A Canopy Photosynthesis Model for the Dynamics of Size Structure and Self-thinning in Plant Populations

A dynamic model for growth and mortality of individual plants in a stand was developed, based on the process of canopy photosynthesis, and assuming an allometric relationship between plant height and weight, i.e. allocation growth pattern of plant height and stem diameter. Functions G(t, x), for the mean growth rate of individuals of size x at time t, and M(t,x), for the mortality rate of individuals of size x at time t, were developed from this model and used in simulations. The dynamics of size structure were simulated, combining the continuity equation model, a simple version of the diffusion model, with these functions. Simulations reproduced several well-documented phenomena: (1) size variability in terms of coefficient of variation and skewness of plant weight increases at first with stand development and then stabilises or decreases with an onset of intensive self-thinning; (2) during the course of self-thinning, there is a power relationship between density and biomass per unit ground area, irrespective of the initial density and of the allocation-growth pattern in terms of the allometric parameter relating plant height and weight. The following were further shown by simulation: (a) competition between individuals in a crowded stand is never completely one-sided but always asymmetrically two-sided, even though competition is only for light; (b) plants of ‘height-growth’ type exhibit a greater asymmetry in competition than plants of ‘diameter-growth’ type, (c) the effect of competition on the growth of individuals in a crowded stand converges to a stationary state, even when the stand structure still changes greatly. All of these theoretical results can explain recent empirical results obtained from several natural plant communities. Finally, a new, general functional form for G(t, x) in a crowded stand is proposed based on these theoretical results, instead of a priori or empirical growth and competition functions.