Appendix S1 Description and discussion of the replacement, richness difference and nestedness indices.

Appendix S2 Simulations showing that the replacement (Repl) and richness/abundance difference (RichDiff and AbDiff) indices respond monotonically to species gradients.

Appendix S3 R function to compute the Podani and Baselga family decompositions of the Jaccard or Sørensen groups into replacement and richness difference (or nestedness) components, for species presence-absence or abundance data.

Appendix S4 R function to compute the dbRDA F-test of significance between response data represented by a Euclidean or non-Euclidean dissimilarity matrix and a matrix of explanatory variables, following McArdle & Anderson (2001).

Appendix S5 R function to compute LCBD indices from a dissimilarity matrix (D) or from beta diversity component matrices (Repl, RichDiff, AbDiff or Nes).

Appendix S6 Principal coordinate ordinations of the replacement and richness difference indices for the fish case study data.

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