hide
Free keywords:
-
Abstract:
Evolutionary dynamics in well-mixed populations have been studied quite extensively. While the respective studies provide a good starting point for a mathematical analysis, populations in the wild are rarely well-mixed. Nat- ural populations often come with spatial structures, resulting in dynamics different from the well-mixed case. Therefore, it is crucial to understand evolution on spatial structures. To this end, we use the framework of evolu- tionary graph theory, where nodes represent asexually reproducing entities, and links define the neighborhood of nodes. First, we develop a model to study population structures adapting to a single-peaked fitness landscape. The mutation rates are considered very low, making the mutation-selection dynamics sequential. Surprisingly, a structure with a poor ability to fix beneficial mutants outcompetes the well-mixed population in the long run by achieving higher fitness. This result is explained by the structure’s ability to reject disadvantageous mutants more efficiently. Subsequently, we discovered that this phenomenon occurs in the majority of randomly generated spatial structures. Consequently, it is not only the beneficial mutant regime that is relevant for adaptive evolution, but the deleterious mutant regime is equally important. Birth-death models are frequently employed to understand the interplay of natural selection and genetic drift in evolving populations. While it is known that the so-called Birth-death and death-Birth updating leads to dif- ferent evolutionary outcomes on spatial structures, the choice of individual moving to vacant sites also considerably affect the dynamics. We observed that allowing parent individuals to replace dead individuals yields substan- tially different results as compared to the default choice of offspring replacing the dead individuals. This observation led to the identification of a new class of graphs, namely amplifiers of fixation, where a structure exhibits a higher probability of fixation than the complete graph, regardless of the mutant’s fitness. Notably, one of the example graphs has a non-zero probability of fixation for deleterious mutants, even when the population size tends to in- finity. This finding contradicts the intuition from the previous studies on structured and well-mixed populations, where the probability of fixation for deleterious mutants diminishes for large population sizes. Furthermore, another category of graphs, known as amplifiers of selection, generally exhibits a longer fixation time than the complete graph, making them more restrictive to the weak mutation approximation. Upon examining high mutation rate dynamics, we observed that the self-looped amplifiers of selection, which achieve higher fitness in the low mutation rate regime, actually attain lower fitness than the well-mixed population and suppressors of selection. This suggests that amplifiers of selection may not be a reliable choice for structures adapting better than the well-mixed population. Finally, to experimentally validate our results obtained from the one- node-one-individual framework, a theoretical extension to structured metapop- ulations is required. We provide a mapping between the network of individ- uals and the network of demes that can be utilised to transfer the one-node- one-individual results to the metapopulation level.
