Abstract
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.
Highlights
The effect of population structure on evolutionary dynamics is a long-lasting research topic in evolutionary ecology and population genetics
For networks where each node represents a single individual, the isothermal theorem of evolutionary graph theory shows that the fixation probability is the same as the fixation probability of a well-mixed population if the temperature distribution is homogeneous across the whole
The temperature of a node defined as the sum over all the weights leads to that node. This theorem extends to structured meta-populations for any migration probability : If the underlying structure of the metapopulation that connects the patches is a regular network and the local population size is identical in each patch, the temperature of all individuals is identical, regardless of the value of the migration probability
Summary
The effect of population structure on evolutionary dynamics is a long-lasting research topic in evolutionary ecology and population genetics. Evolutionary graph theory[1] analyses the evolutionary dynamics in network-structured populations, where individuals are located on the nodes of a graph and can replace each other via the links This approach can be motivated by several biological systems, from the spread of cancerous mutations through colonic crypts to the invasion of ecosystems structured by rivers. An important question that arises in the application of evolutionary graph theory is whether the results derived for networks of individuals carry over to networks of small populations. Such meta-populations have been analyzed extensively in ecology, where they correspond to fragmented habitats[17,18,19]. With few exceptions, see e.g.33, these studies assume a well-mixed population of patches
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