title: Transition Densities and Sample Frequency Spectra of Diffusion Processes with Selection and Variable Population Size.
abstract: Advances in empirical population genetics have made apparent the need for models that simultaneously account for selection and demography. To address this need, we here study the Wright-Fisher diffusion under selection and variable effective population size. In the case of genic selection and piecewise-constant effective population sizes, we obtain the transition density by extending a recently developed method for computing an accurate spectral representation for a constant population size. Utilizing this extension, we show how to compute the sample frequency spectrum in the presence of genic selection and an arbitrary number of instantaneous changes in the effective population size. We also develop an alternate, efficient algorithm for computing the sample frequency spectrum using a moment-based approach. We apply these methods to answer the following questions: If neutrality is incorrectly assumed when there is selection, what effects does it have on demographic parameter estimation? Can the impact of negative selection be observed in populations that undergo strong exponential growth?
authors: Section of Evolutionary Biology, Department of Biology, Ludwig-Maximilian University Munich, 82152 Munich, Germany zivkovic@bio.lmu.de.
authors: Daniel
authors: D
authors: Živković
authors: Department of Statistics, University of California, Berkeley, California 94720 Department of Biostatistics and Epidemiology, University of Massachusetts, Amherst, Massachusetts 01003.
authors: Matthias
authors: M
authors: Steinrücken
authors: Department of Statistics, University of California, Berkeley, California 94720 Computer Science Division and Department of Integrative Biology, University of California, Berkeley, California 94720.
authors: Yun S
authors: YS
authors: Song
authors: Section of Evolutionary Biology, Department of Biology, Ludwig-Maximilian University Munich, 82152 Munich, Germany.
authors: Wolfgang
authors: W
authors: Stephan
mesh_terms: D000465:Algorithms; D005828:Genetics, Population; D008957:Models, Genetic; D011156:Population Density; D012641:Selection, Genetic
keywords: demography; diffusion; frequency spectrum; selection; transition density