The limits to estimating population-genetic parameters with temporal data

The ability to obtain genome-wide sequences of very large numbers of individuals from natural populations raises questions about optimal sampling designs and the limits to extracting information on key population-genetic parameters from temporal-survey data. Methods are introduced for evaluating whether observed temporal fluctuations in allele frequencies are consistent with the hypothesis of random genetic drift, and expressions for the expected sampling variances for the relevant statistics are given in terms of sample sizes and numbers. Estimation methods and aspects of statistical reliability are also presented for the mean and temporal variance of selection coefficients. For nucleotide sites that pass the test of neutrality, the current effective population size can be estimated by a method of moments, and expressions for its sampling variance provide insight into the degree to which such methodology can yield meaningful results under alternative sampling schemes. Finally, some caveats are raised regarding the use of the temporal covariance of allele-frequency change to infer selection. Taken together, these results provide a statistical view of the limits to population-genetic inference in even the simplest case of a closed population.