Effects of the Mode of Competition on Stationary Size Distribution in Plant Populations

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Abstract
The effects of the mode of between-individual competition on the stationary size distribution in uneven-aged and continually reproducing tree populations were investigated theoretically, based on the diffusion and continuity equation models. The B(t, x) function, which gives a measure proportional to total leaf area of individual trees larger than dbh (trunk diameter at breast height) x at time t, expresses the effect of one-sided competition on the subject individual of dbh x. The effect of two-sided competition on individuals of any size is equally given by B(t, x0), i.e. total leaf area of the stand (or LAI), where x0 is the minimum dbh. The following two points, which were shown by Kohyama (1991) from results of model simulation, were theoretically derived: (1) the effect of the diffusion term [D(t, x) function] of the diffusion model on the stationary size distribution is small for the range of parameter values obtained empirically for the warm-temperate and tropical rain forests; (2) the shape of the stationary size distribution under one-sided competition is less changed by a change in the seedling supply rate than under two-sided competition. The following two points were further shown theoretically: (3) one-sided competition is likely to lead to a monotonically decreasing size distribution of dbh with the peak at x = x0, which is a characteristic of the rain forest; (4) the slope of size distribution of dbh steepens as one-sided competition intensifies. Relationships between the mode of competition and the stability of population structure, and general functional forms of one-sided and two-sided competition are discussed.

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