Estimating Contemporary Effective Population Size on the Basis of Linkage Disequilibrium in the Face of Migration

Effective population size (N-e) is an important genetic parameter because of its relationship to loss of genetic variation, increases in inbreeding, accumulation of mutations, and effectiveness of selection. Like most other genetic approaches that estimate contemporary N-e, the method based on linkage disequilibrium (LD) assumes a closed population and (in the most common applications) randomly recombining loci. We used analytical and numerical methods to evaluate the absolute and relative consequences of two potential violations of the closed-population assumption: (1) mixture LD caused by occurrence of more than one gene pool, which would downwardly bias (N) over cap (e), and (2) reductions in drift LD (and hence upward bias in (N) over cap (e)) caused by an increase in the number of parents responsible for local samples. The LD method is surprisingly robust to equilibrium migration. Effects of mixture LD are small for all values of migration rate (m), and effects of additional parents are also small unless m is high in genetic terms. LD estimates of N-e therefore accurately reflect local (subpopulation) N-e unless m > similar to 5-10%. With higher m, (N) over cap (e) converges on the global (metapopulation) N-e. Two general exceptions were observed. First, equilibrium migration that is rare and hence episodic can occasionally lead to substantial mixture LD, especially when sample size is small. Second, nonequilibrium, pulse migration of strongly divergent individuals can also create strong mixture LD and depress estimates of local N-e. In both cases, assignment tests, Bayesian clustering, and other methods often will allow identification of recent immigrants that strongly influence results. In simulations involving equilibrium migration, the standard LD method performed better than a method designed to jointly estimate N-e and m. The above results assume loci are not physically linked; for tightly linked loci, the LD signal from past migration events can persist for many generations, with consequences for N-e estimates that remain to be evaluated.