Intercoalescence Time Distribution of Incomplete Gene Genealogies in Temporally Varying Populations, and Applications in Population Genetic Inference

Chen, Hua

doi:10.1111/ahg.12007

Cited by 8 publications

(14 citation statements)

References 63 publications

(84 reference statements)

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“…It has been well studied using diffusion process since the foundation of population genetics (Kimura 1955). The AFS for any nonequilibrium populations can also be obtained in the coalescent framework using the expected time lengths of gene genealogies (Griffiths and Tavaré 1998;Marth et al 2004;Chen 2012Chen , 2013. The coalescent-based AFS was used extensively in studies of population growth, bottlenecks, and other demographic history (Wooding and Rogers 2002;Marth et al 2004).…”

Section: The Allele Frequency Spectrummentioning

confidence: 99%

Asymptotic Distributions of Coalescence Times and Ancestral Lineage Numbers for Populations with Temporally Varying Size

Chen

2013

Genetics

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The distributions of coalescence times and ancestral lineage numbers play an essential role in coalescent modeling and ancestral inference. Both exact distributions of coalescence times and ancestral lineage numbers are expressed as the sum of alternating series, and the terms in the series become numerically intractable for large samples. More computationally attractive are their asymptotic distributions, which were derived in Griffiths (1984) for populations with constant size. In this article, we derive the asymptotic distributions of coalescence times and ancestral lineage numbers for populations with temporally varying size. For a sample of size n, denote by T m the mth coalescent time, when m + 1 lineages coalesce into m lineages, and A n (t) the number of ancestral lineages at time t back from the current generation. Similar to the results in Griffiths (1984), the number of ancestral lineages, A n (t), and the coalescence times, T m , are asymptotically normal, with the mean and variance of these distributions depending on the population size function, N(t). At the very early stage of the coalescent, when t / 0, the number of coalesced lineages n 2 A n (t) follows a Poisson distribution, and as m / n, nðn 2 1ÞT m =2Nð0Þ follows a gamma distribution. We demonstrate the accuracy of the asymptotic approximations by comparing to both exact distributions and coalescent simulations. Several applications of the theoretical results are also shown: deriving statistics related to the properties of gene genealogies, such as the time to the most recent common ancestor (TMRCA) and the total branch length (TBL) of the genealogy, and deriving the allele frequency spectrum for large genealogies. With the advent of genomic-level sequencing data for large samples, the asymptotic distributions are expected to have wide applications in theoretical and methodological development for population genetic inference. COALESCENT theory provides a fundamental framework for stochastic modeling and likelihood inference in population genetic studies (Griffiths 1980;Kingman 1982a;Hudson 1990;Nordborg 2001). A coalescent process can be decomposed into two independent processes: the topology of the gene genealogy and the sequential process of intercoalescence times (Kingman 1982a). In this article, we aim to investigate the latter process and two important random quantities associated with this process: the coalescence times and the number of ancestral lineages (Kingman 1982a). Studying the two quantities is both biologically and theoretically meaningful. First, inferring the coalescence times and the number of ancient lineages of a contemporary sample or population helps to elucidate ancient demographic history, including population admixture, migration, and founder effect. It can also provide insights into medical studies regarding the origin and genetic architecture of inherited diseases in different populations, as well as to ecological studies, for example, on investigating the process of species invasion (Risch et al. 2003;...

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Section: The Allele Frequency Spectrummentioning

confidence: 99%

Asymptotic Distributions of Coalescence Times and Ancestral Lineage Numbers for Populations with Temporally Varying Size

Chen

2013

Genetics

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“…This is the case for the infinite sites model without recombination, where only the coalescence approach has been used to derive joint site frequency spectra, as far as we are aware. Recently, Chen [44,45] and Kamm et al [46] improved the computational efficiency of the coalescence approach to joint site frequency spectra. We note that changes in the mutation bias, as incorporated into our approach, have not yet been incorporated into the coalescence approach.…”

Section: Discussionmentioning

confidence: 99%

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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“…One limitation of the coalescent-based AFS methods is that we can only analytically derive the AFS for some simple population growth models, such as the n-epoch model and the exponential-growth model or their combinations Marth et al, 2004;Gazave et al, 2014), and generalization to other complex population histories is often impracticable (Chen, 2012(Chen, , 2013. A second limitation is that for large samples (e.g., haplotype number n > 50), it is hard to accurately calculate the expected AFS from the formulae.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Computational Approach for Constructing the Allele Frequency Spectrum of Populations with Arbitrary Complex History

Chen

2018

Preprint

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The allele frequency spectrum (AFS), or site frequency spectrum, is commonly used to summarize the genomic polymorphism pattern of a sample, which is informative for inferring population history and detecting natural selection. Recently, Chen and Chen (2013) developed a method for analytically deriving the AFS for populations with temporally varying size through the coalescence time-scaling function. However, their approach is only applicable for population history scenarios in which the analytical form of the timescaling function is tractable. In this paper, we propose a computational approach to extend the method to populations with arbitrary complex history by numerically approximating the time-scaling function. We demonstrate the performance of the approach by constructing the AFS for two population history scenarios: the logistic growth model and the Gompertz growth model, for which the AFS are unavailable with existing approaches.

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Intercoalescence Time Distribution of Incomplete Gene Genealogies in Temporally Varying Populations, and Applications in Population Genetic Inference

Cited by 8 publications

References 63 publications

Asymptotic Distributions of Coalescence Times and Ancestral Lineage Numbers for Populations with Temporally Varying Size

Asymptotic Distributions of Coalescence Times and Ancestral Lineage Numbers for Populations with Temporally Varying Size

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

An Efficient Computational Approach for Constructing the Allele Frequency Spectrum of Populations with Arbitrary Complex History

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