Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, Konkoly-Thege Miklós út 29-33., Budapest, H-1121, Hungary.
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., Szeged, H-6720, Hungary.
BMC Ecol Evol. 2024 May 20;24(1):65. doi: 10.1186/s12862-024-02257-8.
Classical matrix game models aim to find the endpoint of behavioural evolution for a set of fixed possible interaction outcomes. Here, we introduce an evolutionary model in which not only the players' strategies but also the payoff matrix evolves according to natural selection.
We start out from the hawk-dove matrix game and, in a way that is consistent with the monomorphic model setup of Maynard Smith and Price, introduce an evolving phenotypic trait that quantifies fighting ability and determines the probability of winning and the cost of losing escalated hawk-hawk fights. We define evolutionarily stable phenotypes as consisting of an evolutionarily stable strategy and an evolutionarily stable trait, which in turn describes a corresponding evolutionarily stable payoff matrix.
We find that the maximal possible cost of escalating fights remains constant during evolution assuming a separation in the time scales of fast behavioural and slow trait selection, despite the fact that the final evolutionarily stable phenotype maximizes the payoff of hawk-hawk fights. Our results mirror the dual nature of Darwinian evolution whereby the criteria of evolutionary success, as well as the successful phenotypes themselves, are a product of natural selection.
经典的矩阵博弈模型旨在为一系列固定的可能交互结果找到行为演化的终点。在这里，我们引入了一个进化模型，其中不仅玩家的策略，而且收益矩阵也根据自然选择进化。
我们从鹰鸽博弈开始，以一种与梅纳德·史密斯和普赖斯的单形模型设置一致的方式，引入了一个进化的表型特征，它量化了战斗能力，并确定了赢得和输掉升级鹰鹰战斗的概率。我们将进化稳定的表型定义为由进化稳定策略和进化稳定特征组成，这反过来又描述了相应的进化稳定收益矩阵。
我们发现，假设快速行为选择和缓慢特征选择之间的时间尺度分离，在进化过程中，升级战斗的最大可能成本保持不变，尽管最终进化稳定的表型使鹰鹰战斗的收益最大化。我们的结果反映了达尔文进化的双重性质，即进化成功的标准，以及成功的表型本身，都是自然选择的产物。
