Modeling the Effects of Initial Spacing on Stand Basal Area Development of Loblolly Pine

Abstract

Several studies have reported that in loblolly pine stands with high initial density, basal area declines after reaching maximum carrying capacity. This behavior is not reproduced by most basal area development models because the functions used are sigmoid and nondecreasing, tending toward an asymptote. We used a combined exponential and power function to model the impact of initial density on the basal area development of loblolly pine in a spacing trial. The combined exponential and power function is sufficiently flexible to describe both the asymptotic behavior of the wider initial spacing plots and the decrease in basal area after culmination of the closer spacings. We modified the original function to account for the time lag between stand establishment (age 0) and basal area establishment (age 0), by allowing the origin of the function to be different than age 0. Two final models are presented: a model fitted using the population-average (PA) approach and a model fitted using the mixed-effects (ME) approach. At the fixed-effects level, the PA and ME models are not equivalent, and, therefore, the appropriate model should be selected according to the availability of previous data and the objectives of the prediction. If previous observations are available, they can be used to improve the predictions using the ME model.