Abstract
Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology. Much effort has been made in the past decades to collect extensive and detailed information about the spatial distribution of tropical rainforests, as demonstrated, e.g. in the 50 ha tropical forest plot on Barro Colorado Island, Panama. These kinds of plots have been crucial to shed light on diverse qualitative features, emerging both at the single-species or the community level, like the spatial aggregation or clustering at short scales. Here, we build on the progress made in the study of the density correlation functions applied to biological systems, focusing on the importance of accurately defining the borders of the set of trees, and removing the induced biases. We also pinpoint the importance of combining the study of correlations with the scale dependence of fluctuations in density, which are linked to the well-known empirical Taylor’s power law. Density correlations and fluctuations, in conjunction, provide a unique opportunity to interpret the behaviours and, possibly, to allow comparisons between data and models. We also study such quantities in models of spatial patterns and, in particular, we find that a spatially explicit neutral model generates patterns with many qualitative features in common with the empirical ones.
Highlights
The pair correlation functionWe start defining our main observable, namely the pair correlation (or radial distribution) function, g(r), which is here used to probe density correlations in the spatial distribution of trees in the Barro Colorado Island (BCI) plot
Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology
We are interested in the spatial density correlations of tree patterns, using the so-called pair correlation function, g(r), which quantifies the average density of trees at distance r from any individual tree, normalized by the expected value based on the mean density of vegetation [6,10]
Summary
We start defining our main observable, namely the pair correlation (or radial distribution) function, g(r), which is here used to probe density correlations in the spatial distribution of trees in the BCI plot. Points close to the borders, having less neighbours than those in bulk, can bias the statistics. We count any other points j as neighbour only if its distance from i, rij, is less than that of i from its closest border, di, constraining the sum over trees in equation (2.1). We always use the Hanisch method to avoid border bias. This requires knowledge of the borders, a non-trivial problem with real data [17]. We compare two different definitions of the borders: the edges of the rectangular plot (which for most species approximate to the convex hull of the set), and the borders obtained with the α-shapes method [15,16]. As discussed below and detailed in the electronic supplementary material, S1, the advantage of α-shapes is to provide a geometrical criterion to remove concavities (for other methods, see [12])
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