Inference under a Wright-Fisher model using an accurate beta approximation

Tataru, Paula; Bataillon, Thomas; Hobolth, Asger

doi:10.1101/021261

“…It is built upon combining a Hidden Markov Modeling approach, first proposed by Bollback et al (2008) in the context of genetic time series and parametric approximations to the Wright Fisher process. Within this framework we have shown that using the Beta-with-spikes distribution proposed by Tataru et al (2015) to approximate the Wright Fisher transitions provided a statistical inference comparable to that of the Wright-Fisher model while having a computational cost that does not depend on population size. We have shown this framework allows to perform hypothesis testing by relying on the asymptotic distribution of the Likelihood Ratio Statistic and that the maximum likelihood estimate of the selection intensity parameter had generally good statistical properties.…”

Section: Discussionmentioning

confidence: 97%

“…Using this class of distribution in a multiple populations context therefore requires developing a specific factorization for calculating the multivariate likelihood. An example of such an extension for the problem of estimating branch length in population trees can be found in Tataru et al (2015). For such data, the Gaussian model remains much more practical but still suffers from the limitations mentioned above.…”

Section: Discussionmentioning

confidence: 99%

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Inference of selection from genetic time series using various parametric approximations to the Wright-Fisher model

Paris

¹

,

Servin

²

,

Boitard

³

2019

Preprint

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Detecting genomic regions under selection is an important objective of population genetics.Typical analyses for this goal are based on exploiting genetic diversity patterns in present time data but rapid advances in DNA sequencing have increased the availability of time series genomic data. A common approach to analyze such data is to model the temporal evolution of an allele frequency as a Markov chain. Based on this principle, several methods have been proposed to infer selection intensity. One of their differences lies in how they model the transition probabilities of the Markoiv chain. Using the Wright-Fisher model is a natural choice but its computational cost is prohibitive for large population sizes so approximations to this model based on parametric distributions have been proposed. Here, we compared the performance of some of these approximations with respect to their power to detect selection and estimation of the selection coefficient. We developped a new generic Hidden Markov Model likelihood calculator and applied it on genetic time series simulated under various evolutionary scenarios. The Beta-with-Spikes approximation, which combines discrete fixation probabilities with a continuous Beta distribution, was found to perform consistently better than the others. This distribution provides an almost perfect fit to the Wright-Fisher model in terms of selection inference, for a computational cost that does not increase with population size. We further evaluate this model for population sizes not accessible to the Wright-Fisher model and illustrate its performance on a dataset of two divergently selected chicken populations.Under the null, λ asymptotically follows a χ 2 with one degree of freedom, a property that allows to 107 derive p-values which are useful quantities in particular in a multiple testing context. 108Having described the general framework used in this study, we now turn to its implementation that 109 requires specifying the transition kernel Q k (x, .). One objective of this work was to investigate differ-110 ent models for this transition kernel. A reference model in this context is the one-locus Wright-Fisher 111 (WF) model under diploid selection pressure (Ewens, 2004). However, this model has computational 112 limitations and, in the HMM famework, must generally be approximated. We first present the WF 113 model and then several continuous approximations of this model based on a common approach: the 114 method-of-moments. 115 Wright-Fisher transition model 116The WF model is a discrete time model that assumes random mating and non overlapping generations. 117Let N e be the haploid (constant) effective population size. Under this model, X (t) can take a discrete 118 number of values in {0, 1 Ne , . . . , Ne−1 Ne , 1} and the transition kernel of this process is a transition matrix 119 130 very costly for large N e and large intersample time. To overcome this issue, one approach is to ap-131 proximate the Wright-Fisher process with a continuous space process such that integral calculati...

