BrayCurtis

Bray-Curtis, short for Bray-Curtis dissimilarity, is a statistical measure used in ecology and related fields to quantify how different two samples are in terms of their species composition and abundances. It was introduced by J. T. Bray and J. Verner Curtis in 1957 and has since become a standard tool for beta diversity analyses and community comparison.

The dissimilarity between two samples i and j is calculated as BCij = sum over all species k of |xik - xjk| divided by sum over all species k of (xik + xjk), where xik and xjk are the abundances of species k in samples i and j, respectively. The value ranges from 0 to 1, with 0 indicating identical composition and 1 indicating no shared abundances. The metric is based on absolute differences in species abundances and emphasizes more abundant species.

Bray-Curtis is widely used in ecological research, including studies of plant communities, animal assemblages, and microbial ecosystems. It is commonly employed with ordination methods such as non-metric multidimensional scaling (NMDS) and principal coordinates analysis (PCoA) to visualize patterns of community similarity or dissimilarity across sites or treatments. The method is particularly suited to abundance data and is relatively robust to joint absences, though it can be influenced by differences in sampling effort and does not account for phylogenetic relationships unless combined with other approaches.

In practice, researchers may use presence-absence versions of the metric or apply transformations (e.g., rarefaction, normalization) to mitigate issues related to sample effort and to tailor the analysis to their data.