ArticleRoyal Society open science2015
The duality of spatial death-birth and birth-death processes and limitations of the isothermal theorem.
Article in Royal Society open science, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 51 papers.
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51 citing papers in PubMed.
- Mixed updating in structured populations.PLoS computational biology · 2026Article
- Environment heterogeneity creates fast amplifiers of natural selection in graph-structured populations.Nature communications · 2026Article
- The effect of the fitness gradient on fixation probability.Nature communications · 2026Article
- Population structure reverses selection of variants with proportionally scaled birth and death rates.Nature communications · 2025Article
- Colonization times in Moran process on graphs.PLoS computational biology · 2025Article
- Evolutionary dynamics of nascent multicellular lineages.Proceedings. Biological sciences · 2025Article
- Graph-structured populations elucidate the role of deleterious mutations in long-term evolution.Nature communications · 2025Article
- Compartmental structure in the secondary lymphoid tissue can slow downJournal of the Royal Society, Interface · 2025Article
- Mutant fate in spatially structured populations on graphs: Connecting models to experiments.PLoS computational biology · 2024Article
- The speed of neutral evolution on graphs.Journal of the Royal Society, Interface · 2024Article
- The evolution of environmentally mediated social interactions and posthumous spite under isolation by distance.PLoS computational biology · 2024Article
- Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating.PLoS computational biology · 2024Article
- Frequent asymmetric migrations suppress natural selection in spatially structured populations.PNAS nexus · 2023Article
- Evolutionary dynamics of mutants that modify population structure.Journal of the Royal Society, Interface · 2023Article
- Categorizing update mechanisms for graph-structured metapopulations.Journal of the Royal Society, Interface · 2023Article
- The role of migration in mutant dynamics in fragmented populations.Journal of evolutionary biology · 2023Article
- Suppressors of fixation can increase average fitness beyond amplifiers of selection.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- The role of evolutionary game theory in spatial and non-spatial models of the survival of cooperation in cancer: a review.Journal of the Royal Society, Interface · 2022Review
- Martingales and the fixation time of evolutionary graphs with arbitrary dimensionality.Royal Society open science · 2022Article
- Hydrodynamic flow and concentration gradients in the gut enhance neutral bacterial diversity.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
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3 authors.
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Abstract
Evolutionary models on graphs, as an extension of the Moran process, have two major implementations: birth-death (BD) models (or the invasion process) and death-birth (DB) models (or voter models). The isothermal theorem states that the fixation probability of mutants in a large group of graph structures (known as isothermal graphs, which include regular graphs) coincides with that for the mixed population. This result has been proved by Lieberman et al. (2005 Nature 433, 312-316. (doi:10.1038/nature03204)) in the case of BD processes, where mutants differ from the wild-types by their birth rate (and not by their death rate). In this paper, we discuss to what extent the isothermal theorem can be formulated for DB processes, proving that it only holds for mutants that differ from the wild-type by their death rate (and not by their birth rate). For more general BD and DB processes with arbitrary birth and death rates of mutants, we show that the fixation probabilities of mutants are different from those obtained in the mass-action populations. We focus on spatial lattices and show that the difference between BD and DB processes on one- and two-dimensional lattices is non-small even for large population sizes. We support these results with a generating function approach that can be generalized to arbitrary graph structures. Finally, we discuss several biological applications of the results.
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