Search

The description of spatial patterns in species distributions is central to research throughout ecology. In this manuscript, we demonstrate that five of the most widely used species‐level spatial patterns are not only related, but can in fact be quantitatively derived from each other under minimal assumptions: the occupancy area curve, Taylor's Law, the neighborhood density function, a two‐plot variant of Taylor's Law and two‐plot single‐species turnover. We present an overarching mathematical framework and derivations for several theoretical example cases, along with a simulation study and empirical analysis that applies the framework to data from the Barro Colorado Island tropical forest plot. We discuss how knowledge of this mathematical relationship can support the testing of ecological theory, suggest efficient field sampling schemes, highlight the relative importance of plot area and abundance in driving turnover patterns and lay the groundwork for future unified theories of community‐level spatial metrics and multi‐patch spatial patterns., We show that several widely used single species spatial metrics (the occupancy area curve, Taylor's Law, the neighborhood density function and plot‐based turnover) are all derivable from each other under minimal assumptions. We provide example equations showing this relationship and demonstrate its application to simulated and empirical data.

This article explores the use of spatial point-process analysis as an aid to describe topsoil lead distribution in urban environments. The data used were collected in Glebe, an inner suburb of Sydney. The approach focuses on the locations of punctual events defining a point pattern, which can be statistically described through local intensity estimates and between-point distance functions. F-, G- and K-surfaces of a marked spatial point pattern were described and used to estimate nearest distance functions over a sliding band of quantiles belonging to the marking variable. This provided a continuous view of the point pattern properties as a function of the marking variable. Several random fields were simulated by selecting points from random, clustered or regular point processes and diffusing them. Recognition of the underlying point process using variograms derived from dense sampling was difficult because, structurally, the variograms were very similar. Point-event distance functions were useful complimentary tools that, in most cases, enabled clear recognition of the clustered processes. Spatial sampling quantile point pattern analysis was defined and applied to the Glebe data set. The analysis showed that the highest lead concentrations were strongly clustered. The comparison of this data set with the simulation confidence limits of a Poisson process, a short-radius clustered point process and a geostatistical simulation showed a random process for the third quartile of lead concentrations but strong clustering for the data in the upper quartile. Thus the distribution of topsoil lead concentrations over Glebe may have resulted from several contamination processes, mainly from regular or random processes with large diffusion ranges and short-range clustered processes for the hot spots. Point patterns with the same characteristics as the Glebe experimental pattern could be generated by separate additive geostatistical simulation. Spatial sampling quantile point patterns statistics can, in an easy and accurate way, be used complementarily with geostatistical methods. Copyright © 2005 John Wiley & Sons, Ltd.