A Spatially Explicit Game-Theoretic Model of Optimal Defense Strategies in Herbaceous Plants with Herbivore Movement

Insect behavior has been demonstrated to be influenced by the presence of certain chemicals in herbaceous plants. In particular, host plant choice by insect herbivores has been shown to depend on the the presence and odor of chemical in the plant. Thus, if the chemical plume reaches far enough, allocation to defense may also be influenced by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along with ideas from game theory, to examine how defense strategies in individual plants influence population outcomes in herbaceous plants. We incorporate an individual-based model for the herbivore population and allow the herbivores to move between plants. In this case, defense is only a neighborhood benefit, and this approach yields the possibility of a population evolving to consist of only cooperators or only defectors (pure stable strategy), as well as the possibility of a mixed stable strategy. We show that our model offers a theoretical explanation for the neighborhood effect seen in empirical evidence. This research was done as part of MC's thesis. Data was obtained entirely through simulation and modeling. All code was written by MC, and all analysis, data visualization, and simulation was completed by MC. See the `steps to reproduce' for usage instructions.昆虫行为已被证实受草本植物内特定化学物质的影响。具体而言，植食性昆虫的寄主选择已被证明取决于植物中化学物质的存在及其气味。因此，若化学羽流（chemical plume）的传播距离足够远，环境中其他植物所采用的防御策略，亦可能影响植物的防御资源分配。我们将空间进化博弈论（spatial evolutionary game theory）应用于植物的最优资源分配问题，以此纳入邻域防御效应，其中合作者为投入防御的植物，叛逃者为不投入防御的植物。我们结合随机动态规划模型（stochastic dynamic programming model）与博弈论相关思路，探究单个植物的防御策略如何影响草本植物种群的动态结果。我们还为植食性昆虫种群构建了基于个体的模型（individual-based model），并允许昆虫在不同植物间移动。在此场景下，防御仅能带来邻域收益，该方法得出的种群演化结果既可能仅包含合作者或仅包含叛逃者（纯稳定策略，pure stable strategy），也可能存在混合稳定策略（mixed stable strategy）。我们的模型可为实验证据中观察到的邻域效应提供理论解释。本研究为MC的学位论文的一部分。所有数据均通过模拟与建模获得，所有代码均由MC编写，所有分析、数据可视化（data visualization）与模拟工作均由MC完成。请参阅`复现步骤（steps to reproduce）`以获取使用说明。