Maximum-likelihood and markov chain monte carlo approaches to estimate inbreeding and effective size from allele frequency changes

MLNe: Simulating and Estimating Effective Size and Migration Rate from Temporal Changes in Allele Frequencies

In studies of molecular ecology, conservation biology and evolutionary biology, the current or recent effective size (Ne) of a population is frequently estimated from the marker genotype data of two or more temporally spaced samples of individuals taken from the population. Despite the developments of numerous Bayesian, likelihood and moment estimators, only a couple of them can use both temporally and spatially spaced samples of individuals to estimate jointly the effective size (Ne) of and the migration rate (m) into a population. In this note I describe new implementations of these joint estimators of Ne and m in software MLNe which runs on multiple platforms (Windows, Mac, Linux) with or without a graphical user interface (GUI), has an integrated simulation module to simulate genotype data for investigating the impacts of various factors (such as sample size and sampling interval) on estimation precision and accuracy, exploits both Message Passing Interface (MPI) and openMP for parallel computations using multiple cores and nodes to speed up analysis. The program does not require data pre-processing and accepts multiple formats of a file of original genotype data and a file of parameters as input. The GUI facilitates data and parameter inputs and produces publication-quality output graphs, while the non-GUI version of software is convenient for batch analysis of multiple datasets as in simulations. MLNe will help advance the analysis of temporal genetic marker data for estimating Ne of and m between populations, which are important parameters that will help biologists for the conservation management of natural and managed populations. MLNe can be downloaded free from the website http://www.zsl.org/science/research/software/.

Prediction and estimation of effective population size

Effective population size (Ne) is a key parameter in population genetics. It has important applications in evolutionary biology, conservation genetics and plant and animal breeding, because it measures the rates of genetic drift and inbreeding and affects the efficacy of systematic evolutionary forces, such as mutation, selection and migration. We review the developments in predictive equations and estimation methodologies of effective size. In the prediction part, we focus on the equations for populations with different modes of reproduction, for populations under selection for unlinked or linked loci and for the specific applications to conservation genetics. In the estimation part, we focus on methods developed for estimating the current or recent effective size from molecular marker or sequence data. We discuss some underdeveloped areas in predicting and estimating Ne for future research.

Estimation of effective population sizes from data on genetic markers

The effective population size (Ne) is an important parameter in ecology, evolutionary biology and conservation biology. It is, however, notoriously difficult to estimate, mainly because of the highly stochastic nature of the processes of inbreeding and genetic drift for which Ne is usually defined and measured, and because of the many factors (such as time and spatial scales, systematic forces) confounding such processes. Many methods have been developed in the past three decades to estimate the current, past and ancient effective population sizes using different information extracted from some genetic markers in a sample of individuals. This paper reviews the methodologies proposed for estimating Ne from genetic data using information on heterozygosity excess, linkage disequilibrium, temporal changes in allele frequency, and pattern and amount of genetic variation within and between populations. For each methodology, I describe mainly the logic and genetic model on which it is based, the data required and information used, the interpretation of the estimate obtained, some results from applications to simulated or empirical datasets and future developments that are needed.

An efficient Monte Carlo method for estimating Ne from temporally spaced samples using a coalescent-based likelihood

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.