Variance effective population size is affected by census size in sub-structured populations.

Abstract

Measurement of allele frequency shifts between temporally spaced samples has long been used for assessment of effective population size (Ne ), and this 'temporal method' provides estimates of Ne referred to as variance effective size (NeV ). We show that NeV of a local population that belongs to a sub-structured population (a metapopulation) is determined not only by genetic drift and migration rate (m), but also by the census size (Nc ). The realized NeV of a local population can either increase or decrease with increasing m, depending on the relationship between Ne and Nc in isolation. This is shown by explicit mathematical expressions for the factors affecting NeV derived for an island model of migration. We verify analytical results using high-resolution computer simulations, and show that the phenomenon is not restricted to the island model migration pattern. The effect of Nc on the realized NeV of a local subpopulation is most pronounced at high migration rates. We show that Nc only affects local NeV , whereas NeV for the metapopulation as a whole, inbreeding (NeI ), and linkage disequilibrium (NeLD ) effective size are all independent of Nc . Our results provide a possible explanation to the large variation of Ne /Nc ratios reported in the literature, where Ne is frequently estimated by NeV . They are also important for the interpretation of empirical Ne estimates in genetic management where local NeV is often used as a substitute for inbreeding effective size, and we suggest an increased focus on metapopulation NeV as a proxy for NeI .