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 .