A study of self-thinning using coupled allometric equations: implications for coastal Douglas-fir stand dynamics

The -3/2 self-thinning rule was proposed with the hypothesis that in closed canopy stands, plant mass is proportional to the cube of a linear size dimension, and that density is proportional to the square of this dimension, thus defining the isometric model. To account for the morphological differences among species, the allometric model was proposed as a refinement of the isometric model, therefore linking the self-thinning exponent's dependence to species-specific allometric parameters. In this study, it is proposed that each stand has its own self-thinning trajectory boundary, determined by its own unique stand allometry. An S-system is used to facilitate coupled allometric relationships under the influence of self-thinning. Upon calibrating this model to Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) permanent sample plots, located throughout western Washington, western Oregon, and southwest British Columbia, the implications of coupled allometric equations are discussed and compared with the algebraic, isometric, and allometric models. The results support the use of simultaneous, coupled rate equations versus uncoupled static ones.