Self-thinning rule: a causal interpretation from ecological field theory

The self-thinning rule relates plant mass to plant density in crowded, even-aged stands by a power-law equation with an exponent −3/2. The rule is widely accepted as an empirical generalization and quantitative rule that applies across the plant kingdom. It has been called the only law in plant ecology. But the evidence supporting it has recently come under critical scrutiny. The theoretical and empirical bases for the density–mass boundary have been questioned. Here we use ecological field theory and statistical mechanics to show how the stochastic nature of ecological interactions among individuals, due to spatial field effects such as the availability of neighborhood resources at the microscopic level, leads to self-thinning at the macroscopic level. The self-thinning rule emerges as a natural result of our theoretical approach. Puzzling experimental data that contradict the rule are also explained.