Non‐linear matrix modeling of forest growth with permanent plot data: The case of uneven‐aged Douglas‐fir stands

Abstract

Uneven-aged forest management is acquiring increasing importance throughout the world as an alternative to clear cutting. Simple stage-structured matrix models can be used to predict the growth of uneven-aged stands, and they are easily incorporated in optimization analysis. Parameters of these models can be estimated from readily available permanent plot data. Such a growth and yield model is presented for mixed, uneven-aged Douglas-fir and hardwood stands. The model was calibrated with data from 66 permanent plots in Oregon and Washington. The density-dependent matrix model predicts the number of trees by diameter class and species type, softwood or hardwood. The parameters are based on individual tree growth equations, individual tree mortality equations, and stand ingrowth equations. The individual tree equations are a function of tree diameter, stand density, species, and site index. The stand-level ingrowth equations are a function of stand density. The model was validated in the short term by comparing the number of trees in each diameter and species class at the time of the second inventory with the number predicted by the model, given conditions at the first inventory. A long-term validation of the model was also done by comparing the steady-state stand structure and stand volume with those observed for old-growth stands. The model was applied to show the effects of different cutting cycles on productivity, diversity of tree species and size, and financial returns. The results suggest that uneven-aged management of the Douglas-fir forest type in the Pacific Northwest can be as productive as even-aged management, with the added benefits of continuous cover forestry.

A multi-species density-dependent matrix growth model for the dry woodlands of Uganda

“…The developed matrix model is similar to earlier density-dependent models (e.g. Buongiorno et al, 1995;Lin et al, 1996Lin et al, , 1998Lootens et al, 1999;Ralston et al, 2003).…”

“…Both upgrowth and mortality functions were formulated using individual tree data to compensate for the small number of plots available (e.g. Ralston et al, 2003). The developed matrix model is similar to earlier density-dependent models (e.g.…”

“…The logistic function is the most widely used function in mortality models for individual trees (e.g. Monserud and Sterba, 1999;Eid and Tuhus, 2001;Ralston et al, 2003). The probability, m ijt , that a live tree of species i and diameter class j died between years t and t + 1 was computed as:…”

“…Therefore, the model predictions were compared with the observations on the 42 sample plots. Despite its limitations, this is still a useful test of the complete model structure (1) built from the estimated parameters, and applied recursively over the inventory period (Ralston et al, 2003). Applying GAMS computer program (GAMS Development Corp., 2003), the model was used to predict the diameter frequency distribution of each species class at the second inventory, given the observed distributions for each plot at the first inventory.…”

“…Buongiorno and Michie, 1980;Osho, 1991;Spathelf and Durlo, 2001) or dependent on the stand state (e.g. Lin et al, 1996Lin et al, , 1998Lin and Buongiorno, 1997;Lootens et al, 1999;Ralston et al, 2003). Lin and Buongiorno (1997) compared a density-dependent model (i.e.…”