Distance-Dependent and Distance-Independent Models of Douglas-fir and Western Hemlock Basal Area Growth Following Silvicultural Treatment

Michael C. Wimberly and B. Bruce Bare

Distance-independent and distance-dependent individual-tree basal area growth equations for Douglas-fir and western hemlock growth following thinning and fertilization treatments were developed using regression analysis. Distance-independent models included only non-spatial competition and thinning indices, while distance-dependent models included both spatial and non-spatial indices. The distance-independent models with the highest adjusted multiple coefficient of determination (adjusted R2) for both species included diameter at breast height, crown class, percent basal area removed in thinning, plot basal area greater than the subject tree and stand age as independent variables. The distance-dependent models with the highest adjusted R2 included all of these variables in addition to a variant of the area potentially available index, which is based on the spatial tessellation of the point pattern of trees in the stand. Addition of this spatial index produced only a small (<.01) increase in adjusted R2 for models of both species. The relatively small amount of increase was due to three factors; thinning resulted in an even distribution of growing space among residual trees, tree size explained much of the variation in local competitive stress and the competitive neighborhood of individual trees was large relative to the size of the sample plots. The results suggest that the additional effort and expense required to obtain spatially referenced stand data for developing empirical forest growth models in similar stands is not justified.

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