AI Insight
This study introduces the concept of "fixation location" in evolutionary dynamics on structured populations, defined as the specific node where the last individual of the original type exists before a mutation completely takes over the population. The researchers analyzed this phenomenon across various network structures including small graphs, cycles, tori, random graphs, and island populations, finding that the distribution of fixation locations is highly non-uniform and strongly dependent on network structure and selection strength. Notably, some nodes in many networks can never serve as fixation locations, revealing a previously uncharacterized aspect of how traits spread through structured populations.
Why it matters
Understanding where extinctions occur in structured populations could help predict and potentially prevent the loss of beneficial traits or endangered populations in biological systems, and could inform strategies for managing the spread of cultural traits or disease in social networks.
arXiv:2605.26411v1 Announce Type: new
Abstract: In stochastic evolutionary dynamics, the replacement of an existing genotype or cultural trait by a newly introduced mutant is typically characterized by the quantities of fixation probability and fixation time. But in a structured population, the disappearance of a lineage occurs at a specific place. For evolutionary dynamics on graphs, we define the fixation location as the node occupied by the last wild-type individual immediately before mutant fixation. Conditional on fixation, this location is described by a probability distribution over the nodes of the graph. We study the fixation location for neutral evolution, for the colonization process, and, more generally, for constant selection on small graphs, cycles, tori, random graphs, and island populations. We find that the distribution of the fixation location is often highly nonuniform, depends strongly on the graph structure and the selection strength, and can differ sharply even when classical fixation statistics are similar. For many graphs, some nodes can never be fixation locations. Our results identify fixation location as a fundamental aspect of evolutionary dynamics and suggest new ways to understand, monitor, and potentially mitigate extinction events in biological and social settings.