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
.