Compute directional indices of community change along coenoclines or time.
directional.response(mat, method = "overlap", relativize = NULL)A community composition data matrix with sites in rows and species
in columns. The direction of the physical process is indicated by the order of the
sampling units in mat. The class of mat can be either data.frame
or matrix.
One of the 11 calculation methods available in the function:
"overlap", "gain", "loss", "gaining.turnover",
"neutral.turnover", "losing.turnover", "gaining.nestedness",
"neutral.nestedness", "losing.nestedness",
"gaining.strict.nestedness", "losing.strict.nestedness".
The default value is method="overlap".
Compute relativized indices: relativize="J" for the
Jaccard denominator (a+b+c) or relativize="S" for the Sorensen denominator
(2*a+b+c). If relativize=NULL, the index is not divided by a denominator.
A list containing the following results:
mat.out: A square matrix with the chosen index computed among the sites.
Depending on the method chosen, this matrix may be symmetric or non-symmetric.
total.t: methods #4 to 6, a matrix with total turnover (b+c); else NA.
total.n: For methods #7 to 9, a matrix with total nestedness a+abs(b-c)
if a>0; else NA.
total.strict.n: For methods #10 and 11, a matrix with total strict nestedness
a+abs(b-c) if a>0 and b!=c; else NA.
den: For calculation results with Jaccard or Sorensen denominators:
a square matrix of denominators. If relativize=NULL, den=NA.
The output matrix is non-symmetric, meaning that its upper triangle is not the mirror
image of the lower triangle. Given the direction of the physical process through space
or time indicated by the order of the sampling units, the output matrix mat.out
reflects that direction in its non-symmetric presentation, From (rows of the
matrix) To (columns of the matrix). Users of the function can extract one or the
other of these triangular portions and analyse them separately. See Appendix xx for
examples.
Schmera, D., P. Legendre, T. Eros, M. Toth, E. K. Magyari, B. Baur and J. Podani. 2022. New measures for quantifying directional changes in presence-absence community data. Ecological Indicators 136: 108618. https://doi.org/10.1016/j.ecolind.2022.108618
Verneaux, J. (1973) Cours d'eau de Franche-Comté (Massif du Jura). Recherches écologiques sur le réseau hydrographique du Doubs. Essai de biotypologie. Thèse d'État, Besançon. 1–257.
# Artificial Example
art <- c(1,1,1,0,0,0,
0,0,0,1,1,0,
0,0,0,0,0,1)
art.data <- matrix(art, nrow=3, ncol=6, byrow=TRUE)
art.out <- directional.response(art.data, method="overlap",relativize=NULL)
#> Method: overlap
# Real data example: the Doubs River fish data (Verneaux 1973), available in ade4.
# 30 sites, 27 species. No fish had been caught at site 8; remove that site
if(require("ade4", quietly = TRUE)) {
data(doubs)
dim(doubs$fish)
fish <- doubs$fish[-8,]
dim(fish)
doubs.out <- directional.response(fish, method="gain", relativize="S")
}
#> Method: gain
#> Relativize with denominator: Sorensen