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Weak Selection and the Separation of Eco-evo Time Scales using Perturbation Analysis

We show that under the assumption of weak frequency-dependent selection a wide class of population dynamical models can be analysed using perturbation theory. The inner solution corresponds to the ecological dynamics, where to zeroth order, the genotype frequencies remain constant. The outer solutio...

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Autor principal: Gerlee, Philip
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8934331/
https://www.ncbi.nlm.nih.gov/pubmed/35305188
http://dx.doi.org/10.1007/s11538-022-01009-3
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author Gerlee, Philip
author_facet Gerlee, Philip
author_sort Gerlee, Philip
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description We show that under the assumption of weak frequency-dependent selection a wide class of population dynamical models can be analysed using perturbation theory. The inner solution corresponds to the ecological dynamics, where to zeroth order, the genotype frequencies remain constant. The outer solution provides the evolutionary dynamics and corresponds, to zeroth order, to a generalisation of the replicator equation. We apply this method to a model of public goods dynamics and construct, using matched asymptotic expansions, a composite solution valid for all times. We also analyse a Lotka–Volterra model of predator competition and show that to zeroth order the fraction of wild-type predators follows a replicator equation with a constant selection coefficient given by the predator death rate. For both models, we investigate how the error between approximate solutions and the solution to the full model depend on the order of the approximation and show using numerical comparison, for [Formula: see text] and 2, that the error scales according to [Formula: see text] , where [Formula: see text] is the strength of selection and k is the order of the approximation.
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spelling pubmed-89343312022-04-01 Weak Selection and the Separation of Eco-evo Time Scales using Perturbation Analysis Gerlee, Philip Bull Math Biol Original Research We show that under the assumption of weak frequency-dependent selection a wide class of population dynamical models can be analysed using perturbation theory. The inner solution corresponds to the ecological dynamics, where to zeroth order, the genotype frequencies remain constant. The outer solution provides the evolutionary dynamics and corresponds, to zeroth order, to a generalisation of the replicator equation. We apply this method to a model of public goods dynamics and construct, using matched asymptotic expansions, a composite solution valid for all times. We also analyse a Lotka–Volterra model of predator competition and show that to zeroth order the fraction of wild-type predators follows a replicator equation with a constant selection coefficient given by the predator death rate. For both models, we investigate how the error between approximate solutions and the solution to the full model depend on the order of the approximation and show using numerical comparison, for [Formula: see text] and 2, that the error scales according to [Formula: see text] , where [Formula: see text] is the strength of selection and k is the order of the approximation. Springer US 2022-03-19 2022 /pmc/articles/PMC8934331/ /pubmed/35305188 http://dx.doi.org/10.1007/s11538-022-01009-3 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Research
Gerlee, Philip
Weak Selection and the Separation of Eco-evo Time Scales using Perturbation Analysis
title Weak Selection and the Separation of Eco-evo Time Scales using Perturbation Analysis
title_full Weak Selection and the Separation of Eco-evo Time Scales using Perturbation Analysis
title_fullStr Weak Selection and the Separation of Eco-evo Time Scales using Perturbation Analysis
title_full_unstemmed Weak Selection and the Separation of Eco-evo Time Scales using Perturbation Analysis
title_short Weak Selection and the Separation of Eco-evo Time Scales using Perturbation Analysis
title_sort weak selection and the separation of eco-evo time scales using perturbation analysis
topic Original Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8934331/
https://www.ncbi.nlm.nih.gov/pubmed/35305188
http://dx.doi.org/10.1007/s11538-022-01009-3
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