Tree size frequency distributions, plant density, age and community disturbance

We show that explicit mathematical and biological relationships exist among the scaling exponents and the allometric constants (alpha and beta, respectively) of log-log linear tree-community size frequency distributions, plant density N-T, and minimum, maximum and average stem diameters (D-min, D-max, and (D) over bar, respectively). As individuals grow in size and D-max increases, N-T is predicted to decrease as reflected by a decrease in the numerical value of alpha and an increase in the value of beta. Our derivations further show that N-T decreases as (D) over bar increases even if D-min or D-max remain unchanged. Because D-max and the age of the largest individuals in a community are correlated, albeit weakly, we argue that the interdependent relationships among the numerical values of alpha, beta, N-T, and (D) over bar shed light on the extent to which communities have experienced recent global disturbance. These predicted relationships receive strong statistical support using two large datasets spanning a broad spectrum of tree-dominated communities.