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Considerable progress has been made in the development of statistical tools to quantify trophic relationships using stable isotope ratios, including tools that address size and overlap of isotopic niches. We build upon recent progress and propose a new probabilistic method for determining niche region and pairwise niche overlap that can be extended beyond two dimensions, provides directional estimates of niche overlap, accounts for species-specific distributions in niche space, and, unlike geometric methods, produces consistent and unique bivariate projections of multivariate data. We define the niche region (NR) as a given 95% (or user-defined a) probability region in multivariate space. Overlap is calculated as the probability that an individual from species A is found in the N(R) of species B. Uncertainty is accounted for in a Bayesian framework, and is the only aspect of the methodology that depends on sample size. Application is illustrated with three-dimensional stable isotope data, but practitioners could use any continuous indicator of ecological niche in any number of dimensions. We suggest that this represents an advance in our ability to quantify and compare ecological niches in a way that is more consistent with Hutchinson's concept of an "n-dimensional hypervolume".
Swanson et al. (Thu,) studied this question.