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Fixation probabilities in graph-structured populations under weak selection

A population’s spatial structure affects the rate of genetic change and the outcome of natural selection. These effects can be modeled mathematically using the Birth-death process on graphs. Individuals occupy the vertices of a weighted graph, and reproduce into neighboring vertices based on fitness...

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Autores principales: Allen, Benjamin, Sample, Christine, Steinhagen, Patricia, Shapiro, Julia, King, Matthew, Hedspeth, Timothy, Goncalves, Megan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7880501/
https://www.ncbi.nlm.nih.gov/pubmed/33529219
http://dx.doi.org/10.1371/journal.pcbi.1008695
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author Allen, Benjamin
Sample, Christine
Steinhagen, Patricia
Shapiro, Julia
King, Matthew
Hedspeth, Timothy
Goncalves, Megan
author_facet Allen, Benjamin
Sample, Christine
Steinhagen, Patricia
Shapiro, Julia
King, Matthew
Hedspeth, Timothy
Goncalves, Megan
author_sort Allen, Benjamin
collection PubMed
description A population’s spatial structure affects the rate of genetic change and the outcome of natural selection. These effects can be modeled mathematically using the Birth-death process on graphs. Individuals occupy the vertices of a weighted graph, and reproduce into neighboring vertices based on fitness. A key quantity is the probability that a mutant type will sweep to fixation, as a function of the mutant’s fitness. Graphs that increase the fixation probability of beneficial mutations, and decrease that of deleterious mutations, are said to amplify selection. However, fixation probabilities are difficult to compute for an arbitrary graph. Here we derive an expression for the fixation probability, of a weakly-selected mutation, in terms of the time for two lineages to coalesce. This expression enables weak-selection fixation probabilities to be computed, for an arbitrary weighted graph, in polynomial time. Applying this method, we explore the range of possible effects of graph structure on natural selection, genetic drift, and the balance between the two. Using exhaustive analysis of small graphs and a genetic search algorithm, we identify families of graphs with striking effects on fixation probability, and we analyze these families mathematically. Our work reveals the nuanced effects of graph structure on natural selection and neutral drift. In particular, we show how these notions depend critically on the process by which mutations arise.
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spelling pubmed-78805012021-02-19 Fixation probabilities in graph-structured populations under weak selection Allen, Benjamin Sample, Christine Steinhagen, Patricia Shapiro, Julia King, Matthew Hedspeth, Timothy Goncalves, Megan PLoS Comput Biol Research Article A population’s spatial structure affects the rate of genetic change and the outcome of natural selection. These effects can be modeled mathematically using the Birth-death process on graphs. Individuals occupy the vertices of a weighted graph, and reproduce into neighboring vertices based on fitness. A key quantity is the probability that a mutant type will sweep to fixation, as a function of the mutant’s fitness. Graphs that increase the fixation probability of beneficial mutations, and decrease that of deleterious mutations, are said to amplify selection. However, fixation probabilities are difficult to compute for an arbitrary graph. Here we derive an expression for the fixation probability, of a weakly-selected mutation, in terms of the time for two lineages to coalesce. This expression enables weak-selection fixation probabilities to be computed, for an arbitrary weighted graph, in polynomial time. Applying this method, we explore the range of possible effects of graph structure on natural selection, genetic drift, and the balance between the two. Using exhaustive analysis of small graphs and a genetic search algorithm, we identify families of graphs with striking effects on fixation probability, and we analyze these families mathematically. Our work reveals the nuanced effects of graph structure on natural selection and neutral drift. In particular, we show how these notions depend critically on the process by which mutations arise. Public Library of Science 2021-02-02 /pmc/articles/PMC7880501/ /pubmed/33529219 http://dx.doi.org/10.1371/journal.pcbi.1008695 Text en © 2021 Allen et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Allen, Benjamin
Sample, Christine
Steinhagen, Patricia
Shapiro, Julia
King, Matthew
Hedspeth, Timothy
Goncalves, Megan
Fixation probabilities in graph-structured populations under weak selection
title Fixation probabilities in graph-structured populations under weak selection
title_full Fixation probabilities in graph-structured populations under weak selection
title_fullStr Fixation probabilities in graph-structured populations under weak selection
title_full_unstemmed Fixation probabilities in graph-structured populations under weak selection
title_short Fixation probabilities in graph-structured populations under weak selection
title_sort fixation probabilities in graph-structured populations under weak selection
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7880501/
https://www.ncbi.nlm.nih.gov/pubmed/33529219
http://dx.doi.org/10.1371/journal.pcbi.1008695
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