The effect of population structure on evolutionary dynamics is a long-lasting research topic in evolutionary ecology and population genetics. Evolutionary graph theory is a popular approach to this problem, where individuals are located on the nodes of a network and can replace each other via the links. We study the effect of complex network structure on the fixation probability, but instead of networks of individuals, we model a network of sub-populations with a probability of migration between them. We ask how the structure of such a meta-population and the rate of migration affect the fixation probability. Many of the known results for networks of individuals carry over to meta-populations, in particular for regular networks or low symmetric migration probabilities. However, when patch sizes differ we find interesting deviations between structured meta-populations and networks of individuals. For example, a two patch structure with unequal population size suppresses selection for low migration probabilities.

The structure of a population strongly influences its evolutionary dynamics. In various settings ranging from biology to social systems, individuals tend to interact more often with those present in their proximity and rarely with those far away. A common approach to model the structure of a population is evolutionary graph theory. In this framework, each graph node is occupied by a reproducing individual. The links connect these individuals to their neighbours. The offspring can be placed on neighbouring nodes, replacing the neighbours—or the progeny of its neighbours can replace a node during the course of ongoing evolutionary dynamics. Extending this theory by replacing single individuals with subpopulations at nodes yields a graph-structured metapopulation. The dynamics between the different local subpopulations is set by an update mechanism. There are many such update mechanisms. Here, we classify update mechanisms for structured metapopulations, which allows to find commonalities between past work and illustrate directions for further research and current gaps of investigation.

The effect of population structure on evolutionary dynamics is a long-lasting research topic in evolutionary ecology and population genetics. Evolutionary graph theory is a popular approach to this problem, where individuals are located on the nodes of a network and can replace each other via the links. We study the effect of complex network structure on the fixation probability, but instead of networks of individuals, we model a network of sub-populations with a probability of migration between them. We ask how the structure of such a meta-population and the rate of migration affect the fixation probability. Many of the known results for networks of individuals carry over to meta-populations, in particular for regular networks or low symmetric migration probabilities. However, when patch sizes differ we find interesting deviations between structured meta-populations and networks of individuals. For example, a two-patch structure with unequal population size suppresses selection for low migration probabilities.

No abstract

Evolutionary dynamics in spatially structured populations has been studied for a long time. More recently, the focus has been to construct structures that speeds up evolution -- so called amplifiers of selection. It has been shown that for a structure to amplify selection, self-loops are necessary when mutants appear predominately in nodes that change often. As a result, for low mutation rates, self-looped amplifiers attain higher steady-state average fitness in the mutation-selection than well-mixed populations. But, what happens when the mutation rate increases such that fixation probabilities alone no longer describe the dynamics? We show that self-loops effects are detrimental outside the low mutation rate regime. In the intermediate and high mutation rate regime, amplifiers of selection attain lower steady-state average fitness than the complete graph and the suppressor of selection. We also provide an estimate of mutation rate beyond which the mutation-selection dynamics on a graph deviates from the weak mutation rate approximation. This involves computing how the average fixation time scales with the population size for several graphs.