Estimating interaction matrices from performance data for diverse systems

O_LINetwork theory allows us to understand complex systems by evaluating how their constituent elements interact with one another. Such networks are built from matrices which describe the effect of each element on all others. Quantifying the strength of these interactions from empirical data can be difficult, however, because the number of potential interactions increases non-linearly as more elements are included in the system, and not all interactions may be empirically observable when some elements are rare. C_LIO_LIWe present a novel modelling framework which estimates the strength of pairwise interactions in diverse horizontal systems, using measures of species performance in the presence of varying densities of their potential interaction partners. C_LIO_LIOur method allows us to directly estimate pairwise effects when they are statistically identifiable and approximate pairwise effects when they would otherwise be statistically unidentifiable. The resulting interaction matrices can include positive and negative effects, the effect of a species on itself, and are non-symmetrical. C_LIO_LIThe advantages of these features are illustrated with a case study on an annual wildflower community of 22 focal and 52 neighbouring species, and a discussion of potential applications of this framework extending well beyond plant community ecology. C_LI