Eco-Evolutionary Feedback and the Invasion of Cooperation in Prisoner's Dilemma Games

Unveiling the origin and forms of cooperation in nature poses profound challenges in evolutionary ecology. The prisoner's dilemma game is an important metaphor for studying the evolution of cooperation. We here classified potential mechanisms for cooperation evolution into schemes of frequency- and density-dependent selection, and focused on the density-dependent selection in the ecological prisoner's dilemma games. We found that, although assortative encounter is still the necessary condition in ecological games for cooperation evolution, a harsh environment, indicated by a high mortality, can foster the invasion of cooperation. The Hamilton rule provides a fundamental condition for the evolution of cooperation by ensuring an enhanced relatedness between players in low-density populations. Incorporating ecological dynamics into evolutionary games opens up a much wider window for the evolution of cooperation, and exhibits a variety of complex behaviors of dynamics, such as limit and heteroclinic cycles. An alternative evolutionary, or rather succession, sequence was proposed that cooperation first appears in harsh environments, followed by the invasion of defection, which leads to a common catastrophe. The rise of cooperation (and altruism), thus, could be much easier in the density-dependent ecological games than in the classic frequency-dependent evolutionary games.揭示自然界中合作的起源与形式，是进化生态学领域的重大研究挑战。囚徒困境博弈（Prisoner's Dilemma Game）是研究合作进化的重要隐喻工具。本文将合作进化的潜在机制划分为频率依赖选择与密度依赖选择两大类，并聚焦于生态囚徒困境博弈中的密度依赖选择机制。研究发现，尽管选型相遇（assortative encounter）仍是生态博弈中合作进化的必要条件，但以高死亡率表征的严苛环境，能够促进合作策略的入侵扩散。汉密尔顿法则（Hamilton Rule）通过保障低密度种群中博弈参与者间的亲缘系数提升，为合作进化提供了核心前提条件。将生态动力学融入进化博弈，为合作进化开辟了更为广阔的研究空间，并展现出多样的复杂动力学行为，例如极限环与异宿环。本文提出了一套另类的进化（更准确地说是演替）序列：合作率先在严苛环境中萌生，随后遭遇背叛策略的入侵，最终引发全局性灾变。因此，相较于经典的频率依赖型进化博弈，在密度依赖型生态博弈中，合作（乃至利他行为）的涌现要容易得多。