 1/n)lambda/(phi + lambda), where n is the total number of islands receiving immigrants. Because f(0) and F-ST are inde pendent of the death process, for a BDI model, the population genetic structure for several general demographic situations may be examined u sing our equations. These include stochastic exponential, or logistic (regulated by death rate) growth within islands, or a ''source-sink'' population structure. Because the expected values of both f(0) and F-S T are independent of time, these are achieved immediately, for a BDI m odel, with no need to assume the island populations are at genetic equ ilibrium.