What mark variograms tell about spatial plant interactions

Many if not all data collected in ecology have both a spatial as well as a temporal dimension. This suggests the use of summary characteristics from spatial statistics to gain more refined insight into plant interactions. Spatial tree data can for example be considered as point patterns (formed by tree locations) with attached marks (e.g. tree sizes). If only the pattern of tree locations is of interest one can use for example the pair correlation function. If in addition, the sizes (or some other characteristics) of trees or other plants are of interest, marked summary statistics can be more suitable. In this paper, we propose the so-called mark variogram as a useful tool in ecological studies. This summary characteristic basically indicates how similar two plants within a certain distance from each other are. For example, if two plants are approximately of the same size, the mark variogram has small values, and if their sizes differ somewhat, the mark variogram has large values. Recently, there has been a lot of discussion on how to interpret the shape of mark variograms caused by pairs of plants with different sizes at close proximity. Such variogram shapes exhibiting so-called negative autocorrelation, another expression for high small-scaled size diversity, are assumed to indicate strong competition between plants.