Technical University of Denmark, Department of Applied Mathematics and Computer Science - DTU Compute, Building 303B, Matematiktorvet, 2800, Kgs. Lyngby, Denmark.
Theor Popul Biol. 2022 Aug;146:36-45. doi: 10.1016/j.tpb.2022.06.002. Epub 2022 Jun 28.
Game theory has emerged as an important tool to understand interacting populations in the last 50 years. Game theory has been applied to study population dynamics with optimal behavior in simple ecosystem models, but existing methods are generally not applicable to complex systems. In order to use game-theory for population dynamics in heterogeneous habitats, habitats are usually split into patches and game-theoretic methods are used to find optimal patch distributions at every instant. However, populations in the real world interact in continuous space, and the assumption of decisions based on perfect information is a large simplification. Here, we develop a method to study population dynamics for interacting populations, distributed optimally in continuous space. A continuous setting allows us to model bounded rationality, and its impact on population dynamics. This is made possible by our numerical advances in solving multiplayer games in continuous space. Our approach hinges on reformulating the instantaneous game, applying an advanced discretization method and modern optimization software to solve it. We apply the method to an idealized case involving the population dynamics and vertical distribution of forage fish preying on copepods. Incorporating continuous space and time, we can model the seasonal variation in the migration, separating the effects of light and population numbers. We arrive at qualitative agreement with empirical findings. Including bounded rationality gives rise to spatial distributions corresponding to reality, while the population dynamics for bounded rationality and complete rationality are equivalent. Our approach is general, and can easily be used for complex ecosystems.
博弈论在过去 50 年中已成为理解相互作用的群体的重要工具。博弈论已被应用于研究具有简单生态系统模型中最优行为的种群动态，但现有的方法通常不适用于复杂系统。为了在异质生境中使用博弈论来研究种群动态，生境通常被划分为斑块，并且使用博弈论方法在每个瞬间找到最优的斑块分布。然而，现实世界中的种群在连续空间中相互作用，基于完美信息的决策假设是一个很大的简化。在这里，我们开发了一种方法来研究在连续空间中最优分布的相互作用种群的种群动态。连续的设置允许我们对有限理性进行建模，并对种群动态产生影响。这是通过我们在连续空间中解决多人游戏的数值进展来实现的。我们的方法取决于重新制定瞬时博弈，应用先进的离散化方法和现代优化软件来解决它。我们将该方法应用于涉及以桡足类为食的饲料鱼的种群动态和垂直分布的理想化情况。纳入连续的空间和时间，我们可以模拟光和种群数量的季节性变化。我们得到了与经验发现定性一致的结果。包含有限理性会导致与现实相对应的空间分布，而有限理性和完全理性的种群动态是等效的。我们的方法是通用的，并且可以轻松用于复杂的生态系统。
