Biology – Quantitative Biology – Populations and Evolution
Scientific paper
2009-01-08
Phys. Rev. E 79, 062901 (2009)
Biology
Quantitative Biology
Populations and Evolution
6 pages, 7 figures
Scientific paper
10.1103/PhysRevE.79.062901
We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance $R_{max}$ in Newman-Watts networks with the long-rang connection probability $p$, we depict more realistically the stochastic interactions among species within ecosystems. When we fix mobility and vary the value of $p$ or $R_{max}$, the Monte Carlo simulations show that the spiral waves grow in size, and the system becomes unstable and biodiversity is lost with increasing $p$ or $R_{max}$. These results are similar to recent results of Reichenbach \textit{et al.} [Nature (London) \textbf{448}, 1046 (2007)], in which they increase the mobility only without including long-range interactions. We compared extinctions with or without long-range connections and computed spatial correlation functions and correlation length. We conclude that long-range connections could improve the mobility of species, drastically changing their crossover to extinction and making the system more unstable.
chen Yong
Qi Wei-Kai
Qin Shao-Meng
Zhang Guo-Yong
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