title: An Approximate Markov Model for the Wright-Fisher Diffusion and Its Application to Time Series Data.
abstract: The joint and accurate inference of selection and demography from genetic data is considered a particularly challenging question in population genetics, since both process may lead to very similar patterns of genetic diversity. However, additional information for disentangling these effects may be obtained by observing changes in allele frequencies over multiple time points. Such data are common in experimental evolution studies, as well as in the comparison of ancient and contemporary samples. Leveraging this information, however, has been computationally challenging, particularly when considering multilocus data sets. To overcome these issues, we introduce a novel, discrete approximation for diffusion processes, termed mean transition time approximation, which preserves the long-term behavior of the underlying continuous diffusion process. We then derive this approximation for the particular case of inferring selection and demography from time series data under the classic Wright-Fisher model and demonstrate that our approximation is well suited to describe allele trajectories through time, even when only a few states are used. We then develop a Bayesian inference approach to jointly infer the population size and locus-specific selection coefficients with high accuracy and further extend this model to also infer the rates of sequencing errors and mutations. We finally apply our approach to recent experimental data on the evolution of drug resistance in influenza virus, identifying likely targets of selection and finding evidence for much larger viral population sizes than previously reported.
authors.affiliation: Department of Biology, University, of Fribourg, 1700 Fribourg Switzerland Department of Life Science, Ecole Polytechnique Federal de Lausanne, 1015 Switzerland Swiss Institute of Bioinformatics, 1700 Fribourg, Switzerland.
authors.forename: Anna
authors.initials: A
authors.lastname: Ferrer-Admetlla
authors.affiliation: Department of Mathematics, University, of Fribourg, 1700 Fribourg Switzerland.
authors.forename: Christoph
authors.initials: C
authors.lastname: Leuenberger
authors.affiliation: Department of Life Science, Ecole Polytechnique Federal de Lausanne, 1015 Switzerland Swiss Institute of Bioinformatics, 1700 Fribourg, Switzerland.
authors.forename: Jeffrey D
authors.initials: JD
authors.lastname: Jensen
authors.affiliation: Department of Biology, University, of Fribourg, 1700 Fribourg Switzerland Swiss Institute of Bioinformatics, 1700 Fribourg, Switzerland daniel.wegmann@unifr.ch.
authors.forename: Daniel
authors.initials: D
authors.lastname: Wegmann
mesh_terms: D024882:Drug Resistance, Viral / Q000235:genetics*; D019143:Evolution, Molecular; D008390:Markov Chains; D008957:Models, Genetic; D009975:Orthomyxoviridae / Q000187:drug effects / Q000235:genetics*; D012641:Selection, Genetic
keywords: Wright–Fisher model; diffusion approximation; discrete Markov model; hidden Markov model; time-series data