Abstract
Estimating recent effective population size is of great importance in characterizing and predicting the evolution of natural populations. Methods based on nucleotide diversity may underestimate current day effective population sizes due to historical bottlenecks, whereas methods that reconstruct demographic history typically only detect long-term variations. However, soft selective sweeps, which leave a fingerprint of mutational history by recurrent mutations on independent haplotype backgrounds, holds promise of an estimate more representative of recent population history. Here, we present a simple and robust method of estimation based only on knowledge of the number of independent recurrent origins and the current frequency of the beneficial allele in a population sample, independent of the strength of selection and age of the mutation. Using a forward-time theoretical framework, we show the mean number of origins is a function of and current allele frequency, through a simple equation, and the distribution is approximately Poisson. This estimate is robust to whether mutants preexisted before selection arose and is equally accurate for diploid populations with incomplete dominance. For fast (e.g., seasonal) demographic changes compared with time scale for fixation of the mutant allele, and for moderate peak-to-trough ratios, we show our constant population size estimate can be used to bound the maximum and minimum population size. Applied to the Vgsc gene of Anopheles gambiae, we estimate an effective population size of roughly , and including seasonal demographic oscillations, a minimum effective population size >, and a maximum <, suggesting a mean .
Highlights
Having an accurate estimate of recent effective population size has impact on our ability to predict the outcomes of evolution, as the current population size controls the mutational input through the parameter h 1⁄4 2Nl and the fate of rare variants in a population via the population scaled strength of selection 2Ns (Kimura 1962)
Estimating the recent effective population size is of paramount importance to understanding and predicting the evolutionary dynamics of natural populations
As has been previously suggested (Karasov et al 2010), methods that estimate effective population size based on nucleotide diversity are likely to give estimates which are much smaller than the current day census size, as such metrics are dominated by historical population bottlenecks
Summary
Studying the differences in sequences between individuals in a population has the potential to give new insight into evolutionary processes: the evolutionary forces of selection, mutation, migration, and drift can leave a signature in the pattern and frequency of polymorphisms in time and space, which population genetic theory can be used to infer (Bollback et al 2008; Gutenkunst et al 2009; Liu and Fu 2015; Zanini et al 2015; Khatri 2016; Petkova et al 2016; Feder et al 2017). There is not a single well-defined measure of effective population size and different estimates will depend on the particular evolutionary pressures on the trait or genomic region under consideration, as well as on previous population histories (Charlesworth 2009). A common method to estimate effective population size is from the nucleotide diversity p of neutral regions of a genome, where for 2Nl ( 1, we expect p 1⁄4 2Nl (Charlesworth 2009). This relation represents a balance between mutations introducing variation at rate l and drift removing variation at rate 21N. There are currently no methods that and robustly allow estimation of very recent effective population sizes
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