The Limits to Estimating Population-Genetic Parameters with Temporal Data

Abstract

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.

Keywords: effective population size; fluctuating selection; population genomics; selection coefficient.

Fig. 1.

—Sampling scheme for allele frequencies, with p_i denoting the parametric frequency in the population, ${\widehat{p}}_i$ denoting the estimated frequency after sampling n_i individuals, and ${\widehat{\Delta }}_{ij}$ denoting the interval-specific estimated change in frequency.

Fig. 2.

—(Left) Mean estimates of the selection coefficient s obtained from the least-squares regression approach. Each point is the average of the results from 10⁷ simulations based on Wright–Fisher allele-frequency dynamics incorporating selection and drift, followed by random sampling of n = 100 diploid individuals at each sampling point. Black symbols are for effective population size $N_e={10}^4$, and red for $N_e={10}^6$, and results are reported for a range of starting allele frequencies, p₀. The horizontal dashed lines denote the expectations for four evaluated selection coefficients (with temporal variance, ${\sigma }_s^2$, equal to zero), and the different symbols denote experiments of different durations (T). (Right) Sampling standard deviations for estimates of s for the case of ${\sigma }_s^2=0$, from simulations as noted above for three values of N_e, four of s, and a sample size of 100, compared with the theoretical expectation, equation (10). The diagonal dashed line denotes points of perfect agreement, and many symbols cannot be seen as they overlie each other on this line.

Fig. 3.

—Mean and CV of estimates of ${\sigma }_s^2$ for series of samples taken at T + 1 consecutive time points, each involving sample sizes of n = 100 or 1,000 diploid genomes. Results are given for a range of initial allele frequencies, each based on 10⁶ simulations with an effective population size of 10⁸ individuals, ensuring essentially no genetic drift on the time scale of the analyses, and mean selection coefficient ${\mu }_s=\mathrm{0.0.}$ Closed points refer to situations in which ${\sigma }_s^2={10}^{-3}$, whereas open points are for ${\sigma }_s^2={10}^{-4}.$ Data points are excluded for some cases at low allele frequencies where the mean estimates of ${\sigma }_s^2$ were negative.