Game-Theoretic Optimal Resource Allocation and Defense Strategies in Herbaceous Plants

Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also 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. Our model builds on a stochastic dynamic programming model that accounts for metabolic cost of maintenance of stored resources when predicting optimal resource allocation to growth, reproduction, and storage; this cost is not commonly accounted for in previous models. For both annual and perennial plants, our model predicts an evolutionarily stable proportion of cooperators and defectors (mixed stable strategy), but the proportion of cooperators is higher in a population of perennial plants than in a population of annual plants. We also show that including a metabolic cost of maintaining stored resources does not change the proportion of cooperators but does decrease plant fitness and allocation to overwinter storage.已有实验证据表明，植株对植食动物的吸引程度，既会受到邻株的防御投入影响，也会受到目标植株（focal plant）自身的防御投入影响。因此，植株的防御资源分配不仅会受到植食作用的发生频率与强度的影响，还会受到环境中其他植株所采用的防御策略的调控。我们将空间进化博弈论（spatial evolutionary game theory）应用于植株的最优资源分配模型，以此纳入邻株防御效应：其中合作者指投入防御的植株，背叛者指未投入防御的植株。本模型基于随机动态规划（stochastic dynamic programming）模型构建，该模型在预测植株用于生长、繁殖与储存的最优资源分配时，会考虑储存资源维持所需的代谢成本；而此前的多数模型均未纳入这一成本项。针对一年生植物与多年生植物两类对象，本模型均预测出合作者与背叛者的进化稳定比例（即混合稳定策略），但多年生植物种群中的合作者比例高于一年生植物种群。此外我们还发现，纳入储存资源维持的代谢成本，并不会改变合作者的比例，但会降低植株的适合度以及用于越冬储存的资源分配量。