Competition Models for Plant Stems

TL;DR

This paper develops mathematical models for plant stem competition for sunlight, optimizing stem shapes and leaf density to maximize light capture while considering water transport costs, and analyzes equilibrium among competing plants.

Contribution

It introduces a novel optimization framework for plant stem shapes and proves the uniqueness of competitive equilibria among multiple plants.

Findings

Optimal stem shapes depend on light intensity profiles.

Unique equilibrium solutions exist for the competitive models.

The models provide insights into plant adaptation strategies.

Abstract

The models introduced in this paper describe a uniform distribution of plant stems competing for sunlight. The shape of each stem, and the density of leaves, are designed in order to maximize the captured sunlight, subject to a cost for transporting water and nutrients from the root to all the leaves. Given the intensity of light, depending on the height above ground, we first solve the optimization problem determining the best possible shape for a single stem. We then study a competitive equilibrium among a large number of similar plants, where the shape of each stem is optimal given the shade produced by all others. Uniqueness of equilibria is proved by analyzing the two-point boundary value problem for a system of ODEs derived from the necessary conditions for optimality.