(site profiles) in some way; this removes from the data the total abundance per site,
which is the response of the species to the total productivity of the sites. In the
Hellinger and log-chord transformations, the relative abundance values are respectively square-rooted or their log is taken, which further reduces the importance of the
highest abundance values.
Table 3.1 Some distance and dissimilarity functions in Q mode that are useful to ecologists and are
available in widely used R packages. The symbol ) means that applying the function designed for
quantitative data to presence-absence data produces the same result as computing the corresponding
function designed for presence-absence data.
Quantitative data
Presence-absence data
Community composition data
Ružička dissimilarity
vegdist(.,"jac")
dist.ldc(., "ruzicka")
) Jaccard dissimilarity
vegdist(., "jac",
binary¼TRUE)
dist.ldc(., "jaccard")
dist.binary(., method¼1)
Chord distance
dist.ldc(., "chord")
decostand(., "norm") followed by
vegdist(., "euc")
) Ochiai dissimilarity
dist.ldc(., "ochiai")
dist.binary(., method¼7)
Hellinger distance
dist.ldc(., "hellinger")
decostand(.,"hel") followed by
vegdist(.,"euc")
) Ochiai dissimilarity
dist.ldc(., "ochiai")
dist.binary(., method¼7)
Log-chord distance
dist.ldc(., "log.chord")
decostand(log1p(.), "norm")
followed by vegdist(., "euc")
) Ochiai dissimilarity
dist.ldc(., "ochiai")
dist.binary(., method¼7)
Percentage difference dissimilarity
dist.ldc(., "percentdiff")
vegdist(., "bray")
) Sørensen dissimilarity
dist.ldc(., "sorensen")
dist.binary(., method¼5)
Chi-square distance
dist.ldc(., "chisquare")
decostand(., "chi.square")
followed by vegdist(.,"euc")
Chi-square distance
dist.ldc(., "chisquare")
decostand(.,"chi.square")
followed by vegdist(.,"euc")
Canberra distance
dist.ldc(., "canberra")
vegdist(., "canberra")
Other variables, mixed physical units
Standardized variables:
Euclidean distance
vegdist(., "euc")
Standardized variables:
Simple matching coefficient
dist.binary(., method¼2)
Non-standardized variables:
Gower dissimilarity
daisy(., "gower")
56
3 Association Measures and Matrices