Estimating interaction strengths for diverse horizontal systems using performance data

Abstract

Network 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 nonlinearly as more elements are included in the system, and not all interactions may be empirically observable when some elements are rare. We present a novel modelling framework which 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. 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. 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. 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.

Plant interaction networks reveal the limits of our understanding of diversity maintenance

“…Whilst convergence for the intermediate and shady categories was unproblematic ( � R < 1.01), convergence was more difficult for certain parameters in the open environment (4.3% parameters with � R > 1.1, 21.7 % with � R > 1.01). This was not unexpected as Bimler et al (2023a) had similar difficulties when evaluating the model on the overall dataset with all categories grouped together, indicating problematic geometries in the shape of certain posteriors. We refer to the S. Methods S2.2 for further details and why we are confident our estimates are still informative despite imperfect convergence for a small number of parameters.…”

“…This was not unexpected as Bimler et al. (2023a) had similar difficulties when evaluating the model on the overall dataset with all categories grouped together, indicating problematic geometries in the shape of certain posteriors. We refer to the S. Methods S2.2 for further details and why we are confident our estimates are still informative despite imperfect convergence for a small number of parameters.…”

“…Bimler et al. (2023a) describe the entire design in detail and the data have been publicly archived (Bimler et al., 2023b).…”

“…We quantified interactions between focal species and their neighbours for each of the three shade categories using the joint model framework presented in Bimler et al. (2023a). See S. Methods S2.1 for a summary of this approach.…”

“…We, therefore, felt justified in treating it as an annual species in our model, with mean field estimates of survivorship and germination equivalent to survivorship of the root and likelihood it grows back the next year. Bimler et al (2023a) describe the entire design in detail and the data have been publicly archived (Bimler et al, 2023b).…”