Estimation of a spatial tree-influence model using iterative optimization

Abstract

A method is described that aims at quantifying and modeling single tree spatial effects on forest ecosystem characteristics within complex stand structures. The procedure is based on iterative optimization techniques and it utilizes spatially explicit data of tree stand structure and the environmental variable(s) of interest. The method can be applied to estimate the effects of tree neighborhoods on the distribution of environmental variables, both abiotic (e.g. availability of various growth resources) and biotic (e.g. growth rate or plant community composition affected by the competition for resources). The method was tested in a 9 ha plot of mapped boreal Pinus sylvestris forest. First, known tree influence functions were used to simulate values of a hypothetical tree influence potential at a large number of points ( n=688) in the forest. Then, the ability of the iterative optimization method to estimate or reconstruct these a priori known influence functions of trees was tested. The method was successful in estimating the form of the tree influence functions, and when the estimated functions were used to predict the tree influence potential in the same points within the forest, the correlation between the `real' and predicted values was high ( r=0.99). Secondly, the method was used to examine the effect of trees on two measured ecosystem characteristics, namely humus layer thickness and canopy coverage, the latter having been quantified with the LAI-2000 canopy analyzer. The spatial autocorrelation pattern of these two variables was also examined. These analyses showed that the spatial pattern of humus layer thickness could not be explained satisfactorily by tree influences, because this variable was finer than tree-scale variability. However, the results suggest that in their vicinity the largest trees (dbh 40–50 cm) have a strong positive effect on humus layer thickness. The method was successful in predicting the measured canopy coverage for the measurement points in the forest ( r=0.69). The iterative optimization method presented provides a way to examine whether, and to what extent, the spatial pattern of a given ecosystem characteristic in a forest is regulated by distance-dependent spatial influences of individual trees. The method also makes it possible to derive models to describe the influence of individual trees of different sizes. Knowledge of these small-scale influence domain effects of trees on ecosystem characteristics is useful in revealing the effect of the tree community on the spatial organization of forest ecosystem structure.