In this letter, we investigate the population dynamics in a May-Leonard formulation of the rock-paper-scissors (RPS) game in which one or two species, which we shall refer to as “weak”, have a reduced predation or reproduction probability. We show that in a non-spatial model the stationary solution where all three species coexist is always unstable, while in a spatial stochastic model coexistence is possible for a wide parameter space. We find that a reduced predation probability results in a significantly higher abundance of “weak” species, in models with either one or two “weak” species, as long as the simulation lattices are sufficiently large for coexistence to prevail. On the other hand, we show that a reduced reproduction probability has a smaller impact on the abundance of “weak” species, generally leading to a slight decrease of its population size —the increase of the population size of one of the “weak” species being more than compensated by the reduction of the other, in the two-species case. We further show that the species abundances in models where both predation and reproduction probabilities are simultaneously reduced may be accurately estimated from the results obtained considering only a reduction of either the predation or the reproduction probability.

在这封信中，我们研究了石头剪刀布 (RPS) 游戏的 May-Leonard 公式中的种群动态，其中一两个物种，我们将其称为“弱”物种，其捕食或繁殖概率降低. 我们表明，在非空间模型中，所有三个物种共存的平稳解总是不稳定的，而在空间随机模型中，对于宽参数空间共存是可能的。我们发现，在具有一个或两个“弱”物种的模型中，只要模拟晶格足够大，可以共存，那么捕食概率的降低会导致“弱”物种的丰度显着增加。另一方面，我们表明降低的繁殖概率对“弱”物种的丰度影响较小，通常会导致其种群规模略有减少——在两个物种的情况下，一个“弱”物种的种群规模的增加被另一个物种的减少所抵消。我们进一步表明，在捕食和繁殖概率同时降低的模型中，物种丰度可以从仅考虑减少捕食或繁殖概率的结果中准确估计。