Characterizing dependence of Irish sitka spruce stands using spatio-temporal sum-metric models

Individual tree dependence in forest plots is spatially dependent and changes over time, and the magnitude of spatial dependence may also change over time, particularly in stands subjected to thinning. Models for tree dependence in the literature have been mainly restricted to either spatial models or temporal models. We extend these to spatio-temporal models. The data are from three long-term, repeatedly measured, experimental plots of Sitka spruce (Picea sitchensis [Bong.] Carr.) in Co. Wicklow, Ireland, with thinning treatments of unthinned, 40% thinned, and 50% thinned, respectively. A model for tree by diameter at breast height, over all locations in each plot and all time points, was fitted with fixed covariates and with a sum-metric spatio-temporal variogram for the covariance structure. In the variogram, the spatial correlation component followed a wave function (due to competition at small distances). The correlation over time also followed a wave variogram, whereas the spatio-temporal anisotropy captured the space-time interaction. The models indicate, once fixed effects are accounted for, that spatial variability and correlation are more important than temporal. Models were fitted to plots with three different treatments to demonstrate that model parameters differed by thinning type but were consistent in their interpretation with thinning type. The models show that describing spatial dependence is important for understanding the nature of tree growth and its prediction.