ArticleRoyal Society open science2022
Martingales and the fixation time of evolutionary graphs with arbitrary dimensionality.
Article in Royal Society open science, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- Mixed updating in structured populations.PLoS computational biology · 2026Article
- Sequential analysis and its applications to neuromorphic engineering.Frontiers in neuroscience · 2025Article
- Fixation times on directed graphs.PLoS computational biology · 2024Article
- The speed of neutral evolution on graphs.Journal of the Royal Society, Interface · 2024Article
- 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
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2 authors.
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Abstract
Evolutionary graph theory (EGT) investigates the Moran birth-death process constrained by graphs. Its two principal goals are to find the fixation probability and time for some initial population of mutants on the graph. The fixation probability of graphs has received considerable attention. Less is known about the distribution of fixation time. We derive clean, exact expressions for the full conditional characteristic functions (CCFs) of a close proxy to fixation and extinction times. That proxy is the number of times that the mutant population size changes before fixation or extinction. We derive these CCFs from a product martingale that we identify for an evolutionary graph with any number of partitions. The existence of that martingale only requires that the connections between those partitions are of a certain type. Our results are the first expressions for the CCFs of any proxy to fixation time on a graph with any number of partitions. The parameter dependence of our CCFs is explicit, so we can explore how they depend on graph structure. Martingales are a powerful approach to study principal problems of EGT. Their applicability is invariant to the number of partitions in a graph, so we can study entire families of graphs simultaneously.
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