Genetic estimates of contemporary effective population size: to what time periods do the estimates apply?

Although most genetic estimates of contemporary effective population size (N-e) are based on models that assume N-e is constant, in real populations N-e changes (often dramatically) over time, and estimates (N-e) will be influenced by N-e in specific generations. In such cases, it is important to properly match N-e to the appropriate time periods (for example, in computing N-e/N ratios). Here I consider this problem for semelparous species with two life histories (discrete generations and variable age at maturity - the 'salmon' model), for two different sampling plans, and for estimators based on single samples (linkage disequilibrium, heterozygote excess) and two samples (temporal method). Results include the following. Discrete generations: (i) Temporal samples from generations 0 and t estimate the harmonic mean N-e in generations 0 through t - 1 but do not provide information about N-e in generation t; (ii) Single samples provide an estimate of N-e in the parental generation, not the generation sampled; (iii) single-sample and temporal estimates never provide information about N-e in exactly the same generations; (iv) Recent bottlenecks can downwardly bias estimates based on linkage disequilibrium for several generations. Salmon model: (i) A pair of single-cohort (typically juvenile) samples from years 0 and t provide a temporal estimate of the harmonic mean of the effective numbers of breeders in the two parental years (N-b(0) and N-b(t)), but adult samples are more difficult to interpret because they are influenced by N-b in a number of previous years; (ii) For single-cohort samples, both one-sample and temporal methods provide estimates of N-b in the same years (contrast with results for discrete generation model); (iii) Residual linkage disequilibrium associated with past population size will not affect single-sample estimates of N-b as much as in the discrete generation model because the disequilibrium diffuses among different years of breeders. These results lead to some general conclusions about genetic estimates of N-e in iteroparous species with overlapping generations and identify areas in need of further research.