Individual tree diameter increment model for managed even-aged stands of ponderosa pine throughout the western United States using a multilevel linear mixed effects model

Abstract

A diameter increment model is developed and evaluated for individual trees of ponderosa pine throughout the species range in the United States using a multilevel linear mixed model. Stochastic variability is broken down among period, locale, plot, tree and within-tree components. Covariates acting at tree and stand level, as breast height diameter, density, site index, and competition indices are included in the model as fixed effects in order to explain residual variability. The data set used in this study came from long-term permanent research plots in even-aged, pure stands both planted and of natural origin. The data base consists of six levels-of-growing stock studies supplemented by initial spacing and other permanent-plot thinning studies for a total of 310 plots, 34,263 trees and 153,854 observations. Regression analysis is the preferred technique used in growth and yield modeling in forestry. We choose the mixed effects models instead of the regression analysis approach because it allows for proper treatment of error terms in a repeated measures analysis framework. Regional growth and yield models exist for ponderosa pine. However, data collection and analysis procedures differ. As a result, comparisons of growth responses that may be due to geographic variation of the species are not possible. Our goal is to present a single distance-independent diameter increment model applicable throughout the geographic range of ponderosa pine in the United States and by using only data from long-term permanent plots on sites capable of the productivity estimated by Meyer [Meyer, W.H., 1938. Yield of Even-Aged Stands of Ponderosa Pine. US Department of Agriculture Technical Bulletin 630].