Deriving Tree Crown Distributions from Diameter at Breast Height

Abstract

The distribution of crown diameter is important for assessing crown social class, monitoring forest health and wildlife management. However, the direct measurement of crown diameter is relative difficult, and as such, it is often predicted from diameter at breast based on a simple relationship. Therefore, in this study, the crown diameter distribution of Parkia biglobosa was derived from Dbh using Weibull and Log-Logistic functions. A total of 284 trees were measured from Parkia biglobosa plantation in Makurdi, Nigeria. Four methods were used for Weibull distribution including maximum likelihood (MLE), moments, percentiles and cumulative distribution function regression (CDFreg). MLE and CDFreg were used for Log-Logistic function. Transformation technique was used to transform the Dbh to crown distribution based on a simple allometric relationship between the variables. Kolmogorov-Smirnov (Dn), Cramer-von Mises statistic (W2) and Reynolds error index (EI) were used to assess the derived crown diameter distribution. The result showed that the underlying diameter distribution followed Weibull and Log-Logistic distributions. The fitted allometric equation was of the form:
. MLE and CDFreg were the best methods for Weibull and Log-Logistic functions, respectively. The Dn, W2 and EI were 0.071, 0.0265 and 0.3434, respectively for MLE; and 0.0931, 0.0367 and 0.4171, respectively for CDFreg. In all methods, the observed and derived crown distributions were not significant at 20% (Dα=0.339). Thus, given the diameter distribution, the tree crown distribution of Parkia biglobosa can be derived. This would be useful for determination of the crown social class.