Inference of directional selection and mutation parameters assuming equilibrium

Vogl, Claus; Bergman, Juraj

doi:10.1016/j.tpb.2015.10.003

Cited by 26 publications

(63 citation statements)

References 41 publications

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“…If the boundary mutation model is assumed, these estimators are maximum likelihood, rather than approximations in the limit of small-scaled mutation rates θ [4].…”

Section: Inference Based On the Beta Equilibrium Distributionmentioning

confidence: 99%

“…Starting from a Moran model that only allows for mutations from the boundaries, Vogl and Clemente [10] derive a generalization of the estimator also for the case with directional selection, without assuming outgroup information. Vogl and Bergman [4] derive ML estimators for all three parameters: mutation bias α, scaled mutation rate θ and scaled selection strength γ, with the same assumptions, but base the analysis on a diffusion model.…”

Section: Inference Based On the Assumptions Of Equilibrium And Rare Mmentioning

confidence: 99%

“…Further in the text, we will follow Vogl and Bergman [4] and model mutations as only affecting the boundaries. Then, φ(x, t) must be interpreted as a generalized probability measure that integrates to one over the unit interval, but may contain point masses at the boundaries (compare [32]).…”

Section: The Boundary-mutation Modelmentioning

confidence: 99%

“…The slightly less familiar Moran model only allows transitions between neighboring states, which simplifies the math. This simplification pertains also to the boundaries [4]. With the boundary-mutation model, mutations are assumed to arise only at the boundaries; a transition from x = 0 to x = 1/N corresponds to a mutation from a monomorphic state with only A/T to a polymorphic state with a single C/G in the population; conversely, a transition from x = 1 to x = (N − 1)/N corresponds to a mutation from C/G to A/T.…”

Section: The Boundary-mutation Modelmentioning

confidence: 99%

“…We base the following description on the theory of hierarchical Bayesian models and the empirical Bayes method [16] that we also employed earlier [3,4]. In a frequentist context, one would rather use the context of marginal likelihoods.…”

Section: Starting and Prior Distributionsmentioning

confidence: 99%

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Computation of the Likelihood of Joint Site Frequency Spectra Using Orthogonal Polynomials

Vogl

Bergman

2016

Computation

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Abstract:In population genetics, information about evolutionary forces, e.g., mutation, selection and genetic drift, is often inferred from DNA sequence information. Generally, DNA consists of two long strands of nucleotides or sites that pair via the complementary bases cytosine and guanine (C and G), on the one hand, and adenine and thymine (A and T), on the other. With whole genome sequencing, most genomic information stored in the DNA has become available for multiple individuals of one or more populations, at least in humans and model species, such as fruit flies of the genus Drosophila. In a genome-wide sample of L sites for M (haploid) individuals, the state of each site may be made binary, by binning the complementary bases, e.g., C with G to C/G, and contrasting C/G to A/T, to obtain a "site frequency spectrum" (SFS). Two such samples of either a single population from different time-points or two related populations from a single time-point are called joint site frequency spectra (joint SFS). While mathematical models describing the interplay of mutation, drift and selection have been available for more than 80 years, calculation of exact likelihoods from joint SFS is difficult. Sufficient statistics for inference of, e.g., mutation or selection parameters that would make use of all the information in the genomic data are rarely available. Hence, often suites of crude summary statistics are combined in simulation-based computational approaches. In this article, we use a bi-allelic boundary-mutation and drift population genetic model to compute the transition probabilities of joint SFS using orthogonal polynomials. This allows inference of population genetic parameters, such as the mutation rate (scaled by the population size) and the time separating the two samples. We apply this inference method to a population dataset of neutrally-evolving short intronic sites from six DNA sequences of the fruit fly Drosophila melanogaster and the reference sequence of the related species Drosophila sechellia.

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“…If the boundary mutation model is assumed, these estimators are maximum likelihood, rather than approximations in the limit of small-scaled mutation rates θ [4].…”

Section: Inference Based On the Beta Equilibrium Distributionmentioning

confidence: 99%

Section: Inference Based On the Assumptions Of Equilibrium And Rare Mmentioning

confidence: 99%

Section: The Boundary-mutation Modelmentioning

confidence: 99%

Section: The Boundary-mutation Modelmentioning

confidence: 99%

Section: Starting and Prior Distributionsmentioning

confidence: 99%

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Computation of the Likelihood of Joint Site Frequency Spectra Using Orthogonal Polynomials

Vogl

Bergman

2016

Computation

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The stationary distribution of a sample from the Wright–Fisher diffusion model with general small mutation rates

Burden

Griffiths

2018

J. Math. Biol.

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The stationary distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree to the first order in the rates. The sample probabilities characterize an approximation for the stationary distribution from the Wright-Fisher diffusion. The approach is different from Tang (2016, 2017) who use a probability flux argument to obtain the same results from a forward diffusion generator equation. The solution has interest because the solution is not known when rates are not small.An analogous solution is found for the configuration of alleles in a general exchangeable binary coalescent tree. In particular an explicit solution is found for a pure birth process tree when individuals reproduce at rate λ .

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The transition distribution of a sample from a Wright–Fisher diffusion with general small mutation rates

Burden

Griffiths

2019

J. Math. Biol.

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The transition distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree of the sample up to the most recent common ancestor with additional mutations occurring on the lineage from the most recent common ancestor to the time origin if complete coalescence occurs before the origin. The sampling distribution leads to an approximation for the transition density in the diffusion with small mutation rates. This new solution has interest because the transition density in a Wright-Fisher diffusion with general mutation rates is not known.

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Inference of directional selection and mutation parameters assuming equilibrium

Cited by 26 publications

References 41 publications

Computation of the Likelihood of Joint Site Frequency Spectra Using Orthogonal Polynomials

Computation of the Likelihood of Joint Site Frequency Spectra Using Orthogonal Polynomials

The stationary distribution of a sample from the Wright–Fisher diffusion model with general small mutation rates

The transition distribution of a sample from a Wright–Fisher diffusion with general small mutation rates

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