What mark variograms tell about spatial plant interactions
Artikel i vetenskaplig tidskrift, 2013

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. In this study, we reconstructed two spatial tree time series where negative autocorrelation has occurred and also simulated four alternative forest development paths in order to experimentally explore the causes of negative autocorrelation. Interestingly the results highlighted that man-made disturbances (e.g. thinnings) often result in a significant number of pairs of large and small trees at close proximity leading to negative autocorrelation. We could also show that whilst negative autocorrelation can be the consequence of natural forest development including competition processes, it can, however, also be the consequence of disturbances and of subsequent colonisation by small trees. Since disturbances play an important role in the development of negative autocorrelation, the mark variogram is a key summary characteristic in disturbance ecology.

Negative autocorrelation


stand structure


Individual-based model




Evolution of spatial tree

point process statistics

Plant interactions



A. Pommerening

Bern University of Applied Sciences

Aila Särkkä

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Ecological Modelling

0304-3800 (ISSN)

Vol. 251 64-72


Geovetenskap och miljövetenskap