title: Generalized linear mixed models can detect unimodal species-environment relationships.
abstract: Niche theory predicts that species occurrence and abundance show non-linear, unimodal relationships with respect to environmental gradients. Unimodal models, such as the Gaussian (logistic) model, are however more difficult to fit to data than linear ones, particularly in a multi-species context in ordination, with trait modulated response and when species phylogeny and species traits must be taken into account. Adding squared terms to a linear model is a possibility but gives uninterpretable parameters. This paper explains why and when generalized linear mixed models, even without squared terms, can effectively analyse unimodal data and also presents a graphical tool and statistical test to test for unimodal response while fitting just the generalized linear mixed model. The R-code for this is supplied in Supplemental Information 1.
authors.affiliation: Biometris, Wageningen University and Research Centre , Wageningen , The Netherlands ; Department of Mathematics, COMSATS Institute of Information Technology , Islamabad , Pakistan.
authors.forename: Tahira
authors.initials: T
authors.lastname: Jamil
authors.forename: Cajo J F
authors.initials: CJ
authors.lastname: Ter Braak
keywords: Environmental gradient; Gaussian logistic model; Generalized linear mixed model; Niche theory; Testing unimodal response