Sampling theory inspires quantitative forest ecology: The story of the relascope kernel function

Understanding and modelling plant interactions is an important field in quantitative forest ecology. Many spatially explicit techniques have been devised for shedding light into these processes. One of these methods includes the application of kernel functions, which describe the decay with increasing distance of interaction effects of each plant of a given community on others. In forest inventory, a method referred to as relascope sampling is often applied to collect information on the state and change of tree resources: somewhat unexpectedly, the mathematical principles of this technique have been turned into measures of competition for use in ecological modelling. In this study, we combined methods from quantitative ecology and sampling theory by defining a parameter-parsimonious relascope kernel function, thus generalising the concept of individual-tree basal-area factors. By using both relative and absolute growth rates as response variables in the regression we compared the performance of the relascope kernel with an alternative, the exponential kernel function. Our results indicated that the relascope kernel can indeed be applied to both types of growth rates in individual-based models. Using individual-tree basal-area factors, it is even possible to anticipate the performance of the relascope kernel. In most cases the estimation efficiency was greater, when absolute growth rate was the response variable. The exponential kernel was more efficient than the relascope kernel, but at the expense of parameter parsimony and estimation robustness. Our study has shown that simple, parsimonious models, inspired by another field of natural sciences, such as the relascope kernel, can effectively encapsulate the interaction dynamics of forest ecosystems.