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

Measurement of allele frequency shifts between temporally spaced samples has long been used for assessment of effective population size (N e ), and this 'temporal method' provides estimates of N e referred to as variance effective size (N eV ). We show that N eV 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 (N c ). The realized N eV of a local population can either increase or decrease with increasing m, depending on the relationship between N e and N c in isolation. This is shown by explicit mathematical expressions for the factors affecting N eV 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 N c on the realized N eV of a local subpopulation is most pronounced at high migration rates. We show that N c only affects local N eV , whereas N eV for the metapopulation as a whole, inbreeding (N eI ), and linkage disequilibrium (N eLD ) effective size are all independent of N c . Our results provide a possible explanation to the large variation of N e /N c ratios reported in the literature, where N e is frequently estimated by N eV . They are also important for the interpretation of empirical N e estimates in genetic management where local N eV is often used as a substitute for inbreeding effective size, and we suggest an increased focus on metapopulation N eV as a proxy for N eI .