Function-valued adaptive dynamics and optimal control theory
Function-valued adaptive dynamics and optimal control theory
复制标题
函数值自适应动力学和最优控制理论
DOI：
10.1007/s00285-012-0549-2
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发表时间：
2012
影响因子：
1.9
通讯作者：
U. Dieckmann
中科院分区：
文献类型：
--
作者：
K. Parvinen;M. Heino;U. Dieckmann
在本文中，我们进一步发展了功能价值特质的适应性动力学理论。以前的工作集中在模型上，其中入侵适应度可以写成积分，其中每个参数值的被积函数仅是该参数值处策略值的函数。对于这种类型的直接效应模型，可以使用变分法找到奇异策略，奇异策略需要满足环境反馈的欧拉方程。在更广泛、更机械化的模型类别中，函数值策略影响微分方程描述的过程，并且适应度可以表示为积分，其中每个参数值的被积函数既取决于策略又取决于该参数值处的过程变量。一般来说，变分法无助于分析这一更广泛的模型类别。在这里，我们解释如何使用最优控制理论在此类过程介导模型中找到奇异策略。特别是，我们表明单一策略需要满足庞特里亚金的环境反馈最大化原则。我们通过研究决定季节性开花时间表的策略的演变来证明这种方法的实用性。
In this article we further develop the theory of adaptive dynamics of function-valued traits. Previous work has concentrated on models for which invasion fitness can be written as an integral in which the integrand for each argument value is a function of the strategy value at that argument value only. For this type of models of direct effect, singular strategies can be found using the calculus of variations, with singular strategies needing to satisfy Euler’s equation with environmental feedback. In a broader, more mechanistically oriented class of models, the function-valued strategy affects a process described by differential equations, and fitness can be expressed as an integral in which the integrand for each argument value depends both on the strategy and on process variables at that argument value. In general, the calculus of variations cannot help analyzing this much broader class of models. Here we explain how to find singular strategies in this class of process-mediated models using optimal control theory. In particular, we show that singular strategies need to satisfy Pontryagin’s maximum principle with environmental feedback. We demonstrate the utility of this approach by studying the evolution of strategies determining seasonal flowering schedules.