Understanding tree growth as a function of tree size is important for a multitude of applications. What variables limit growth is of central interest for many of these applications, and forest inventory permanent plots are an abundant and valuable source of long-term information to study growth limitation. Unfortunately even high-quality research forest data are highly complex. In modeling these data, observation error is often treated in an unsatisfactory way, and there are multiple sources of shared variation between measurements that need to be accounted for. These include repeated measures on trees, uneven time intervals and missing data, and spatial nesting of plots within sites. These common problems make permanent plot data difficult to use for growth estimation using simple statistical models. We account for these complexities using a hierarchical state-space model, extending previous methods to include multiple temporal and spatial random effects on both overall growth increment and size-dependent growth. We additionally incorporate explanatory environmental variables independently representing both competition and resource supply as well as their interactions with size. We estimate the diameter growth of white fir in the Sierra Nevada of California from forest inventory permanent plots in a Bayesian framework using popular Markov chain Monte Carlo tools.
We show that estimating such a model is feasible. In this forest, white fir growth depends strongly on tree size, local population density, and individual tree quality. Resource supply variables (elevation, topographic slope, soil type, annual water deficit, and insolation) have little effect on this species' growth at our site, while total basal area and tree diameter are significant predictors of growth. We estimate observation error due to bark loss or improperly placed measurement tapes at 0.26 cm/year (95% credible interval: 0.19 to 0.33 cm/year). This is approximately twice the variation due to individual tree quality (0.1444 cm/year, CI: 0.1283, 0.1614) and plot-level effects (0.1258 cm/year, CI: 0.0957, 0.1592), both of which are also significant sources of variation. This observation error for diameter tape measurements is much smaller than estimates from other studies. This modeling approach can be applied to permanent plots around the world, leading to greater insights regarding patterns of tree growth and ultimately population and community dynamics over larger ecological scales, greater environmental gradients, and different ecosystem types.