An application of bole surface growth model: a transitional status of -3/2 rule

TL;DR

This paper investigates the -3/2 rule in forest stand self-thinning, showing it as a transitional, obligatory state during growth rather than an asymptote, using a geometric model applied to Douglas-fir and Scots pine data.

Contribution

It demonstrates that the -3/2 slope is a transitional phase in forest self-thinning, not a final state, and introduces a geometric model to analyze this process.

Findings

The -3/2 slope occurs at a specific transitional stage.

Total bole surface area remains constant at -3/2 slope.

The model aligns well with real forest data.

Abstract

In the research scope of forest stand self-thinning, the analysis reveals a broad picture in which the -3/2 rule takes a definite and special place. The 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 probable, 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. Inevitably, a time will come when the slope is exactly equals -3/2. In other words, the slope -3/2 is an obligatory state in the course of self-thinning of a forest stand. At the very time of -3/2 slope two particular features coincide with it. One is that the total bole surface area remains constant. The length of the constancy stage would probably vary with species, initial stand densities, their spatial arrangements, conditions of growth, and other specific factors. Another feature of the time is that a geometric similarity in the growth of the forest stand takes place, which is not in a contradiction with the -3/2 rule as it had been formulated by its authors. To put it shortly, the slope -3/2: i) is a very specific and obligatory state in the process of forest stand growth and ii) is not an asymptote but rather a transitional point (span) in the time of growth. These two assertions may be called a transitional status of the -3/2 rule. The geometric model of a forest stand (Gavrikov, 2014) has proved to be rather helpful at analyzing of real forest stand structure and dynamics. Despite of its extreme simplicity (it uses cones as representations of trees) the model looks like having enough similarity with real even-aged forests since the model's predictions are often reasonably close to measured values of power exponents.