Estimating effective population size from temporal allele frequency changes in experimental evolution

Abstract

The effective population size (N e ) is a major factor determining allele frequency changes in natural and experimental populations. Temporal methods provide a powerful and simple approach to estimate short-term N e : They use allele frequency shifts between temporal samples to calculate the standardized variance, which is directly related to N e : Here we focus on experimental evolution studies that often rely on repeated sequencing of samples in pools (Pool-seq). Pool-seq is cost-effective and often outperforms individual-based sequencing in estimating allele frequencies, but it is associated with atypical sampling properties: Additional to sampling individuals, sequencing DNA in pools leads to a second round of sampling, which increases the variance of allele frequency estimates. We propose a new estimator of N e ; which relies on allele frequency changes in temporal data and corrects for the variance in both sampling steps. In simulations, we obtain accurate N e estimates, as long as the drift variance is not too small compared to the sampling and sequencing variance. In addition to genome-wide N e estimates, we extend our method using a recursive partitioning approach to estimate N e locally along the chromosome. Since the type I error is controlled, our method permits the identification of genomic regions that differ significantly in their N e estimates. We present an application to Pool-seq data from experimental evolution with Drosophila and provide recommendations for whole-genome data. The estimator is computationally efficient and available as an R package at https://github.com/ThomasTaus/Nest. KEYWORDS effective population size; genetic drift; Pool-seq; experimental evolution D URING experimental evolution studies, populations are maintained under specific laboratory conditions (Kawecki et al. 2012;Long et al. 2015;Schlötterer et al. 2015). In sexually reproducing organisms, the census population size is typically kept fixed at fairly low numbers, rarely exceeding 2000 individuals. With such small population sizes, genetic drift causes stochastic fluctuations in allele frequencies. Under neutrality, the level of random frequency changes is determined by the effective population size (N e ) (Wright 1931). Furthermore, the efficacy of selection is influenced by N e : For weakly selected alleles, the probability of fixation is directly proportional to the product of N e and the intensity of selection (Fisher 1930;Kimura 1964). As changes in allele frequency are greatly affected by the population size, it is fundamental to estimate N e accurately to understand molecular variation in experimental evolution studies. Krimbas and Tsakas (1971) estimated N e using the standardized variance of allele frequency (F, see also Falconer and Mackay 1996) from longitudinal samples in natural populations of olive flies. As F was calculated from these samples, they accounted for the sampling variance that also contributed to the true allele frequency variance. This approach was further improved and used by sev...

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“…However, neither of these estimators explicitly addresses the variance component arising due to pooled sequencing (Jónás et al. ). Each of the estimates derived assumed N = 5000 and excluded SNPs with minor allele frequency <0.04.…”

“…This is plausible where the number of generations between estimates is small—as was the case for these trials—and actual N e is relatively large, such that drift has not yet had a significant effect on allele frequencies (Jónás et al. ).…”

“…Although the Jorde and Ryman () method gave smaller estimates, simulations performed with pooled sequencing data by Jónás et al. () found that this method had a downward bias, particularly for allele frequency estimates made only a few generations apart, due to additional sampling variance.…”

“…Sync files were read using the read.sync function from the Nest package (Jónás et al 2016) in R. Estimates of N e were then produced using the estimateNe function from the Nest package with arguments of 't = 22, ploidy = 2, truncAF = 0.04, method = c("P.planI", "JR.planI", "W.planI"), Ncensus = 5000, poolSize = c(152,152)' for allele frequency estimates over the April to November time interval, or 't = 11' for either the April to July or July to November intervals.…”

Do estimates of contemporary effective population size tell us what we want to know?

“…A large number of approaches and computer programs are available for estimating effective size from genetic marker data (reviews by e.g., Gilbert & Whitlock, ; Luikart et al, ; Palstra & Ruzzante, ; Wang, ,). Until recently, most studies were based on the “temporal method” that compares allele frequencies in samples collected one or more generations apart to assess variance effective size ( N eV ; e.g., Jónás, Taus, Kosiol, Schlötterer, & Futschik, ; Jorde & Ryman, ,; Nei & Tajima, ; Wang & Whitlock, ; Waples, ). During the past decade, however, estimation procedures that only require a single sample, collected at one point in time, have become prevailing (Palstra & Fraser, ; Waples, ).…”