ArticleJournal of mathematical biology2019
A mathematical formalism for natural selection with arbitrary spatial and genetic structure.
Article in Journal of mathematical biology, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 21 papers.
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21 citing papers in PubMed, 39 citations in OpenAlex.
- Hyperedge approximation for stochastic processes on higher-order networks.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Public goods games on any population structure.Science advances · 2026Article
- Matrix games between full siblings in Mendelian populations.PloS one · 2025Article
- Survival cost sharing among altruistic full siblings in Mendelian population.BMC ecology and evolution · 2024Article
- Multiscale selection in spatially structured populations.Proceedings. Biological sciences · 2024Article
- Nonlinear social evolution and the emergence of collective action.PNAS nexus · 2024Article
- Imitation dynamics on networks with incomplete information.Nature communications · 2023Article
- Symmetry in models of natural selection.Journal of the Royal Society, Interface · 2023Article
- Categorizing update mechanisms for graph-structured metapopulations.Journal of the Royal Society, Interface · 2023Article
- Evaluating the structure-coefficient theorem of evolutionary game theory.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- Weak Selection and the Separation of Eco-evo Time Scales using Perturbation Analysis.Bulletin of mathematical biology · 2022Article
- Evolution of cooperation with joint liability.Journal of the Royal Society, Interface · 2022Article
- Evolution of prosocial behaviours in multilayer populations.Nature human behaviour · 2022Article
- Evolution of cooperation with contextualized behavior.Science advances · 2022Article
- Evolution of cooperation with asymmetric social interactions.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- Aspiration dynamics generate robust predictions in heterogeneous populations.Nature communications · 2021Article
- Fixation probabilities in evolutionary dynamics under weak selection.Journal of mathematical biology · 2021Article
- Fixation probabilities in graph-structured populations under weak selection.PLoS computational biology · 2021Article
- Social goods dilemmas in heterogeneous societies.Nature human behaviour · 2020Article
- Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs.PLoS computational biology · 2020Article
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Authors and funding
2 authors at 2 institutions in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
We define a general class of models representing natural selection between two alleles. The population size and spatial structure are arbitrary, but fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be asexual or sexual. Biological events (e.g. births, deaths, mating, dispersal) depend in arbitrary fashion on the current population state. Our formalism is based on the idea of genetic sites. Each genetic site resides at a particular locus and houses a single allele. Each individual contains a number of sites equal to its ploidy (one for haploids, two for diploids, etc.). Selection occurs via replacement events, in which alleles in some sites are replaced by copies of others. Replacement events depend stochastically on the population state, leading to a Markov chain representation of natural selection. Within this formalism, we define reproductive value, fitness, neutral drift, and fixation probability, and prove relationships among them. We identify four criteria for evaluating which allele is selected and show that these become equivalent in the limit of low mutation. We then formalize the method of weak selection. The power of our formalism is illustrated with applications to evolutionary games on graphs and to selection in a haplodiploid population.
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