Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India.
Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA.
Chaos. 2024 Feb 1;34(2). doi: 10.1063/5.0190800.
While quite a few recent papers have explored game-resource feedback using the framework of evolutionary game theory, almost all the studies are confined to using time-continuous dynamical equations. Moreover, in such literature, the effect of ubiquitous chaos in the resulting eco-evolutionary dynamics is rather missing. Here, we present a deterministic eco-evolutionary discrete-time dynamics in generation-wise non-overlapping population of two types of harvesters-one harvesting at a faster rate than the other-consuming a self-renewing resource capable of showing chaotic dynamics. In the light of our finding that sometimes chaos is confined exclusively to either the dynamics of the resource or that of the consumer fractions, an interesting scenario is realized: The resource state can keep oscillating chaotically, and hence, it does not vanish to result in the tragedy of the commons-extinction of the resource due to selfish indiscriminate exploitation-and yet the consumer population, whose dynamics depends directly on the state of the resource, may end up being composed exclusively of defectors, i.e., high harvesters. This appears non-intuitive because it is well known that prevention of tragedy of the commons usually requires substantial cooperation to be present.
虽然最近有相当多的论文使用进化博弈论的框架探索了游戏资源反馈，但几乎所有的研究都局限于使用时间连续的动力方程。此外，在这些文献中，普遍存在的混沌对生态进化动力学的影响相当缺失。在这里，我们提出了一种确定性的生态进化离散时间动力学，在两代非重叠的两种收割者种群中，一种收割者的收割速度比另一种快，消耗一种自我更新的资源，这种资源能够表现出混沌动力学。根据我们的发现，有时混沌仅局限于资源或消费者群体的动力学，就会出现一个有趣的场景：资源状态可以持续地、混沌地波动，因此，它不会消失，导致公共资源的悲剧——由于自私的无差别开发而导致资源的灭绝——而消费者群体的动力学直接依赖于资源的状态，最终可能完全由缺陷者组成，即高收割者。这似乎不符合直觉，因为众所周知，预防公共资源悲剧通常需要存在大量的合作。
