We investigate the problem of the predominance and survival of “weak” species in the context of the simplest generalization of the spatial stochastic rock-paper-scissors model to four species by considering models in which one, two, or three species have a reduced predation probability. We show, using lattice based spatial stochastic simulations with random initial conditions, that if only one of the four species has its probability reduced, then the most abundant species is the prey of the “weakest” (assuming that the simulations are large enough for coexistence to prevail). Also, among the remaining cases, we present examples in which “weak” and “strong” species have similar average abundances and others in which either of them dominates—the most abundant species being always a prey of a weak species with which it maintains a unidirectional predator-prey interaction. However, in contrast to the three-species model, we find no systematic difference in the global performance of weak and strong species, and we conjecture that a similar result will hold if the number of species is further increased. We also determine the probability of single species survival and coexistence as a function of the lattice size, discussing its dependence on initial conditions and on the change to the dynamics of the model which results from the extinction of one of the species.

中文翻译：

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在石头剪刀布模型最简单的泛化为四个物种的情况下，弱物种的性能。

我们通过考虑其中一种，两种或三种物种的捕食性降低的模型，在将空间随机石头剪刀布模型最简单地概括为四种物种的情况下，研究了“弱”物种的优势和生存问题。可能性。我们显示，使用具有随机初始条件的基于格的空间随机模拟，如果只有四个物种之一的概率降低，则最丰富的物种是“最弱”物种的猎物（假设模拟足够大，可以共存）占上风）。另外，在其余情况下，我们提供了一些示例，其中“弱”和“强”物种的平均丰度相似，而其他物种则以其中的一个为主-最丰富的物种始终是弱物种的猎物，与之保持单向的捕食者－猎物相互作用。但是，与三物种模型相反，我们发现弱物种和强物种的整体性能没有系统上的差异，并且我们推测，如果物种数量进一步增加，也会产生相似的结果。我们还确定了单个物种存活和共存的概率与晶格大小的关系，并讨论了其对初始条件的依赖以及对一种物种灭绝导致的模型动力学变化的依赖性。我们发现弱种和强种的全球性能没有系统上的差异，并且我们推测，如果进一步增加种的数量，也会得到相似的结果。我们还确定了单个物种存活和共存的概率与晶格大小的关系，并讨论了其对初始条件的依赖以及对一种物种灭绝导致的模型动力学变化的依赖性。我们发现弱种和强种的全球性能没有系统上的差异，并且我们推测，如果进一步增加种的数量，也会得到相似的结果。我们还确定了单个物种存活和共存的概率与晶格大小的关系，并讨论了其对初始条件的依赖以及对一种物种灭绝导致的模型动力学变化的依赖性。