Characteristics of the variance effective population size over time using an age structured model with variable size

The variance effective population size (NeV) is a key concept in population biology, because it quantifies the microevolutionary process of random genetic drift, and understanding the characteristics of NeV is thus of central importance. Current formulas for NeV for populations with overlapping generations weight age classes according to their reproductive values (i.e. reflecting the contribution of genes from separate age classes to the population growth) to obtain a correct measure of genetic drift when computing the variance of the allele frequency change over time. In this paper, we examine the effect of applying different weights to the age classes using a novel analytical approach for exploring NeV. We consider a haploid organism with overlapping generations and populations of increasing, declining, or constant expected size and stochastic variation with respect to the number of individuals in the separate age classes. We define NeV, as a function of how the age classes are weighted, and of the span between the two points in time, when measuring allele frequency change. With this model, time profiles for NeV can be calculated for populations with various life histories and with fluctuations in life history composition, using different weighting schemes. We examine analytically and by simulations when NeV, using a weighting scheme with respect to reproductive contribution of separate age classes, accurately reflect the variance of the allele frequency change due to genetic drift over time. We show that the discrepancy of NeV, calculated with reproductive values as weights, compared to when individuals are weighted equally, tends to a constant when the time span between the two measurements increases. This constant is zero only for a population with a constant expected population size. Our results confirm that the effect of ignoring overlapping generations, when empirically assessing NeV from allele frequency shifts, gets smaller as the time interval between samples increases. Our model has empirical applications including assessment of (i) time intervals necessary to permit ignoring the effect of overlapping generations for NeV estimation by means of the temporal method, and (ii) effects of life table manipulation on NeV over varying time periods.