Optimal Allocation of Two Resources in Annual Plants

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 throughout its growing season as well as develop numerical schemes to implement the models in MATLAB. Our results suggest that what is optimal for an individual plant is highly dependent on initial conditions, and optimal growth has the effect of driving a wide range of initial conditions toward common configurations of biomass by the end of a growing season