the comparison of categorical variables (chi-square statistic and derived forms). For
presence-absence data, binary coefficients such as the Jaccard, Sørensen and Ochiai
coefficients can be used in the R mode to compare species.
3.4.1 R Mode: Species Abundance Data
Covariances as well as parametric and non-parametric correlation coefficients are
often used to compare species distributions through space or time. Note that doublezeros as well as the joint variations in abundance contribute to increase the correlations. In the search for species associations, Legendre (2005) applied one of the
transformations described in Sect. 3.5 in order to remove the effect of the total
abundance per site prior to the calculation of parametric and non-parametric correlations. Some concepts of species association use only the positive covariances or
correlations to recognize associations of co-varying species.
Besides correlations, the chi-square distance, which was used in the Q mode, can
also be computed on transposed matrices (R mode).
The example below shows how to compute and display an R-mode chi-square
dissimilarity matrix of the 27 fish species:
# Transpose matrix of species abundances
spe.t <- t(spe)
# Chi-square pre-transformation followed by Euclidean distance
spe.t.chi <- decostand(spe.t, "chi.square")
spe.t.D16 <- dist(spe.t.chi)
coldiss(spe.t.D16, diag = TRUE)
Can you identify groups of species in the right-hand display?
3.4.2 R Mode: Species Presence-Absence Data
For binary species data, the Jaccard (S 7 ), Sørensen (S 8 ) and Ochiai (S 14 ) coefficients
can also be used in the R mode. Apply S 7 to the fish presence-absence data after
transposition of the matrix (object spe.t):
# Jaccard index on fish presence-absence
spe.t.S7 <- vegdist(spe.t, "jaccard", binary = TRUE)
coldiss(spe.t.S7, diag = TRUE)
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3 Association Measures and Matrices
presence-absence data, binary coefficients such as the Jaccard, Sørensen and Ochiai
coefficients can be used in the R mode to compare species.
3.4.1 R Mode: Species Abundance Data
Covariances as well as parametric and non-parametric correlation coefficients are
often used to compare species distributions through space or time. Note that doublezeros as well as the joint variations in abundance contribute to increase the correlations. In the search for species associations, Legendre (2005) applied one of the
transformations described in Sect. 3.5 in order to remove the effect of the total
abundance per site prior to the calculation of parametric and non-parametric correlations. Some concepts of species association use only the positive covariances or
correlations to recognize associations of co-varying species.
Besides correlations, the chi-square distance, which was used in the Q mode, can
also be computed on transposed matrices (R mode).
The example below shows how to compute and display an R-mode chi-square
dissimilarity matrix of the 27 fish species:
# Transpose matrix of species abundances
spe.t <- t(spe)
# Chi-square pre-transformation followed by Euclidean distance
spe.t.chi <- decostand(spe.t, "chi.square")
spe.t.D16 <- dist(spe.t.chi)
coldiss(spe.t.D16, diag = TRUE)
Can you identify groups of species in the right-hand display?
3.4.2 R Mode: Species Presence-Absence Data
For binary species data, the Jaccard (S 7 ), Sørensen (S 8 ) and Ochiai (S 14 ) coefficients
can also be used in the R mode. Apply S 7 to the fish presence-absence data after
transposition of the matrix (object spe.t):
# Jaccard index on fish presence-absence
spe.t.S7 <- vegdist(spe.t, "jaccard", binary = TRUE)
coldiss(spe.t.S7, diag = TRUE)
52
3 Association Measures and Matrices