Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.
Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.
J Theor Biol. 2018 Aug 7;450:22-29. doi: 10.1016/j.jtbi.2018.04.005. Epub 2018 Apr 5.
The rock-paper-scissors (RPS) game is known as one of the simplest cyclic dominance models. This game is key to understanding biodiversity. Three species, rock (R), paper (P) and scissors (S), can coexist in nature. In the present paper, we first present a metapopulation model for RPS game with mutation. Only mutation from R to S is allowed. The total population consists of spatially separated patches, and the mutation occurs in particular patches. We present reaction-diffusion equations which have two terms: reaction and migration terms. The former represents the RPS game with mutation, while the latter corresponds to random walk. The basic equations are solved analytically and numerically. It is found that the mutation induces one of three phases: the stable coexistence of three species, the stable phase of two species, and a single-species phase. The phase transitions among three phases occur by varying the mutation rate. We find the conditions for coexistence are largely changed depending on metapopulation models. We also find that the mutation induces different paradoxes in different patches.
石头-剪刀-布（RPS）游戏是众所周知的最简单的循环优势模型之一。这个游戏是理解生物多样性的关键。在自然界中，有三种物种可以共存：石头（R）、剪刀（P）和布（S）。在本文中，我们首先提出了一个具有突变的 RPS 游戏的复域模型。只允许从 R 到 S 的突变。总种群由空间分离的斑块组成，突变发生在特定的斑块中。我们提出了具有两个项的反应-扩散方程：反应项和迁移项。前者代表具有突变的 RPS 游戏，而后者对应于随机游动。基本方程可以进行解析和数值求解。结果表明，突变会导致三种状态之一：三种物种的稳定共存、两种物种的稳定状态和单一物种状态。通过改变突变率，三个状态之间会发生相变。我们发现共存的条件会根据复域模型发生很大的变化。我们还发现，突变会在不同的斑块中引起不同的悖论。
