The spatial dilemmas of evolution. (English) Zbl 0870.92011

Nowak, Martin A.; May, Robert M.

Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, No. 1, 35-78 (1993).

Summary: Evolutionary game theory can be extended to include spatial dimensions. The individual players are placed in a two-dimensional spatial array. In each round every individual “plays the game” with its immediate neighbours. After this, each site is occupied by its original owner or by one of the neighbours, depending on who scored the highest payoff. These rules specify a deterministic cellular automaton.
We find that spatial effects can change the outcome of frequency dependent selection. Strategies may coexist that would not coexist in homogeneous populations. Spatial games have interesting mathematical properties. There are static or chaotically changing patterns. For symmetrical starting conditions we find “dynamical fractals” and “evolutionary kaleidoscopes.” There is a new world to be explored.

MSC:

92D15	Problems related to evolution
91A40	Other game-theoretic models

Keywords:

dynamical fractals; evolutionary kaleidoscopes; two-dimensional spatial array; deterministic cellular automaton; frequency dependent selection