Model-based ordination for species with unequal niche widths

O_LIIt 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. C_LIO_LIMost multivariate methods assume species respond linearly to the environment of the niche, or with a quadratic curve that is of equal width and height for all species. However, it is widely understood that some species are generalists who 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. C_LIO_LIWe 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 and equal maxima. C_LIO_LIBy explicitly estimating species optima, tolerances, and maxima, per ecological gradient, we can better predict change in species communities, and understand how species relate to each other. C_LI