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

The effects of the mode of between-individual competition onthe stationary size distribution in uneven-aged and continuallyreproducing 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 leafarea of individual trees larger than dbh (trunk diameter atbreast height) x at time t, expresses the effect of one-sidedcompetition on the subject individual of dbh x. The effect oftwo-sided competition on individuals of any size is equallygiven by B(t, x₀), i.e. total leaf area of the stand (or LAI),where x₀ is the minimum dbh. The following two points, whichwere shown by Kohyama (1991) from results of model simulation,were theoretically derived: (1) the effect of the diffusionterm D(t, x) function] of the diffusion model on the stationarysize distribution is small for the range of parameter valuesobtained empirically for the warm-temperate and tropical rainforests; (2) the shape of the stationary size distribution underone-sided competition is less changed by a change in the seedlingsupply rate than under two-sided competition. The followingtwo points were further shown theoretically: (3) one-sided competitionis likely to lead to a monotonically decreasing size distributionof dbh with the peak at x = x₀, which is a characteristic ofthe rain forest; (4) the slope of size distribution of dbh steepensas one-sided competition intensifies. Relationships betweenthe mode of competition and the stability of population structure,and general functional forms of one-sided and two-sided competitionare discussed. Diffusion model, one-sided competition, stability of population structure, stationary size distribution, two-sided competition