Classification of ecological stability in finite populations Ching-I Huang ^{1*}, Hsiu-Hau Lin^{1}, Chun-Chung Chen^{2}^{1}Department of Physics, National Tsing Hua University, Hsinchu, Taiwan^{2}Institute of Physics, Academia Sinica, Taipei, Taiwan* presenting author:Ching-I Huang, email:microdreamy@gmail.com 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 g
_{c} = 1. Though the evolutionary dynamics is dramatically different depending on the sign of the relative payoff Δg = g - g_{c}, 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 |