An Efficient Monte Carlo Method for Estimating Ne From Temporally Spaced Samples Using a Coalescent-Based Likelihood

Abstract

This article presents an efficient importance-sampling method for computing the likelihood of the effective size of a population under the coalescent model of Berthier et al . Previous computational approaches, using Markov chain Monte Carlo, required many minutes to several hours to analyze small data sets. The approach presented here is orders of magnitude faster and can provide an approximation to the likelihood curve, even for large data sets, in a matter of seconds. Additionally, confidence intervals on the estimated likelihood curve provide a useful estimate of the Monte Carlo error. Simulations show the importance sampling to be stable across a wide range of scenarios and show that the N e estimator itself performs well. Further simulations show that the 95% confidence intervals around the N e estimate are accurate. User-friendly software implementing the algorithm for Mac, Windows, and Unix/Linux is available for download. Applications of this computational framework to other problems are discussed. T HE effective size N e of a population is an importantWang (2001) developed a faster method for approximating the likelihood and conducted numerous simulaparameter determining the rate at which genetic drift and inbreeding occur in the population, as well as tions demonstrating the superiority of the likelihoodbased method over moment-based estimators. the population's capacity to respond to natural selection Berthier et al. (2002) introduced a likelihood method and to purge itself of deleterious mutations. It is confor two temporally spaced samples based on a different sequently a parameter of great interest. However, it is underlying model-they derive the likelihood using the difficult to estimate N e using demographic data alone, coalescent (Kingman 1982;Hudson 1990). This proespecially for organisms with high fecundity and high vides a computational advantage when a large number juvenile mortality. For this reason, a variety of methods of generations separate the samples. Additionally, it is have been developed for estimating N e from genetic easier to understand how this model applies to a condata, including the "temporal methods" in which a poptinuously reproducing population rather than the likeliulation's effective size is estimated using data on the hood models based on the discrete-generation Wrightchange of allele frequencies observed in two or more et al. 2002). Furpopulation model. They showed the likelihood-based ther, since the posterior density curves for N e are obestimator to be less biased than the moment-based estitained by performing density estimation on values of N e mators, but their formulation allowed only for the analygenerated from a Markov chain, it is difficult to assess sis of loci with two alleles. Anderson et al. (2000) extheir accuracy. tended that work to loci with more than two alleles, The purpose of this article is to present a more effiusing a computationally intensive Monte Carlo likeli-

Genetic Variation and Selection Response in Model Breeding Populations of Brassica rapa Following a Diversity Bottleneck

“…The maximum likelihood estimates of N e were determined by a coalescent-based model developed by Berthier et al (2002). Markov chain Monte Carlo was used to calculate the estimates and 95% confidence intervals for N e using the software CoNe (Anderson 2005).…”

Coalescent Inference Using Serially Sampled, High-Throughput Sequencing Data from Intrahost HIV Infection

“…There is now a sizeable literature on these and related approaches, focusing on various complications of the basic coalescent, depending on the species under study. For example, there are methods to account for recombination [MCMC (Kuhner et al 2000;Wang and Rannala 2008;Rasmussen et al 2014) and IS (Griffiths and Marjoram 1996;Fearnhead and Donnelly 2001;McVean et al 2002;Griffiths et al 2008;Jenkins and Griffiths 2011)], changing population size [MCMC (Beaumont 1999;Drummond et al 2002Drummond et al , 2005Wilson et al 2003;Minin et al 2008) and IS (Griffiths and Tavaré 1994a;Beaumont 2003;Leblois et al 2014)], and heterochronous sequence data [MCMC (Drummond et al 2002, 2005Minin et al 2008) and IS (Beaumont 2003;Anderson 2005;Fearnhead 2008)]. …”

Evaluation and Interpretation of Genetic Effective Population Size of Delta Smelt from 2011–2014

“…There are two basic methods for using genotype data to estimate N e : temporal methods and single-sample methods. Temporal methods use the mathematical relationship between N e and genetic drift to estimate N e (Kimura and Crow 1963;Nei and Tajima 1981;Lande and Barrowclough 1987;Crow and Denniston 1988;Waples 1989;Wang 2001;Anderson 2005), and require a population to be sampled twice, ideally with several intervening generations. Temporal methods estimate the variance in effective population size (N eV ) of the population during the intervening generations between the two sample points (see Waples 1989 and citations therein).…”