Dynamics of Self-Thinning Plant Stands

The growth of plants in even-aged, pure stands and the declinein the number of these plants are represented with a set ofS-system differential equations. The S-system representationcaptures the observed interdependence between average size andnumber of plants, demonstrates how a plant stand approachesthe well-established 3/2 power relationship between number andsize, and also accounts for the observation that in stands ofperennial species, old plants usually remain smaller than predictedby the relationship. The model includes, as special cases, earliermodels that only partially represent the mutual dependence betweennumber and average size. The S-system model incorporates well-knowngrowth laws, and thus circumvents the problem of identifyingthe most appropriate growth and decline functions in the analysisof actual data. For particular parameter settings, the S-systemcan be solved analytically to yield explicit closed-form relationshipsbetween the numbers and sizes of plants, not only in the rangewhere the stand dynamics moves along the size-limiting relationship,but also for large numbers of small plants and small numbersof large plants. Growth, plant stands, self-thinning, 3/2 power rule, S-system model