A stochastic model and the moment dynamics of the growth and size distribution in plant populations

Abstract

A stochastic model for growth and size distribution in plant populations is proposed, which is described by the Kolmogorov forward equation (diffusion equation). The moments of size distribution are calculated based on the diffusion process. Theoretical analyses are made of the mechanisms and the dynamics of size distribution pattern of an even-aged plant population based on the experiemntal data of Impatiens balsamina L. Plant height, stem diameter and individual plant weight have their specific size-dependent growth pattern, and show almost normal, positively skewed and more positively skewed size distribution, respectively. The stochastic model incorporating size-dependence of individual growth explains these phenomena theoretically. The ecological meaning of the growth and size distribution patterns is discussed. The hypothesis that dry matter production by photosynthesis is first allocated to height growth and then to diameter growth is proposed.