Using Maximum Likelihood to Estimate Population Size From Temporal Changes in Allele Frequencies

Williamson, E. G.; Slatkin, Montgomery

doi:10.1093/genetics/152.2.755

Cited by 126 publications

(19 citation statements)

References 20 publications

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“…In addition to the deviation of the LRS distribution from the χ 2 distribution, the most likely population size under the null hypothesis, Ň , systematically overestimates the true population size, N , especially when the number of data points is small (see Tables 1 and S1). This phenomenon is consistent with previous reports (WAPLES, 1989;WILLIAMSON and SLATKIN, 1999;WANG, 2001). The bias in the inferred population size decreases with increasing number of data points, almost independently of the true population size or the observation time (see Figure S2).…”

Section: Likelihood Of Time-series Data and The Likelihood Ratio Stat...supporting

confidence: 92%

“…There is a well-developed literature on inferring population sizes from genetic time-series data assuming neutrality (POL-LAK, 1983;WAPLES, 1989;WILLIAMSON and SLATKIN, 1999;WANG, 2001) and a rapidly growing literature on inferring natural selection from such time series (BOLLBACK et al, 2008;ILLINGWORTH and MUSTONEN, 2011;ILLINGWORTH et al, 2012;MALASPINAS et al, 2012;MATHIESON and MCVEAN, 2013). However, even the simplest case -the dynamics of two alternative alleles at a single genetic locus independent of all other loci -presents a number of statistical challenges that have not been resolved.…”

Section: Introductionmentioning

confidence: 99%

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Identifying Signatures of Selection in Genetic Time Series

Feder,

Kryazhimskiy,

Plotkin

2013

Preprint

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Both genetic drift and natural selection cause the frequencies of alleles in a population to vary over time.Discriminating between these two evolutionary forces, based on a time series of samples from a population, remains an outstanding problem with increasing relevance to modern data sets. Even in the idealized situation when the sampled locus is independent of all other loci this problem is difficult to solve, especially when the size of the population from which the samples are drawn is unknown. A standard χ 2 -based likelihood ratio test was previously proposed to address this problem. Here we show that the χ 2 test of selection substantially underestimates the probability of Type I error, leading to more false positives than indicated by its P -value, especially at stringent P -values. We introduce two methods to correct this bias. The empirical likelihood ratio test (ELRT) rejects neutrality when the likelihood ratio statistic falls in the tail of the empirical distribution obtained under the most likely neutral population size. The frequency increment test (FIT) rejects neutrality if the distribution of normalized allele frequency increments exhibits a mean that deviates significantly from zero. We characterize the statistical power of these two tests for selection, and we apply them to three experimental data sets. We demonstrate that both ELRT and FIT have power to detect selection in practical parameter regimes, such as those encountered in microbial evolution experiments. Our analysis applies to a single diallelic locus, assumed independent of all other loci, which is most relevant to full-genome selection scans in sexual organisms, and also to evolution experiments in asexual organisms as long as clonal interference is weak. Different techniques will be required to detect selection in time series of co-segregating linked loci.

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Section: Likelihood Of Time-series Data and The Likelihood Ratio Stat...supporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Identifying Signatures of Selection in Genetic Time Series

Feder,

Kryazhimskiy,

Plotkin

2013

Preprint

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“…An alternative approach to estimating local density is to measure the rate of genetic drift in an area. To do this, one compares allele frequencies in at least two samples collected in a region in different generations, either at different points in time, or, in a species with overlapping generations, between contemporaneous individuals of different life stages, e.g., saplings and mature trees (Williamson & Slatkin, 1999). The rate of drift is governed by, and therefore provides an estimate of, local population size; this is analogous to the variance effective size of a population (Ewens, 2004, Charlesworth, 2009, Wang et al, 2016.…”

Section: Population Densitymentioning

confidence: 99%

Spatial Population Genetics: It's About Time

Bradburd

Ralph

2019

Annu. Rev. Ecol. Evol. Syst.

112

123

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Many questions that we have about the history and dynamics of organisms have a geographical component: How many are there, and where do they live? How do they move and interbreed across the landscape? How were they moving a thousand years ago, and where were the ancestors of a particular individual alive today? Answers to these questions can have profound consequences for our understanding of history, ecology, and the evolutionary process. In this review, we discuss how geographic aspects of the distribution, movement, and reproduction of organisms are reflected in their pedigree across space and time. Because the structure of the pedigree is what determines patterns of relatedness in modern genetic variation, our aim is to thus provide intuition for how these processes leave an imprint in genetic data. We also highlight some current methods and gaps in the statistical toolbox of spatial population genetics.

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“…For short evolutionary timescales, a discrete-time Wright-Fisher model of random mating is often used to describe the dynamics of the population allele frequency in the underlying HMM. This approach has been used to estimate the effective population size from temporal allele frequency variation, assuming a neutral model of evolution [Williamson and Slatkin (1999)]. More recently, temporal and spatial variations of advantageous alleles have been investigated through an HMM framework that can incorporate migration between multiple subpopulations [Mathieson and McVean (2013)].…”

mentioning

confidence: 99%

A novel spectral method for inferring general diploid selection from time series genetic data

Steinrücken¹,

Bhaskar²,

Song³

2014

Ann. Appl. Stat.

175

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The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated fitness parameters. However, it is a challenging problem to compute the likelihood of non-neutral models for the population allele frequency dynamics, given the observed temporal DNA data. Here, we develop a novel spectral algorithm to analytically and efficiently integrate over all possible frequency trajectories between consecutive time points. This advance circumvents the limitations of existing methods which require fine-tuning the discretization of the population allele frequency space when numerically approximating requisite integrals. Furthermore, our method is flexible enough to handle general diploid models of selection where the heterozygote and homozygote fitness parameters can take any values, while previous methods focused on only a few restricted models of selection. We demonstrate the utility of our method on simulated data and also apply it to analyze ancient DNA data from genetic loci associated with coat coloration in horses. In contrast to previous studies, our exploration of the full fitness parameter space reveals that a heterozygote-advantage form of balancing selection may have been acting on these loci.

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Using Maximum Likelihood to Estimate Population Size From Temporal Changes in Allele Frequencies

Cited by 126 publications

References 20 publications

Identifying Signatures of Selection in Genetic Time Series

Identifying Signatures of Selection in Genetic Time Series

Spatial Population Genetics: It's About Time

A novel spectral method for inferring general diploid selection from time series genetic data

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