Abstract
The spatial structure of a forest stand is typically modeled by spatial point process models. Motivated by aerial forest inventories and forest dynamics in general, we propose a sequential spatial approach for modeling forest data. Such an approach is better justified than a static point process model in describing the long-term dependence among the spatial location of trees in a forest and the locations of detected trees in aerial forest inventories. Tree size can be used as a surrogate for the unknown tree age when determining the order in which trees have emerged or are observed on an aerial image. Sequential spatial point processes differ from spatial point processes in that the realizations are ordered sequences of spatial locations, thus allowing us to approximate the spatial dynamics of the phenomena under study. This feature is useful in interpreting the long-term dependence and spatial history of the locations of trees. For the application, we use a forest data set collected from the Kiihtelysvaara forest region in Eastern Finland.
Highlights
This paper discusses the modeling of sequential spatial point processes in the context of forest tree data
In the case of size-determined ordering, we hypothesize that the boundary effect is small in the early part of the sequence, which consists of large trees, the points in the reduced observation window are near the boundary
The mechanism of the sequential model introduced in this paper for forest tree data represents a powerful modeling tool since it offers a causal description through successive conditioning
Summary
Where individual tree crowns are recorded by an aircraft. small trees often remain undetected below the crowns of bigger trees. If the sample plot of interest is homogeneous in terms of growing conditions, the tree order with respect to age can be well approximated by their order with respect to size (Møller et al 2016) given a suitable size variable, such as tree height, stem diameter or tree crown dimensions In this case, the size distribution has to be involved in the model and the correlation between the size variable and spatial locations should be taken into account. Point xk+1 is accommodated by the model, which determines the probability law We apply these models to forest data consisting of tree locations associated with quantitative marks representing the diameters of the tree stems at breast height (DBH) and providing a natural ordering for the trees. We develop new dynamic summary statistics that measure different features of the tree data, take the temporal order into account, and are meaningful for forest tree data
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