title: Competition and cooperation in one-dimensional stepping-stone models.
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.
authors.affiliation: Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. papers.korolev@gmail.com
authors.forename: K S
authors.initials: KS
authors.lastname: Korolev
authors.forename: David R
authors.initials: DR
authors.lastname: Nelson
mesh_terms: D005075:Biological Evolution; D003163:Competitive Behavior; D003299:Cooperative Behavior; D017753:Ecosystem; D008962:Models, Theoretical; D011157:Population Dynamics