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“…Our inference procedure could also be used in the typical population phylogenetic setting to infer the divergence history of a group of populations, but this application is limited by the relatively small number of loci (< O(1000)) that our method can accept due to the computational costs of likelihood evaluations with the pruning algorithm. A maximum-likelihood implementation of our model, requiring fewer likelihood evaluations, may be applicable to genome-scale SNP data, possibly comparing to Kim Tree (Gautier and Vitalis, 2013) and SpikeyTree (Tataru et al, 2015).…”

Section: Discussionmentioning

confidence: 99%

A Population Phylogenetic View of Mitochondrial Heteroplasmy

Wilton

¹

,

Zaidi

²

,

Makova

³

et al. 2018

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The mitochondrion has recently emerged as an active player in a myriad of cellular processes. Additionally, it was recently shown that more than 200 diseases are known to be linked to variants in mitochondrial DNA or in nuclear genes interacting with mitochondria. This has reinvigorated interest in its biology and population genetics. Mitochondrial heteroplasmy, or genotypic variation of mitochondria within an individual, is now understood to be common in humans and important in human health. However, it is still not possible to make quantitative predictions about the inheritance of heteroplasmy and its proliferation within the body, partly due to the lack of an appropriate model. Here, we present a population-genetic framework for modeling mitochondrial heteroplasmy as a process that occurs on an ontogenetic phylogeny, with genetic drift and mutation changing heteroplasmy frequencies during the various developmental processes represented in the phylogeny. Using this framework, we develop a Bayesian inference method for inferring rates of mitochondrial genetic drift and mutation at different stages of human life. Applying the method to previously published heteroplasmy frequency data, we demonstrate a severe effective germline bottleneck comprised of the cumulative genetic drift occurring between the divergence of germline and somatic cells in the mother and the separation of germ layers in the offspring. Additionally, we find that the two somatic tissues we analyze here undergo tissue-specific bottlenecks during embryogenesis, less severe than the effective germline bottleneck, and that these somatic tissues experience little additional genetic drift during adulthood. We conclude with a discussion of possible extensions of the ontogenetic phylogeny framework and its possible applications to other ontogenetic processes in addition to mitochondrial heteroplasmy.

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“…The pruning algorithm also requires a distribution of allele frequencies at the root of the phylogeny, which, in our application (see below), represents the unobservable distribution of heteroplasmy allele frequencies in the mother as an embryo. Following Tataru et al (2015), we use a discretized, symmetric beta distribution with additional, symmetric probability weights at frequencies 0 and 1. The two parameters specifying this distribution are inferred jointly with genetic drift and mutation parameters.…”

Section: Likelihood Calculationmentioning

confidence: 99%

A population phylogenetic view of mitochondrial heteroplasmy

Wilton

¹

,

Zaidi

²

,

Makova

³

et al. 2017

Preprint

View full text Add to dashboard Cite

The mitochondrion has recently emerged as an active player in a myriad of cellular processes. Additionally, it was recently shown that more than 200 diseases are known to be linked to variants in mitochondrial DNA or in nuclear genes interacting with mitochondria. This has reinvigorated interest in its biology and population genetics. Mitochondrial heteroplasmy, or genotypic variation of mitochondria within an individual, is now understood to be common in humans and important in human health. However, it is still not possible to make quantitative predictions about the inheritance of heteroplasmy and its proliferation within the body, partly due to the lack of an appropriate model. Here, we present a population-genetic framework for modeling mitochondrial heteroplasmy as a process that occurs on an ontogenetic phylogeny, with genetic drift and mutation changing heteroplasmy frequencies during the various developmental processes represented in the phylogeny. Using this framework, we develop a Bayesian inference method for inferring rates of mitochondrial genetic drift and mutation at different stages of human life. Applying the method to previously published heteroplasmy frequency data, we demonstrate a severe effective germline bottleneck comprised of the cumulative genetic drift occurring between the divergence of germline and somatic cells in the mother and the separation of germ layers in the offspring. Additionally, we find that the two somatic tissues we analyze here undergo tissue-specific bottlenecks during embryogenesis, less severe than the effective germline bottleneck, and that these somatic tissues experience little additional genetic drift during adulthood. We conclude with a discussion of possible extensions of the ontogenetic phylogeny framework and its possible applications to other ontogenetic processes in addition to mitochondrial heteroplasmy.

show abstract

Inference under a Wright-Fisher model using an accurate beta approximation

Cited by 10 publications

References 37 publications

Inference of selection from genetic time series using various parametric approximations to the Wright-Fisher model

Inference of selection from genetic time series using various parametric approximations to the Wright-Fisher model

A Population Phylogenetic View of Mitochondrial Heteroplasmy

A population phylogenetic view of mitochondrial heteroplasmy

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