Mutation-selection stationary distribution in structured populations

2023

J. R. Soc. Interface.

Self Cite

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.

Section: Update Mechanisms For Graphs Of Individualsmentioning

confidence: 99%

Categorizing update mechanisms for graph-structured metapopulations

Yagoobi

2023

J. R. Soc. Interface.

Self Cite

“…In graphs of individuals, three main events influence the evolution of a population: birth, mutation, and death. In the long run, a mutation-selection balance is reached [15][16][17][18]. Here, we focus on the low mutation regime in which the system reaches fixation or extinction of the mutant before the next mutation occurs.…”

Section: Update Mechanisms In Graphs Of Individualsmentioning

confidence: 99%

Categorising update mechanisms for graph-structured metapopulations

Yagoobi

2022

Preprint

Self Cite

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.

“…A model that investigates such long evolutionary trajectories in graph structured populations has been missing so far. This problem has been studied for two types [12], but not for the case of continuously arising mutations with a potentially infinite number of types. The neutrality counterpart of this problem has been investigated in [13] where equilibrium properties are shown to be independent of the population structure.…”

Section: Introductionmentioning

confidence: 99%

Do amplifiers of selection maximise average fitness?

2022

Preprint

Evolutionary dynamics on graphs has remarkable features: For example, it has been shown that amplifiers of selection exist that -- compared to an unstructured population -- increase the fixation probability of advantageous mutations, while they decrease the fixation probability of disadvantageous mutations. So far, the theoretical literature has focused on the case of a single mutant entering a graph structured population, asking how the graph affects the probability that a mutant takes over a population and the time until this typically happens. For continuously evolving systems, the more relevant case is when mutants constantly arise in an evolving population. Typically, such mutations occur with a small probability during reproduction events. We thus focus on the low mutation rate limit. The probability distribution for the fitness in this process converges to a steady state at long times. Intuitively, amplifiers of selection are expected to increase the population's mean fitness in the steady-state. Similarly, suppressors of selection are expected to decrease the population's mean fitness in the steady-state. However, we show that another category of graphs, called suppressor of fixation, can attain the highest population mean fitness. The key reason behind this is their ability to efficiently reject deleterious mutants. This illustrates the importance of the deleterious mutant regime for the long-term evolutionary dynamics, something that seems to have been overlooked in the literature so far.