We develop a \(2\times 2\) evolutionary matrix game to model vegetation dynamics due to the effect of autotoxicity. The phenomenon of autotoxicity refers to the rise in soil of negative conditions for plant performance induced by the plants themselves. Relating the Nash Equilibrium Strategies of the game to the stability of the equilibrium points of the induced population dynamics, we investigate under which conditions coexistence of low and highly sensitive to autotoxicity plants occurs and under which a monospecific population dominates the competition. Based on this classification, we investigate the optimal distribution of the two distinct types of plants in order to maximize the cumulative total fitness and determine if this distribution is stable. The primary outcome of this study is to analyze the necessary conditions for achieving the highest total fitness in both mixed and monospecific populations of low-sensitivity plants. In contrast, we argue that a monospecific population of highly sensitive plants can never maximize overall fitness.

我们开发了一个\(2\times 2\)进化矩阵游戏来模拟由于自毒性作用而产生的植被动态。自毒现象是指植物自身引起的土壤中不利于植物生长的不利条件的增加。将博弈的纳什均衡策略与诱导种群动态平衡点的稳定性联系起来，我们研究了在什么条件下对自毒性植物低度和高度敏感的植物会发生共存，以及在什么情况下单特异性种群在竞争中占主导地位。基于这种分类，我们研究了两种不同类型植物的最佳分布，以便最大化累积总适应度并确定该分布是否稳定。这项研究的主要成果是分析低敏感性植物的混合和单一种群实现最高总体适应度的必要条件。相比之下，我们认为高度敏感植物的单一种群永远无法最大化整体适应性。