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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...
Autores principales: | , , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2021
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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. |
format | Online Article Text |
id | pubmed-7880501 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
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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