Data from: Model-based ordination for species with unequal niche widths

It is common practice for ecologists to examine species niches in the
study of community composition. The response curve of a species in the
fundamental niche is usually assumed to be quadratic. The center of a
quadratic curve represents a species' optimal environmental
conditions, and the width its ability to tolerate deviations from the
optimum. Most multivariate methods assume species respond linearly to the
environment of the niche, or with a quadratic curve that is of equal width
for all species. However, it is widely understood that some species are
generalists that can tolerate deviations from their optimal environment
better than others. Rare species often tolerate a smaller range of
environments than more common species, corresponding to a narrow
niche.  We propose a new method, for ordination and fitting Joint
Species Distribution Models, based on Generalized Linear Mixed-Effects
Models, which relaxes the assumptions of equal tolerances. By explicitly
estimating species maxima, and species optima, and tolerances per
ecological gradient, we can better understand how species relate to each
other.