A method to distribute mortality in diameter distribution models

Abstract

Bailey (1980) derived tree diameter growth models by transforming variables which preserved the functional form of the probability density function that approximated diameter distributions. The necessary assumption was either no mortality, or that mortality was proportionally distributed among diameter classes. The latter assumption might not be realistic since smaller trees should suffer more from competition than large trees and are more likely to die. This paper deals with the case when mortality is not proportionally distributed. If diameters in a stand originally follow a Weibull distribution and mortality for a growing period can be assumed to occur at the beginning of that period, then a Weibull was found to successfully approximate the diameter distribution immediately after mortality. The stand then grows without further mortality and reaches the end of the period with its diameters remaining Weibull. A similar method to derive a diameter distribution after mortality was developed for the beta distribution. The Weibull technique was applied to data from loblolly plantations. Results showed that the new approach worked reasonably well and was comparable with a diameter distribution model in approximating diameter distribution of a stand at the end of the growth period.