Calculating Ne and Ne/N in age-structured populations: a hybrid Felsenstein-Hill approach

The concept of effective population size (N-e) was developed under a discrete-generation model, but most species have overlapping generations. In the early 1970s, J. Felsenstein and W. G. Hill independently developed methods for calculating N-e in age-structured populations; the two approaches produce the same answer under certain conditions and have contrasting advantages and disadvantages. Here, we describe a hybrid approach that combines useful features of both. Like Felsenstein's model, the new method is based on age-specific survival and fertility rates and therefore can be directly applied to any species for which life table data are available. Like Hill, we relax the restrictive assumption in Felsenstein's model regarding random variance in reproductive success, which allows more general application. The basic principle underlying the new method is that age structure stratifies a population into winners and losers in the game of life: individuals that live longer have more opportunities to reproduce and therefore have a higher mean lifetime reproductive success. This creates different classes of individuals within the population, and grouping individuals by age at death provides a simple means of calculating lifetime variance in reproductive success of a newborn cohort. The new method has the following features: (1) it can accommodate unequal sex ratio and sex-specific vital rates and overdispersed variance in reproductive success; (2) it can calculate effective size in species that change sex during their lifetime; (3) it can calculate N-e and the ratio N-e/N based on various ways of defining N; (4) it allows one to explore the relationship between N-e and the effective number of breeders per year (N-b), which is a quantity that genetic estimators of contemporary N-e commonly provide information about; and (5) it is implemented in freely available software (AgeNe).