Monte Carlo Evaluation of the Likelihood for Ne From Temporally Spaced Samples

Abstract

A population’s effective size is an important quantity for conservation and management. The effective size may be estimated from the change of allele frequencies observed in temporally spaced genetic samples taken from the population. Though moment-based estimators exist, recently Williamson and Slatkin demonstrated the advantages of a maximum-likelihood approach that they applied to data on diallelic genetic markers. Their computational methods, however, do not extend to data on multiallelic markers, because in such cases exact evaluation of the likelihood is impossible, requiring an intractable sum over latent variables. We present a Monte Carlo approach to compute the likelihood with data on multiallelic markers. So as to be computationally efficient, our approach relies on an importance-sampling distribution constructed by a forward-backward method. We describe the Monte Carlo formulation and the importance-sampling function and then demonstrate their use on both simulated and real datasets.

WFABC: a Wright–Fisher ABC‐based approach for inferring effective population sizes and selection coefficients from time‐sampled data

“…Moment--based methods (Kimura and Crow 1963; Pamilo and Varvio--Aho 1980; Nei and Tajima 1981; Waples 1989; Jorde and Ryman 2007) have been proposed utilizing the variance of gene frequency changes to infer effective population size (Ne). In addition, likelihood--based methods (Williamson and Slatkin 1999;Anderson et al 2000;Berthier et al 2002;Anderson 2005) have been proposed to calculate the probability of a given data observation given a pre--defined model. Efforts to incorporate selection into these estimation procedures have only recently begun, and given the rapidly increasing availability of such sequencing datasets, we now have a unique opportunity to re--address the puzzle of distinguishing genetic drift from selection with greater precision and power.…”

A brief history and popularity of methods and tools used to estimate micro-evolutionary forces

“…The r-PaCkage nD (Hui & Burt, 2015) overcomes some of these limitations (to the applicable population sizes) by using a hidden Markov model to reduce computational load and raise the upper bounds (of N E ) to several million individuals. MCLeePs (Anderson et al, 2000) implicitly involves a Markov Chain and uses a Monte Carlo algorithm to overcome the computationally intensive nature of generating probability distributions for the effective population size. Despite the complexities involved, the temporal method makes fewer assumptions and is considered more robust for real populations (Wang et al, 2016).…”

MLNe: Simulating and estimating effective size and migration rate from temporal changes in allele frequencies

“…The methods were subsequently further developed by many others (e.g. Nei and Tajima 1981;Pollak 1983;Waples 1989), and were extended to use more powerful statistical techniques such as likelihood or Bayesian methods (Williamson and Slatkin 1999;Anderson et al 2000;Wang 2001;Berthier et al 2002;Beaumont 2003;Laval et al 2003;Hui and Burt 2015). These sophisticated methods are more flexible (e.g.…”