fuzzySim (version 2.0)

fuzSim: Fuzzy similarity

Description

This function calculates fuzzy similarity, based on a fuzzy version of the binary similarity index specified in method, between two binary (0 or 1) or fuzzy (between 0 and 1) variables.

Usage

fuzSim(x, y, method, na.rm = TRUE)

Arguments

x

a vector of (optionally fuzzy) presence-absence data, with 1 meaning presence, 0 meaning absence, and values in between meaning fuzzy presence (or the degree to which each locality belongs to the set of species presences, or to which each species belongs to the locality; Zadeh, 1965). Fuzzy presence-absence can be obtained, for example, with functions multGLM, distPres or multTSA in this package.

y

a vector similar to x, of the same length and in the same order.

method

the similarity index to use. Currently available options are "Jaccard", "Sorensen", "Simpson" and "Baroni" (see Details).

na.rm

logical value indicating whether NA values should be ignored. The default is TRUE.

Value

The function returns a value between 0 and 1 representing the fuzzy similarity between x and y. Note, for example, that Jaccard similarity can be converted to dissimilarity (or Jaccard distance) if subtracted from 1, while 1-Sorensen is not a proper distance metric as it lacks the property of triangle inequality (see http://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient).

Details

Similarity between ecological communities, beta diversity patterns, biotic regions, and distributional relationships among species are commonly determined based on pair-wise (dis)similarities in species' occurrence patterns. Some of the most commonly employed similarity indices are those of Jaccard (1901), Sorensen (1948), Simpson (1960) and Baroni-Urbani & Buser (1976), which are here implemented in their fuzzy versions (Barbosa, 2015), able to deal with both binary and fuzzy data. Jaccard's and Baroni's indices have associated tables of significant values (Baroni-Urbani & Buser 1976, Real & Vargas 1996, Real 1999).

References

Barbosa A.M. (2015) fuzzySim: applying fuzzy logic to binary similarity indices in ecology. Methods in Ecology and Evolution, 6: 853-858.

Baroni-Urbani C. & Buser M.W. (1976) Similarity of Binary Data. Systematic Zoology, 25: 251-259

Jaccard P. (1901) Etude comparative de la distribution florale dans une portion des Alpes et des Jura. Memoires de la Societe Vaudoise des Sciences Naturelles, 37: 547-579

Olivero J., Real R. & Vargas J.M. (1998) Distribution of breeding, wintering and resident waterbirds in Europe: biotic regions and the macroclimate. Ornis Fennica, 75: 153-175

Real R. (1999) Tables of significant values of Jaccard's index of similarity. Miscellania Zoologica 22: 29:40

Real R. & Vargas J.M (1996) The probabilistic basis of Jaccard's index of similarity. Systematic Biology 45: 380-385

Simpson, G.G. (1960) Notes on the measurement of faunal resemblance. Amer. J. Sci. 258A, 300-311

Sorensen T. (1948) A method of establishing groups of equal amplitude in plant sociology based on similarity of species and its application to analyses of the vegetation on Danish commons. Kongelige Danske Videnskabernes Selskab, 5(4): 1-34

Zadeh L.A. (1965) Fuzzy sets. Information and Control, 8: 338-353

See Also

simMat; modOverlap

Examples

# NOT RUN {
data(rotif.env)

names(rotif.env)


# you can calculate similarity between binary species occurrence patterns:

fuzSim(rotif.env[, "Abrigh"], rotif.env[, "Afissa"], method = "Jaccard")
fuzSim(rotif.env[, "Abrigh"], rotif.env[, "Afissa"], method = "Sorensen")
fuzSim(rotif.env[, "Abrigh"], rotif.env[, "Afissa"], method = "Simpson")
fuzSim(rotif.env[, "Abrigh"], rotif.env[, "Afissa"], method = "Baroni")


# or you can model environmental favourability for these species
# and calculate fuzzy similarity between their environmental predictions
# which goes beyond the strict coincidence of their occurrence records:

fav <- multGLM(rotif.env, sp.cols = 18:19, var.cols = 5:17, step = TRUE, 
FDR = TRUE, trim = TRUE, P = FALSE, Fav = TRUE) $ predictions

fuzSim(fav[, "Abrigh_F"], fav[, "Afissa_F"], method = "Jaccard")
fuzSim(fav[, "Abrigh_F"], fav[, "Afissa_F"], method = "Sorensen")
fuzSim(fav[, "Abrigh_F"], fav[, "Afissa_F"], method = "Simpson")
fuzSim(fav[, "Abrigh_F"], fav[, "Afissa_F"], method = "Baroni")
# }