Estimating interaction strengths for diverse horizontal systems using performance data

1. Network theory allows us to understand complex systems by evaluating how their constituent elements interact with one another. Such networks are built from matrices that 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. 2. We present a novel modelling framework that uses measures of species performance in the presence of varying densities of their potential interaction partners to estimate the strength of pairwise interactions in diverse horizontal systems. 3. Our method allows us to directly estimate pairwise effects when they are statistically identifiable and to 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 allows for non-symmetrical interactions. 4. We show how to link the parameters inferred by our framework to a population dynamics model to make inferences about the effect of interactions on community dynamics and diversity. 5. The 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.