Spatial and spatio-temporal modelling of Sitka spruce tree growth from forest plots in Co. Wicklow

Individual tree growth in forest plots is spatially dependent, changes overtime and the magnitude of spatial dependence may also change over time,particularly in stands subjected to thinning. Models for tree growth in theliterature have been mainly restricted to either spatial models or temporalmodels. Spatial models have been mostly restricted to those that haveGaussian variograms with comparisons at single time points while dynamicmodels ignore tree competition caused by close spatial proximity. Spatio-temporalmodels were therefore developed to represent the individual treegrowth of Sitka spruce (Picea sitchensis (Bong.) Carr.) based on data fromthree long-term, repeatedly measured, experimental plots in Co. Wicklow,Ireland.The initial thinning treatments for the three plots were: unthinned, 40%thinned and 50% thinned. Tree growth was defined as the difference inthe measured diameter at breast height (DBH) (cm) at regular intervals.Thinned and unthinned plots were modelled separately as they were notadjacent. A model for tree growth over all locations in a plot and all timepoints was fitted using a sum-metric spatio-temporal variogram. Negativespatial correlation at small distances (due to competition) is evident atseparate time points while at larger distances it is positive and this isadequately modelled with a wave function. The correlation of a singletree over time also followed a wave variogram while the spatio-temporalanisotropy parameter captured the changing spatial wave intensity.Models with fixed effects of age, number of neighbours and polygon areawere also considered. Predicted values for models were computed usingregression-kriging and mean squared error of prediction was used tocompare models and thinning strategies. Both thinned plots clearly outperformedthe unthinned plot in terms of total individual tree DBH growthand also at a stand level. Spatio-temporal bootstrap methods were usedto assess the precision of the spatio-temporal model parameter estimates.The models indicate, once fixed effects are accounted for, that spatialvariability and correlation is more important than temporal. The modelsprovide insights into the nature of tree growth and it is seen that modellingspatial dependence is important in the understanding of managementstrategies and silvicultural decision making.