Periodicity in spatial data and geostatistical models: autocorrelation between patches

Several recent studies in landscape ecology have found periodicity in corre lograms or semi-variograms calculated, for instance, from spatial data of s oils, forests, or animal populations. Some of the studies interpreted this as an indication of regular or periodic landscape patterns. This interpreta tion is in disagreement with other studies that doubt whether such analysis is valid. The objective of our study was to explore the relationship betwe en periodicity in landscape patterns and geostatistical models. We were esp ecially interested in the validity of the assumption that periodicity in ge ostatistical models indicates periodicity in landscape pattern, and whether the former can characterize frequency and magnitude of the latter. We crea ted maps containing various periodic spatial patterns, derived correlograms from these, and examined periodicity in the correlograms. We also created non-regular maps that we suspected would cause periodicity in correlograms. Our results demonstrate that a) Various periodic spatial patterns produce periodicity in correlograms derived from them, b) the distance-lags at whic h correlograms peak correspond to the average distances between patch cente rs, c) periodicity is strongest when the diameter of patches is equal to th e distance between patch edges, d) periodicity in omni-directional correlog rams of complex spatial patterns (such as checkerboards) are combinations o f several waves because inter-patch distances differ with direction; multip le directional correlograms can decompose such complexity, and e) periodici ty in correlograms can also be caused when the number bf patches in a study site is small. These results highlight that correlograms can be used to de tect and describe regular spatial patterns. However, it is crucial to ensur e that the assumption of stationarity is not violated, i.e., that the study area contains a sufficiently large number of patches to avoid incorrect co nclusions.