Abstract
One of the more difficult challenges in community ecology is inferring species interactions on the basis of patterns in the spatial distribution of organisms. At its core, the problem is that distributional patterns reflect the 'realized niche', the net result of a complex interplay of processes involving dispersal, environmental, and interaction effects. Disentangling these effects can be difficult on at least two distinct levels. From a statistical point of view, splitting a population's variation into contributions from its interaction partners, abiotic environment and spatial proximity requires 'natural experiments' where all three factors somehow vary independently from each other. On a more conceptual level, it is not even clear how to meaningfully separate these processes: for instance, species interactions could depend on the state of the abiotic and biotic environment, and these two processes may combine in highly non-additive ways. Here we show that the latter issue arises almost inescapably, even in a simple theoretical setting designed to minimize it. Using a model of competitive metacommunity dynamics where direct species interactions are assumed to be context-independent, we show that inferring these interactions accurately from cross-species correlations is a major challenge under all but the most restrictive assumptions. However, we also find that it is possible to estimate the statistical moments (mean value and variance) of the species interactions distribution much more robustly, even if the precise values cannot be inferred. Consequently, we argue that study of multi-species spatial patterns can still be informative for theoretical approaches that build on statistical distributions of species parameters to predict macroscopic outcomes of community assembly.