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Generalized linear mixed models can detect unimodal species-environment relationships

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Author(s): Tahira Jamil | Cajo J.F. ter Braak

Journal: PeerJ
ISSN 2167-8359

Volume: 1;
Start page: e95;
Date: 2013;
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Keywords: Environmental gradient | Testing unimodal response | Niche theory | Generalized linear mixed model | Gaussian logistic model

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.

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