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Computation 2016, 4(1), 6; doi:10.3390/computation4010006

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

1
Institute of Animal Breedings and Genetics, Veterinärmedizinische Universität Wien, Veterinärplatz 1, A-1210 Vienna, Austria
2
Institut für Populationsgenetik, Veterinärmedizinische Universität Wien, Veterinärplatz 1, A-1210 Vienna, Austria
3
Vienna Graduate School of Population Genetics, Veterinärmedizinische Universität Wien, Veterinärplatz 1, A-1210 Vienna, Austria
*
Author to whom correspondence should be addressed.
Academic Editor: Rainer Breitling
Received: 28 September 2015 / Revised: 26 January 2016 / Accepted: 26 January 2016 / Published: 4 February 2016
(This article belongs to the Section Computational Biology)
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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. View Full-Text
Keywords: bi-allelic mutation-drift model; small-scaled mutation rate; orthogonal polynomials; transition probability bi-allelic mutation-drift model; small-scaled mutation rate; orthogonal polynomials; transition probability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Vogl, C.; Bergman, J. Computation of the Likelihood of Joint Site Frequency Spectra Using Orthogonal Polynomials. Computation 2016, 4, 6.

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