Predicting the annual effective size of livestock populations

Abstract

Effective population size (N_e) is an important parameter determining the genetic structure of small populations. In natural populations, the number of adults (N) is usually known and N_e can be estimated on the basis of an assumed ratio N_e/N, usually found to be close to 0·5. In farm animal populations, apart from using pedigrees or genetic marker information, N_e can be estimated from the number N of breeding animals, and a value of 1 is commonly assumed for the ratio N_e/N. The purpose of this paper is to show the relation between effective population size and breeding herd size in livestock species. With overlapping generations, N_e can be predicted knowing the number of individuals entering the population per generation and the variance of family size, the latter being directly related to the survival pattern (or replacement policy) in the breeding herd. Assuming an ideal survivorship leading to a geometric age distribution, it can be shown that the number of breeding animals tends to overestimate effective size, particularly in early-maturing species. The ratio of annual effective size to the number of breeding animals is shown to be equal to [1+(a−1)(1−s)]²/(1−s²), where a is the age at first offspring and s is the survival rate (including culling) of the parents between successive births. This expression shows to what extent inbreeding may be determined by demography or culling policy independently of the actual herd size. In many situations a fast replacement or an early culling will increase annual effective size. Consequences for the management of small populations are discussed.