Mathematical and Statistical Analysis of the -3/2 Power Rule of Self-Thinning in Even-Aged Plant Populations

摘要

The self-thinning rule for even-aged plant populations (also called the -3/2 power law or Yoda's law) is reviewed. This widely accepted but poorly understood generalization predicts that, through time, growth and mortality in a crowded population trace a straight thinning line of slope -3/2 in a log-log plot of average plant weight versus plant density. The evidence for this rule is examined, then reanalyzed to objectively evaluate the strength of support for the rule. Mathematical models are constructed to produce testable predictions about causal factors. Major problems in the evidence for the thinning rule include inattention to contradictory data, lack of hypothesis testing, inappropriate curve-fitting techniques, and the use of an invalid data transformation. The evidence does not support acceptance of the self-thinning rule as a quantitative biological law. The slopes and intercepts of size-density relationships are variable, and the slopes can be explained by simple geometric arguments. 30 figs., 28 tabs. (ERA citation 10:049647)