Self-thinning exponent correlated with allometric measures of plant geometry

The -3/2 power rule of self-thinning, which describes the course of growth and mortality in crowded, even-aged plant stands, predicts that average mass is related to plant density by a power equation with exponent -3/2. The rule is widely accepted as an empirical generalization and quantitative rule or law. Simple geometric models of space occupation by growing plants yield a power equation, but the exponent can differ from -3/2 when realistic assumptions about the allometric growth of plants are considered. Because such deviations conflict with the empirical evidence for the -3/2 value as a law-like constant, the geometric model have not produced an accepted explanation and the thinning rule remains poorly understood. Recent studies have concluded that thinning exponents can deviate more widely from -3/2 than previously thought, motivating the present re-evaluation of the geometric explanation. I extend the simple models to predict the relationships of the thinning exponent to allometric exponents derived from commonly measured stand dimensions, such as height, average mass, average bole diameter at breast height (DBH), and average bole basal area. If the form and exponent of the thinning equation arise from the geometry of space filling, then thinning exponents should be systematically related to the exponents of allometric equations relating average height to average mass, average height to average DBH, and average height to average basal area. I also predict some values for the slopes and intercepts of regression lines relating thinning exponents to the allometric exponents. The predictions are verified by statistically comparing the thinning exponents and allometric exponents of self-thinning populations. The expected negative correlations are present and statistically significant (P @< .05), and the slopes and intercepts of linear regressions relating thinning exponents to allometric exponents are near the predicted values. These results support the hypothesis that the thinning equation arises from the geometry of space filling, but recognition that thinning exponents differ from -3/2 as predicted by simple geometric considerations weakens the case for a quantitative rule or law.