MODELING THE SPATIAL STRUCTURE OF WHITE SPRUCE PLANTATIONS

The spatial distribution of trees has important implications for forest management (Batista & Maguire 1998, Pommerening 2006), even if it is seldom used. It is very useful to understand complex forest structures (Pretzsch, 1997) and to simulate forest dynamics by integrating interactions between trees (Genet et al., 2014). In addition, spatialized data may, under certain circumstances, improve the accuracy of some models (growth, quality, regeneration, survival rate, etc.) (Weiskittel et al., 2011). However, measuring the coordinates of all trees in a stand can be long and costly. The development of LiDAR technology improves the speed and accuracy of these measurements (Martin Ducup et al., 2016). The objective of this study was to analyse the spatial patterns of trees and to develop a simulator able to reproduce the spatial structure of the forest by attributing coordinates to non-spatial inventory data. Fifty-nine plots were sampled in four white spruce plantations in eastern Quebec, Canada (33 plots of 450m² and 26 of 1000m²). An experimental design was established in which five commercial thinning treatments were randomly assigned to each plot (Gagne et al. 2016). The plots were scanned with a Focus3D Faro, a terrestrial laser scanner, to cover the entire surface and minimize occlusion. From the three-dimensional point cloud obtained, the coordinates of all the trees was extracted. Tree species was determined during the forest inventory of the plots. White spruce ( Picea glauca ) (WS) and balsam fir ( Abies balsamea ) (BF) were considered separately and the hardwoods with commercial interest were grouped together (VH). At the plot level, the spatial distribution was studied with the Clark-Evans Aggregation Index (CEI). For species that tend to cluster, the number of groups per hectare (NbGroup) was modelled with a Poisson regression using stand characteristics (CEI, thinning treatment, tree density) and the number of trees for the studied species as predictive variables. Within these groups, the closest distance between two trees of the same species (MinDistGroup) was modeled with a Gamma regression using stand characteristics and the diameter at breast height (Dbh) of the two neighboring trees as predictive variables. At the individual tree scale, the minimum distances between a tree and its two closest neighbours among all trees (MinDist1, MinDist2) were modelled with a Gamma regression using stand characteristics and the characteristics of the three neighbouring trees (species, Dbh) as predictive variables. At the plot scale, we observed that WS had a regular distribution (CEI > 1) whereas BF and VH tended to be more aggregated (CEI < 1). The root-mean-square error (RMSE) of NbGroup model was 0.16 (R² = 0.41), 3.22 (R² = 0.19) and 2.39 (R² = 0.28) for WS, BF and VH, respectively. An RMSE of 0.48 (R² = 0.38) and 0.56 (R² = 0.32) were obtained for MinDist1 and MinDist2. Statistically significant differences between the different sylvicultural treatments were also observed. In order to attribute spatial coordinates to a non-spatialized inventory, the tree list is first sorted by Dbh. The first tree is randomly placed within the plot boundaries. For the other trees, a random position is generated within the plot, and the distance from the two nearest trees (d1 and d2, or if the second tree, only d1) are compared to the minimum distances (MinDist1 and MinDist2). If d1 is greater than MinDist1 and d2 is greater than MinDist2, the position is considered acceptable. Otherwise, a new random position is tested. For species that tend to cluster (i.e. BF and VH), the area where to randomly chose the location of the tree is restricted by the CEI, which depends on the tree species and its size. The simulated CEI was compared to the observed CEI within the calibration plots, with very little differences observed. In most inventories, the coordinates of the trees are not available. Under certain circumstances, this information is necessary as, for example, the input into certain growth simulators. The 'spatializer' presented here accounts for the attractive behaviours between trees of the same species (NgGroup, MinDistGroup) and repulsive behaviours between trees too close to each other (MinDist1, MinDist2). The spatialisation model has been added to the PlantaBSL growth simulator programmed in Capsis. It is a tree growth simulator for plantations in Quebec where many sylvicultural treatments can be tested and evaluated.

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