Analysis on the spatial structures of spruce-fir stands in northwest Maine

Spatial information is very important to forest and ecosystem management. The traditional forest growth and yield models have been criticized for their inability to provide precise spatial information. In this study the spatial structures of the softwood stands (represented by 50 spruce-fir plots) in the Northeast, USA were explored, and modeled both horizontally and vertically. The stand horizontal structure was first analyzed for spatial patterns by various spatial point pattern analysis methods. Among these methods, the results from the nearest neighbor statistics (13 were employed in this study) were proved not reliable because of the violations of the assumptions of independent distance measures and the requirement of large sample size for these plots. Based on the results of refined nearest neighbor statistic, Ripley's K function analysis and the pair correlation function analysis, 24 plots had CSR point pattern, 17 had regular point pattern, and 9 had clustering point pattern out of the 50 plots. Then, Gibbs point process models with three different pair potential functions were fit to the data. It was found that the three pair potential functions performed similarly in modeling the spatial patterns, i.e. 42 out of the 50 plots can be modeled well. Generally, the CSR and regular point patterns were modeled better than the clustering plots by all three pair potentials. The vertical structure of the stands was modeled by bivariate distributions of generalized beta distribution (GBD-2) and Johnson's S BB. The goodness-of-fit results indicated the GBD-2 performed better in fitting the marginal and joint tree diameter and height distribution than did SBB. Finally, regression relationships between the parameters of the spatial models and ordinary forest inventory data were built using the principle component regression technique. Thus, the spatial models developed in this study could be incorporated into traditional growth and yield models. Consequently, the updated growth and yield models could provide useful spatial information for forest managers and researchers.