Abstract
Mutualism is a major force driving evolution and sustaining ecosystems. Although the importance of spatial degrees of freedom and number fluctuations is well known, their effects on mutualism are not fully understood. With range expansions of microbes in mind, we show that, even when mutualism confers a selective advantage, it persists only in populations with high density and frequent migrations. When these parameters are reduced, mutualism is generically lost via a directed percolation (DP) process, with a phase diagram strongly influenced by an exceptional symmetric DP (DP2) transition.
Highlights
Cooperative mutualism is a major force driving evolution and sustaining ecosystems
When these parameters are reduced, mutualism is generically lost via a directed percolation process, with a phase diagram strongly influenced by an exceptional DP2 transition
C B mutualistic interactions, their existence is often difficult I to explain by a naive application of Darwinian natural selection: Cooperation can succumb to cheating [1] and, W R as we show here, to number fluctuations
Summary
The importance of spatial degrees of freedom and number fluctuations is well-known, their effects on mutualism are not fully understood. Such models do not allow systematic investigation of the role of migration and the magnitude of number fluctuations, which are important for the applications of the theory to natural and experimental populations.
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