A path integral formulation of the Wright–Fisher process with genic selection

Schraiber, Joshua G.

doi:10.1016/j.tpb.2013.11.002

Cited by 11 publications

(34 citation statements)

References 46 publications

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“…The key innovation of our method is to apply high-frequency path augmentation methods [Roberts and Stramer, 2001] to analyze genetic time series. The logic of the method is similar to the logic of a path integral, in which we average over all possible allele frequency trajectories that are consistent with the data [Schraiber, 2014]. By choosing a suitable reference probability distribution against which to compute likelihood ratios, we were able to adapt these methods to infer the age of alleles and properly account for variable population sizes through time.…”

Section: Discussionmentioning

confidence: 99%

Bayesian Inference of Natural Selection from Allele Frequency Time Series

Schraiber

Evans

Slatkin

2016

Preprint

125

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Abstract. The advent of accessible ancient DNA technology now allows the direct ascertainment of allele frequencies in ancestral populations, thereby enabling the use of allele frequency time series to detect and estimate natural selection. Such direct observations of allele frequency dynamics are expected to be more powerful than inferences made using patterns of linked neutral variation obtained from modern individuals. We developed a Bayesian method to make use of allele frequency time series data and infer the parameters of general diploid selection, along with allele age, in non-equilibrium populations. We introduce a novel path augmentation approach, in which we use Markov chain Monte Carlo to integrate over the space of allele frequency trajectories consistent with the observed data. Using simulations, we show that this approach has good power to estimate selection coefficients and allele age. Moreover, when applying our approach to data on horse coat color, we find that ignoring a relevant demographic history can significantly bias the results of inference. Our approach is made available in a C++ software package.

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Section: Discussionmentioning

confidence: 99%

Bayesian Inference of Natural Selection from Allele Frequency Time Series

Schraiber

Evans

Slatkin

2016

Preprint

125

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“…The logic of the method is similar to the logic of a path integral, in which we average over all possible allele frequency trajectories that are consistent with the data (Schraiber 2014). By choosing a suitable reference probability distribution against which to compute likelihood ratios, we were able to adapt these methods to infer the age of alleles and properly account for variable population sizes through time.…”

Section: Discussionmentioning

confidence: 99%

Bayesian Inference of Natural Selection from Allele Frequency Time Series

2016

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The advent of accessible ancient DNA technology now allows the direct ascertainment of allele frequencies in ancestral populations, thereby enabling the use of allele frequency time series to detect and estimate natural selection. Such direct observations of allele frequency dynamics are expected to be more powerful than inferences made using patterns of linked neutral variation obtained from modern individuals. We developed a Bayesian method to make use of allele frequency time series data and infer the parameters of general diploid selection, along with allele age, in nonequilibrium populations. We introduce a novel path augmentation approach, in which we use Markov chain Monte Carlo to integrate over the space of allele frequency trajectories consistent with the observed data. Using simulations, we show that this approach has good power to estimate selection coefficients and allele age. Moreover, when applying our approach to data on horse coat color, we find that ignoring a relevant demographic history can significantly bias the results of inference. Our approach is made available in a C++ software package.KEYWORDS Bayesian inference; diffusion theory; natural selection; path augmentation T HE ability to obtain high-quality genetic data from ancient samples is revolutionizing the way that we understand the evolutionary history of populations. One of the most powerful applications of ancient DNA (aDNA) is to study the action of natural selection. While methods making use of only modern DNA sequences have successfully identified loci evolving subject to natural selection (Nielsen et al. 2005;Voight et al. 2006;Pickrell et al. 2009), they are inherently limited because they look indirectly for selection, finding its signature in nearby neutral variation. In contrast, by sequencing ancient individuals, it is possible to directly track the change in allele frequency that is characteristic of the action of natural selection. This approach has been exploited recently, using whole-genome data to identify candidate loci under selection in European humans (Mathieson et al. 2015).To infer the action of natural selection rigorously, several methods have been developed to explicitly fit a population genetic model to a time series of allele frequencies obtained via aDNA. Initially, Bollback et al. (2008) extended an approach devised by Williamson and Slatkin (1999) to estimate the population-scaled selection coefficient, a ¼ 2N e s; along with the effective size, N e : To incorporate natural selection, Bollback et al. (2008) used the continuous diffusion approximation to the discrete Wright-Fisher model. This required them to use numerical techniques to solve the partial differential equation (PDE) associated with transition densities of the diffusion approximation to calculate the probabilities of the population allele frequencies at each time point. Ludwig et al. (2009) obtained an aDNA time series from six coatcolor-related loci in horses and applied the method of Bollback et al. (2008) to find that two of the...

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“…This approach was extended by Song and Steinrücken (2012) to improve the convergence properties for stronger selection, whereas Steinrücken et al (2016) developed it further to model selection coefficients that vary over time in a piecewise constant manner. The DAF was also calculated using a finite-difference scheme ( Bollback et al 2008 ), finite-volume scheme ( Zhao et al 2013 ), a path integral formalism ( Schraiber 2014 ) and other numerical approaches ( Malaspinas et al 2012 ; Ferrer-Admetlla et al 2016 ).…”

Section: B I-allelic W Right –Fmentioning

confidence: 99%

Statistical Inference in the Wright–Fisher Model Using Allele Frequency Data

Tataru¹,

Simonsen²,

Bataillon³

et al. 2016

Syst Biol

101

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The Wright–Fisher model provides an elegant mathematical framework for understanding allele frequency data. In particular, the model can be used to infer the demographic history of species and identify loci under selection. A crucial quantity for inference under the Wright–Fisher model is the distribution of allele frequencies (DAF). Despite the apparent simplicity of the model, the calculation of the DAF is challenging. We review and discuss strategies for approximating the DAF, and how these are used in methods that perform inference from allele frequency data. Various evolutionary forces can be incorporated in the Wright–Fisher model, and we consider these in turn. We begin our review with the basic bi-allelic Wright–Fisher model where random genetic drift is the only evolutionary force. We then consider mutation, migration, and selection. In particular, we compare diffusion-based and moment-based methods in terms of accuracy, computational efficiency, and analytical tractability. We conclude with a brief overview of the multi-allelic process with a general mutation model. [Allele frequency, diffusion, inference, moments, selection, Wright–Fisher.]

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A path integral formulation of the Wright–Fisher process with genic selection

Cited by 11 publications

References 46 publications

Bayesian Inference of Natural Selection from Allele Frequency Time Series

Bayesian Inference of Natural Selection from Allele Frequency Time Series

Bayesian Inference of Natural Selection from Allele Frequency Time Series

Statistical Inference in the Wright–Fisher Model Using Allele Frequency Data

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