Dynamics of Self-Thinning Plant Stands

Abstract

The growth of plants in even-aged, pure stands and the decline in the number of these plants are represented with a set of S-system differential equations. The S-system representation captures the observed interdependence between average size and number of plants, demonstrates how a plant stand approaches the well-established 3/2 power relationship between number and size, and also accounts for the observation that in stands of perennial species, old plants usually remain smaller than predicted by the relationship. The model includes, as special cases, earlier models that only partially represent the mutual dependence between number and average size. The S-system model incorporates well-known growth laws, and thus circumvents the problem of identifying the most appropriate growth and decline functions in the analysis of actual data. For particular parameter settings, the S-system can be solved analytically to yield explicit closed-form relationships between the numbers and sizes of plants, not only in the range where the stand dynamics moves along the size-limiting relationship, but also for large numbers of small plants and small numbers of large plants.