Plant population growth and competition in a light gradient: A mathematical model of canopy partitioning

Abstract

Can a difference in the heights at which plants place their leaves, a pattern we call canopy partitioning, make it possible for two competing plant species to coexist? To find out, we examine a model of clonal plants living in a nonseasonal environment that relates the dynamical behavior and competitive abilities of plant populations to the structural and functional features of the plants that form them. This examination emphasizes whole plant performance in the vertical light gradient caused by selfshading. This first of three related papers formulates a prototype single species CANOPY STRUCTURE MODEL from biological first principles and shows how all plant properties work together to determine population persistence and equilibrium abundance. Population persistence is favored, and equilibrium abundance is increased, by high irradiance, high maximum photosynthesis rate, rapid saturation of the photosynthetic response to increased irradiance, low tissue respiration rate, small amounts of stem and root tissue necessary to support the needs of leaves, and low density of leaf, stem, and root tissue. In particular, equilibrium abundance decreases as mean leaf height increases because of the increased cost of manufacturing and maintaining stem tissue. All conclusions arise from this formulation by straightforward analysis. The argument concludes by stating this formulation's straightforward extension, called a CANOPY PARTITIONING MODEL, to two competing species.

Understanding height-structured competition in forests: is there anR*for light?

“…Although the literature contains other analytical and computational examinations of height-structured competition, and its implications for community dynamics (e.g. Kohyama 1993Kohyama , 1994Nakashizuka & Kohyama 1995;Perry et al 2003;Vance & Nevai 2007), we are not aware of any other model formulation that has been compared with the dynamics of real forest communities to this extent.…”

Kolmogorov-type competition model with finitely supported allocation profiles and its applications to plant competition for sunlight

“…System (1) describes the interactions of two clonal plant species that compete for sunlight by placing their leaves at multiple heights [21,32]. For species i, its total leaf area is denoted by x i , its vertical leaf area density with respect to height z (i.e.…”

“…The growth and cost parameters γ i and C i in turn depend on close to a dozen primary plant parameters such as tissue mass, mean stem height, and tissue metabolic rate. For a complete description of these parameters and functions and how they relate to Equation (1) see [32].…”

A Kolmogorov-type competition model with multiple coexistence states and its applications to plant competition for sunlight

“…The system (1.1) arises in a recent study of plant competition for sunlight [11,16]. It describes the interactions of two competing plant species whose leaves are positioned at different heights within a light gradient.…”

“…for grasses which distribute their photosynthetic material uniformly over a range of heights (with 0 a < b) and φ i (x) = φ max I in I in + J e κx , x 0, (1.2) for the photosynthetic reaction of their leaves to shade [16]. The resulting canopy partitioning model has been used to predict that the competitive exclusion principle [6] may not apply to some plants that compete for sunlight [11].…”