Adapting distance-independent forest growth models to represent spatial variability: Effects of sampling design on model coefficients

Abstract

If sampling variability of competition variables can be accommodated, a distance-independent growth model can (1) simulate patchy stands inventoried by a grid of sampling locations; (2) prescribe treatments for each location; and (3) update inventories using plot sizes differing from those used in model calibration. Ignoring sampling properties of competition biases estimates of stand development and management responses. Our solution to reduce this bias has three steps: First, we model the sampling properties of the competition estimates depending on plot sizes and on spatial patterns. Then we use the modeled error variances when estimating parameters of the structural relation of growth to competition. Finally, we join these two products in a Structural Based Prediction (SBP) procedure that dynamically modifies coefficients during simulation. SBP increases sensitivity to spatial variation and permits valid analyses of location-specific prescriptions for varying inventory designs. In a model of diameter change for individual Pseudostuga menziesii var. glauca (Beissn.) Franco, coefficients of the competition variables estimated under the structural model were three times as large as when estimated under an ordinary least-squares criterion. This increase reduced sensitivity to crown ratio. Two variants of the Prognosis Model for Stand Development were constructed to compare behavioral changes: (1) using SBP, and (2) using the OLS-based coefficient estimates of the same diameter-growth submodel. Projections with the two variants differed in the internal structures of both uniform and irregular stands and using several sampling methods. Stand averages of volume growth were similar for uniform stands-either from uniform regeneration or from uniformity created by thinning patchy stands. However, the thinning response in patchy stands differed between the two variants. Analysis of the variance model showed little sensitivity within the range of half to twice the Poisson-based estimates of competition variance.