Classification of ecological stability in finite populations
Ching-I Huang1*, Hsiu-Hau Lin1, Chun-Chung Chen2
1Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
2Institute of Physics, Academia Sinica, Taipei, Taiwan
* presenting author:Ching-I Huang,
We investigate the ecological stability of Rock-Paper-Scissors like ecosystems with finite population N by the extinction time in numerical simulation. The strength of payoff is characterized by a single parameter g with a critical strength gc = 1. Though the evolutionary dynamics is dramatically different depending on the sign of the relative payoff Δg = g - gc, it is quite remarkable that the extinction time with different Δg and N falls onto a universal scaling function. However, the universal scaling function disappears when individuals are placed in two-dimensional grids. This implies the strength of payoff is renormalized by the spatial networks among individuals. By introducing the biodiversity indicator N*, we are able to construct the global payoff matrix and also find the universal scaling function for two-dimensional ecological systems. The notion and the techniques developed here can be generally applied to the investigation of biodiversity of different systems with different spatial structures.

Keywords: Rock-Paper-Scissors games, ecological stability, spatial network