Abstract
We analyze evolutionary dynamics on graphs, where the nodes represent individuals of a population. The links of a node describe which other individuals can be displaced by the offspring of the individual on that node. Amplifiers of selection are graphs for which the fixation probability is increased for advantageous mutants and decreased for disadvantageous mutants. A few examples of such amplifiers have been developed, but so far it is unclear how many such structures exist and how to construct them. Here, we show that almost any undirected random graph is an amplifier of selection for Birth-death updating, where an individual is selected to reproduce with probability proportional to its fitness and one of its neighbors is replaced by that offspring at random. If we instead focus on death-Birth updating, in which a random individual is removed and its neighbors compete for the empty spot, then the same ensemble of graphs consists of almost only suppressors of selection for which the fixation probability is decreased for advantageous mutants and increased for disadvantageous mutants. Thus, the impact of population structure on evolutionary dynamics is a subtle issue that will depend on seemingly minor details of the underlying evolutionary process.
Highlights
In the past years, it has been shown that evolution can be strongly affected by population structure, extending the classical result that “certain quantities are independent of the geographical structure of a population” [1]
Evolutionary dynamics describes the spread of individuals with different features within a population
A population structure can amplify the evolutionary success of a type
Summary
It has been shown that evolution can be strongly affected by population structure, extending the classical result that “certain quantities are independent of the geographical structure of a population” [1]. It has been shown that all regular graphs do not change the probability that a mutant will either take over or go extinct compared to well-mixed populations, which can be described by a fully connected graph [1,2,3] This result has been obtained for a microscopic evolutionary process, called Birth-death (Bd) update, in which first an individual is sampled from the whole population at random, but proportional to fitness, and its identical offspring replaces a neighboring individual. Such results depend on the details of the microscopic evolutionary process [6, 7], which makes it challenging to disentangle structure from dynamics. The temporal dynamics of this process has interesting aspects, as amplifiers of selection may slow down the process of fixation itself [8,9,10]
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