Estimation of the non-linear parameter in Generalised Diversity-Interactions models is unaffected by change in structure of the interaction terms

Abstract

Many approaches for modelling the biodiversity and ecosystem function (BEF) relationship have been developed over recent decades. Diversity-Interactions modelling, a regression-based approach, models the BEF relationship by expressing ecosystem functions as a linear combination of species-specific effects, species’ proportions, and species’ interactions. The species interactions in a Diversity-Interactions model can take different forms (e.g., a unique interaction term for each pair of species, or a single interaction term for any pair of species) and may include a non-linear parameter (theta) as an exponent to the species interactions to capture non-linear relationships, giving rise to Generalized Diversity-Interactions (GDI) modelling. The structure of the interaction terms describes the underlying biological processes in the ecosystem, while the value of theta can determine the shape of the BEF relationship. When fitting GDI models, it is unclear whether one should choose the interaction structure first and then estimate θ, or vice versa. It is also unknown whether the estimate of theta is robust to changes in the structure of the linear interaction terms of the model. Using a simulation study, we test the robustness of theta and compare multiple model selection approaches to identify an optimal and computationally efficient model selection procedure for GDI models. Results show that the estimate of theta is robust and remains unbiased regardless of changes in the underlying structure of interaction terms, and that the most efficient model selection procedure is to first estimate theta for one interaction structure and then reuse this estimate for the other interaction structures.