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University of Nebraska - Lincoln
Department of Mathematics: Dissertations, Theses, and Student Research
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Full-Text Articles in Physical Sciences and Mathematics
Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar
Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar
Department of Mathematics: Dissertations, Theses, and Student Research
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. We use a stochastic dynamic programming model, along …
Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris
Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris
Department of Mathematics: Dissertations, Theses, and Student Research
The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process. We introduce two models for resource allocation in annual plants which extend classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits in annual plants. In each case, we use optimal control theory to determine the optimal resource allocation strategy for the plant …