Data from: 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 not available with classical indices. In addition, we find
that when characterizing niche breadth, niche overlap and specialization
in terms of vectors of proportions, these concepts are naturally
integrated in a coherent unifying framework. When data are categorical, we
recommend the use of compositional indices for the statistical analysis of
specialization metrics, niche breadth and niche overlap. We believe that
the unified framework emerging from our compositional approach to niche
metrics will allow a more thorough understanding of specialization at
multiple levels of biological organization and provide novel insights in
complex phenomena such as invasions and niche shifts.