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Description
The evolutionary dynamics of a finite population where resident individuals are replaced by invader or mutant ones depend on its spatial structure. The population adopts the form of an undirected graph where the place occupied by each individual is represented by a node and it is bidirectionally linked to the places that can be occupied by its clonal offspring. There are undirected graph structures that act as amplifiers of selection increasing the probability that the offspring of an advantageous mutant spreads through the graph reaching any node. But there also are undirected graph structures acting as suppressors of selection. Here, we show that some undirected graphs exhibit phase transitions between both evolutionary states when the mutant fitness varies. Firstly, as was already observed by Hindersin and Traulsen, we show that most graphs of order 10 or less are amplifiers of selection or suppressors for weak selection that become amplifiers from a unique transition phase. However, in order 7, we give examples of amplifiers for weak selection that become suppressors from some critical value. The analysis of all graphs from order 8 to 10 reveals a complex and rich evolutionary dynamics.
