A Fast and Reliable Computational Method for Estimating Population Genetic Parameters
Vasco, Daniel A., Genetics
The estimation of ancestral and current effective population sizes in expanding populations is a fundamental problem in population genetics. Recently it has become possible to scan entire genomes of several individuals within a population. These genomic data sets can be used to estimate basic population parameters such as the effective population size and population growth rate. Full-data-likelihood methods potentially offer a powerful statistical framework for inferring population genetic parameters. However, for large data sets, computationally intensive methods based upon full-likelihood estimates may encounter difficulties. First, the computational method may be prohibitively slow or difficult to implement for large data. Second, estimation bias may markedly affect the accuracy and reliability of parameter estimates, as suggested from past work on coalescent methods. To address these problems, a fast and computationally efficient least-squares method for estimating population parameters from genomic data is presented here. Instead of modeling genomic data using a full likelihood, this new approach uses an analogous function, in which the full data are replaced with a vector of summary statistics. Furthermore, these least-squares estimators may show significantly less estimation bias for growth rate and genetic diversity than a corresponding maximum-likelihood estimator for the same coalescent process. The least-squares statistics also scale up to genome-sized data sets with many nucleotides and loci. These results demonstrate that least-squares statistics will likely prove useful for nonlinear parameter estimation when the underlying population genomic processes have complex evolutionary dynamics involving interactions between mutation, selection, demography, and recombination.
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THE estimation of ancestral and current effective population sizes in expanding populations is central to understanding the genetics of natural populations (CRANDALL et al. 1999). It is now possible to scan entire genomes of several individuals within a population (NIELSEN et al. 2005; SCHAFFNER et al. 2005; MCVEAN and SPENCER 2006). In this article I present a fast and reliable statistical method for estimating population parameters such as effective population size and growth rate using genomic data. Although the method is applicable to more complex population and selection models, I focus in this article on illustrating the method in a model of exponential population growth.
The problem of determining the parameters of a demographic expansion is a fundamental problem in population genetics theory and coalescents (AVISE 2000). Several article have appeared addressing this problem, ranging from methods based upon summary statistics (ROGERS and HARPENDING 1993) to those using the full data in a sample such as maximum-likelihood (ML) estimators (GRIFFITHS and TAVARÉ 1994; KUHNER et al. 1998). However, for large data sets and complex models, computationally intensivemethods may exhibit difficulties.
First, the methods may be prohibitively slow or difficult to implement on large data, especially when integrating the Felsenstein equation (STEPHENS 1999; HEY and NIELSEN 2007). This often involves analysis of the "mixing properties" of a complex Markov chain Monte Carlo (MCMC) algorithm-a technically difficult task (SISSON 2007). In previous work, VASCOET al. (2001) demonstrated the close relationship of summary-statisticsbased phylogenetic estimation methods to earlier coalescent methods (WATTERSON 1975; TAJIMA 1983, 1989; Fu 1995) as well as those based on full-likelihood approaches. They argued that instead of utilizing the full likelihood, an analogous function, determined by leastsquares (LS) fitting of the data, may be computed in which the full data are replaced by a vector of summary statistics. These are still standard methods that are widely used for coalescent data analysis across the subdisciplines of evolutionary genetics (AVISE 2000; EMERSON et al. …