The peril of proportions: robust niche indices for categorical data

Indices of niche breadth and niche overlap for categorical data are typically expressed in terms of proportions of resources use. These are unit-sum constrained data; hence, direct application of standard general linear modelling methods to such indices can lead to spurious correlations and misleading inference.
To overcome these limitations, we introduce a compositional data analysis (CoDA) approach and derive compositional expressions of niche breadth, niche overlap and specialization. Compositional data analysis is specifically devoted to the analysis of vectors of proportions (i.e. compositions) and represents the appropriate framework for the study of sets of data with unit-sum constraint as those typically used in the calculation of niche indices.
We show that compositional indices exhibit suitable statistical properties that make them flexible and robust, allowing downstream application of the full toolbox of multivariate analysis techniques to these estimators, a possibility n...