Local analysis and modeling of tree competition and growth

This study focuses on local analysis of tree competition and local modeling of tree growth. First, relationships between the Local Indicator of Spatial Association (LISA) and traditional tree competition indices and individual tree growth are investigated. The results show that like most of the competition indices, LISA has moderate correlations with tree basal area growth. For predicting the tree basal area growth, one of LISA, the local G_i, performs better than many (73%) competition indices at a plot aggregation level, and has higher explanatory power than most (91%) competition indices at an individual plot level. The LISA also has strong linear relationships with some traditional competition indices, e.g. Lorimer index. The relationships are stronger ( > 0.90) at an individual plot level than for all plots combined ( > 0.75). The LISA can be statistically tested to identify local clusters of trees of similar sizes (“hot spots”) or dissimilar sizes (“cold spots”), even though without discernible spatial pattern. These significant “hot spots” or “cold spots” indicate the subareas in a forest stand where the competition among trees may be more severe than the average. Therefore, the LISA can replace the traditional competition indices for exploring the competitive status of neighboring trees, investigating the relationships between tree competition and growth, and estimating individual tree growth. The hot spots or cold spots identified by the LISA provide useful information for the design of silvicultural and management treatments. Second, the spatial heterogeneity of multivariate relationships between tree growth and diameter is explored using Geographically Weighted Regression (GWR). GWR attempts to capture spatial variation by calibrating a multiple regression model fitted at each tree in a sample plot, weighting all neighboring trees by a function of distance from the subject tree. GWR produces a set of parameter estimates and model statistics (e.g., model R2) for each tree in the sample plot. It is evident that the GWR model not only predicts individual tree growth better than the traditional OLS model, but also provides useful information on the nature of the growth variation caused by neighboring competitors and surrounding environmental factors. The parameter estimates and model statistics of the GWR model can be mapped using visualization tools such as Geographical Information System (GIS) to illustrate local spatial variation in the regression relationship under study. The influence of micro-site variation, competition status, growth potential, and the impacts of management activities on trees can be evaluated, tested, modeled, and readily visualized by GWR. This study indicates that LISA and GWR are useful to provide us much more information on spatial relationships in aid to both model development and better understanding of spatial processes.