An application of bole surface growth model: a transitional status of ‘−3/2’ rule

Abstract

The findings regarding the self-thinning rule in forest stands indicate that the rule may have a sort of ‘asymptotic’ status. It means the admittance of two theses: (1) the slopes of self-thinning trajectories may deviate from −3/2 value; (2) in the space ‘size–density,’ a limiting line exists that serves as a ‘goal’ for population dynamics which this dynamics tends to. An application of the simple geometrical model to the Douglas-fir and Scots pine data suggests that the slope of the self-thinning curve will not remain constant during the course of growth and self-thinning of a single forest stand. Most probably, at the initial stages of stand growth, the slope will be less than −3/2, and at old ages of the stand, the slope will be higher than −3/2. The slope −3/2 is thus an obligatory state in the course of self-thinning of a forest stand. At the very time of −3/2 slope, two particular features fit together. One is that the total bole surface area remains constant. Another feature of the −3/2 slope time is that geometric similarity holds in the growth of the forest stand, which is not in a contradiction with the ‘−3/2’ rule as it had been formulated by its authors. That is, the slope −3/2 (1) is a very specific and obligatory state in the process of forest stand growth and (2) is not an asymptote-like ‘goal’ but rather a transitional point (or may be a span) in the time of growth. These two assertions may be called a transitional status of the ‘−3/2’ rule.