Defensive alliances in spatial models of cyclical population interactions.
As a generalization of the three-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated, and a neutral interacting partner. Depending on their interaction topologies, all imaginable systems can be classified into four (isomorphic) groups exhibiting significantly different behaviors as a function of mutation rate. In three out of four cases three (or four) species form defensive alliances that maintain themselves in a self-organizing polydomain structure via cyclic invasions. Varying the mutation rate, this mechanism results in an ordering phenomenon analogous to that of magnetic Ising systems. The model explains a very basic mechanism of community organization, which might gain important applications in biology, economics, and sociology.
Szabó
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G
Research Institute for Technical Physics and Materials Science, PO 49, H-1525 Budapest, Hungary.
Czárán
T
T
D004463:Ecology; D017753:Ecosystem; D005716:Game Theory; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D009154:Mutation; D011153:Population