Predicting the Probability of Stand Disturbance’

-Forest managers are often interested in identifying and scheduling future stand treatment opportunities. One of the greatest management opportunities is presented following major stand level disturbances that result from natural or anthropogenic forces. Remeasurement data from the Forest Inventory and Analysis (FIA) permanent plot system are used to fit a set of models that predict the probability of harvest for the five FIA survey units of Georgia. We assume a logistic function that establishes asymptotes at 0 and 1. We found that geographic region, ownership, number of trees per acre, and average stand diameter are correlated to the probability of harvest. A plot was considered harvested if any tree > 5 in. d.b.h. was art The average probability of harvest over the last 8.5 years was approximately 33 percent for the central and southern regions of Georgia. The average rate of harvesting in northern Georgia was 21 percent. These models can be used to predict the probability of harvest for a set of stand conditions and when combined with area expansion factors, to estimate the acreage of harvested stands. INTRODUCTION 1. The logistic function meets all of these prerequisites and has been used to model event probabilities such as individual tree mortality for several decades (Monserud 1976). The general form of the logistic function is: A study to model disturbance rates resulted from two potential uses. Firstly, the recent move to annual forest inventones by the Forest Inventory and Analysis (FIA) program of the USDA Forest Service, Southern Research Station has raised some interesting questions regarding efficient allocation of sample plots. Specifically, the greatest change in an inventory often occurs in conjunction with major disturbances. A nonexhaustive list of disturbances that can significantly alter an inventory includes harvesting, insects and disease, and wind damage and other weather retated events. p(h)= exofX) + E 1 +w (8 (1) where P(h) = the probability of harvest, in the Southern U.S., harvesting is the largest dis!urbance and thus, estimating the probability of harvest and comparing the actual rates of disturbance to disturbance detection techniques is a prerequisite for implementation of an inventory based on disturbance detection. Second, and more important to the silvic~ltural community, is the need to estimate the type and acreage of stands available for site preparation, planting, or other treatment opportunities following harvest. The recently completed seventh forest survey of Georgia (Thompson 1998) provides an ideal ~opportunitjitoodelrvesting r a t e s . INVENTORY METHODS Estimates of change and rates of change were available from the 1997 remeasurement of 5,386 permanent sample p!ots established in the previous survey in 1989. The plot design for the previous inventory was based on a cluster of 10 points. Variable radius plots were systematically spaced within a single forest condition at three to five points. At each point, trees 25.0 in. d.b.h. were selected for measurement on a variable radius plot defined by a 375factor prism. Trees c 5.0 in. d.b.h. were tallied on a fixed-radius plot around each plot center. wGl = the exponential function eX , X = the set of predictor variables, and 8 = the error term. The probability of harvest is related to many variables, including volume per acre by tree species, size, quantity, and quality of the trees, and the species mix per unit area. The correlation between these potential predictor variables at time 1 (1989 measurement) and harvesting rates at time 2 (1997 measurement) can be easily investigated with FIA’s remeasurement data. Other potentially influential variables such as operability, distance to mill, distance to roads or urban populations (Wear and others l999), and planted versus natural stands are variables that were not included in this study. With the exception of planted versus natural stands, these variables could not be investigated because the variables are either not collected or readily available for analysis. Future studies are planned to investigate the excepted variables. RESULTS AND DISCUSSION MODEL DEVELOPMENT When the dependent variable is an indicator variable, the shape of the response function will often be curvilinear. For our specific application of modeling harvest rates, the response variable is either 1 or 0 depending on whether an inventory plot was harvested or not. An additional necessary requirement is to use a model that has asymptotes at 0 and The logistic regression model (1) was fit to the 1997 FlA remeasurement data for the five survey units (Southeast, Southwest, Central, North Central, and North) of Georgia (fig. 1). A sample plot is considered harvested if any tree (> 5 in. d.b.h. at time 1) was cut. This study does not distinguish levels of cutting and includes the full spectmm of harvesting practices. The average remeasurement interval across the state was 8.5 years. The average tree diameter by species group and number of trees per acre by species group are listed for each of the survey units (table 1). The fitted coefficients to model (1) for each of the survey regions are listed in table 2. Under each survey unit are ’ Paper presented at the Tenth Biennial Southern Silvioultural Research Conference, Shreveport, LA, February 18-18.1999. zSupervisory Mathematical Stetktidan and Mathematical Statistician, USDA Forest Service, Southern Research Station, Forest irn@ntrxY and Analysis, Asheville, NC 28802, respectively. Figure l-The five forest survey regions in Georgia. forward selection procedure for variable inclusion. Because users desire to differentiate harvest event probabilities by ownership, we retained all ownership variables in the models. With the exception of forest industry (FORCO) lands, nonindustrial private forest (NIPF) lands, and other corporate (CORP) lands, for both the interaction and main effects model in the Northern survey unit and the interaction model in the North Central survey unit, all ownership variables are different from each other at the p = 0.05 level. Forest industry, private nonindustrial, and other corporate lands have harvest rates greater than the government but are not distinguishable from each other. Other significant variables (p = 0.05) in the models include mean initial stand diameter (d.b.h.), mean initial pine stand diameter (PDBH), mean initial hardwood stand diameter (HDBH), number of initial pine trees per acre (PTPA), number of initial hardwood trees acre (HTPA), and a number of interaction terms (table 1). All mean stand diameter and trees per acre variables are based on sample plots with trees z= 5 in. d.b.h. Plots with no trees > 5 in. d.b.h. were excluded from model fitting. Interpretation of the model coefficients proceeds as follows. Positive coefficients are associated with increased rates of harvest and negative coefficients with decreased rates of harvest. For example, in the main effects model for survey unit 1, other corporate lands are harvested at higher rates than all other ownership categories (table 2). The variables Table l-Average tree diameter and numbers of trees per acre for trees >5 inches d.b.h. by species group (all species, hardwoods, and conifers). Plots with no trees >5 inches d.b.h. were excluded from the analysis. Average d.b.h. and number of trees per acre are based on time 1 measurements (1989). The Georgia survey units are the Southeastern (unit I), Southwestern (unit 2), Central (unit 3), North Central (unit 4), and Northern (unit 5)