Improving inverse model fitting in trees—Anisotropy, multiplicative effects, and Bayes estimation

Model fitting for individual-based effects in forests has some problems. Because samples measuring the separate influence of each individual are rarely available, the measured value in the sample represents the influence of all surrounding individual trees. Therefore, it is helpful to build inverse models that use the spatial pattern of the variable as well as that of the source trees. For example, since seed dispersal is influenced by wind effects, a model is discussed describing anisotropic effects to ensure an unbiased estimate of the total fruit number. Further, we present a model describing the absorption of radiation by trees. In this case a multiplicative combination of individual effects yields the total effect. Our approach uses logarithmic transformations of the original data to model multiplicative combinations as sum of transformed single effects. For fitting model parameters we propose an approach based on Bayesian statistics, to ensure ecologically interpretable parameters.