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Journal of Mathematical Biology

, Volume 55, Issue 1, pp 105–145

# Plant interspecies competition for sunlight: a mathematical model of canopy partitioning

• Andrew L. Nevai
• Richard R. Vance
Article

## Abstract

We examine the influence of canopy partitioning on the outcome of competition between two plant species that interact only by mutually shading each other. This analysis is based on a Kolmogorov-type canopy partitioning model for plant species with clonal growth form and fixed vertical leaf profiles (Vance and Nevai in J. Theor. Biol., 2007, to appear). We show that canopy partitioning is necessary for the stable coexistence of the two competing plant species. We also use implicit methods to show that, under certain conditions, the species’ nullclines can intersect at most once. We use nullcline endpoint analysis to show that when the nullclines do intersect, and in such a way that they cross, then the resulting equilibrium point is always stable. We also construct surfaces that divide parameter space into regions within which the various outcomes of competition occur, and then study parameter dependence in the locations of these surfaces. The analysis presented here and in a companion paper (Nevai and Vance, The role of leaf height in plant competition for sunlight: analysis of a canopy partitioning model, in review) together shows that canopy partitioning is both necessary and, under appropriate parameter values, sufficient for the stable coexistence of two hypothetical plant species whose structure and growth are described by our model.

## Keywords

Canopy partitioning model Plant competition Light competition Mathematical model Stable coexistence Canopy structure model

## Mathematics Subject Classification (2000)

92D25 34C23 34D23 92C80 92D40

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## Copyright information

© Springer-Verlag 2007

## Authors and Affiliations

1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
2. 2.Mathematical Biosciences InstituteThe Ohio State UniversityColumbusUSA
3. 3.Department of Ecology and Evolutionary BiologyUniversity of CaliforniaLos AngelesUSA