A Model for Growth and Self-thinning in Even-aged Monocultures of Plants

Abstract

A theoretical model is derived from simple postulates to describe the rates of growth and mortality of plants in populations of different densities. The growth rate is described by a modification of the logistic growth differential equation in which the increase in weight of an individual plant depends on its area, s_i rather than on its weight. The effective area for growth of a plant is reduced by an empirical function, f(s_i) with two terms: one term expresses the constraint imposed upon the increasing total area of plants by the limited physical area of the plot; the other term allows for a competitive advantage or disadvantage for plants of varying sizes. Depending on the value of the parameter controlling the relative competitive advantage term, intrinsic variability between plants can be amplified or suppressed. An individual plant dies if the f(s_i) results in a negative growth rate for that plant. Computer simulations of the growth and survival of plants at different population densities were run. The results exhibit characteristics that appear realistic upon comparison with published data: a survival of the fittest occurring during thinning; a line of slope close to −3/2 bounding the graphs of log weight versus log density; and the occurrence of bimodality, associated with subsequent mortality, on frequency distribution of log weight.