Estimation of the non-linear parameter in Generalised Diversity-Interactions models is unaffected by change in structure of the interaction terms
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Research over the past few decades has assumed the richness (number of species) to be the primary driver of the biodiversity and ecosystem function (BEF) relationship. However, biodiversity is multi-dimensional, and richness alone does not capture all its attributes. Diversity-Interactions modelling is a regression-based framework that models the biodiversity and ecosystem function relationship by incorporating species-specific effects along with the interactions between species. The species interactions in a Diversity-Interactions model can take several different forms ranging in complexity from a single interaction term (assuming all pairs of species interact in the same way) to many interaction terms (e.g. assuming a separate interaction for all pairs of species). The specification of the interactions may also include a non-linear parameter (θ) as an exponent to the product of the species proportions to allow for non-linear relationship between the response and species interactions, giving rise to Generalized Diversity-Interactions modelling. The structure of the interaction terms describes the underlying biological processes and thus the selection of a correct structure is important. The inclusion of θ introduces complexity to the model selection process: we could (a) select the interaction structure first by assuming θ=1 and then estimate θ, or (b) estimate θ first and then select the appropriate interaction structure by fixing θ, or (c) test for θ and its inclusion for each interaction structure. It is also unknown whether θ is robust to changes in the underlying interaction structure. Using a simulation study, we test the robustness of θ and compare multiple model selection approaches to identify an optimal and computationally efficient model selection procedure for Generalized Diversity-Interactions models.
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