Similarity

similarity(object, ...)

# S4 method for CountMatrix
similarity(object, method = c("brainerd", "bray",
  "jaccard", "morisita", "sorenson", "binomial"), ...)

# S4 method for IncidenceMatrix
similarity(object, method = c("jaccard",
  "sorenson"), ...)

Arguments

object

A \(m \times p\) matrix of count data.

...

Further arguments to be passed to internal methods.

method

A character string specifying the method to be used (see details). Any unambiguous substring can be given.

Value

similarity returns a symmetric matrix of class SimilarityMatrix.

Details

\(\beta\)-diversity can be measured by addressing similarity between pairs of samples/cases (Brainerd-Robinson, Jaccard, Morisita-Horn and Sorenson indices). Similarity between pairs of taxa/types can be measured by assessing the degree of co-occurrence (binomial co-occurrence).

Jaccard, Morisita-Horn and Sorenson indices provide a scale of similarity from 0-1 where 1 is perfect similarity and 0 is no similarity. The Brainerd-Robinson index is scaled between 0 and 200. The Binomial co-occurrence assessment approximates a Z-score.

binomial

Binomial co-occurrence assessment. This assesses the degree of co-occurrence between taxa/types within a dataset. The strongest associations are shown by large positive numbers, the strongest segregations by large negative numbers.

brainerd

Brainerd-Robinson quantitative index. This is a city-block metric of similarity between pairs of samples/cases.

bray

Sorenson quantitative index (Bray and Curtis modified version of the Sorenson index).

jaccard

Jaccard qualitative index.

morisita

Morisita-Horn quantitative index.

sorenson

Sorenson qualitative index.

References

Brainerd, G. W. (1951). The Place of Chronological Ordering in Archaeological Analysis. American Antiquity, 16(04), 301-313. DOI: 10.2307/276979.

Bray, J. R. & Curtis, J. T. (1957). An Ordination of the Upland Forest Communities of Southern Wisconsin. Ecological Monographs, 27(4), 325-349. DOI: 10.2307/1942268.

Kintigh, K. (2006). Ceramic Dating and Type Associations. In J. Hantman and R. Most (eds.), Managing Archaeological Data: Essays in Honor of Sylvia W. Gaines. Anthropological Research Paper, 57. Tempe, AZ: Arizona State University, p. 17-26.

Magurran, A. E. (1988). Ecological Diversity and its Measurement. Princeton, NJ: Princeton University Press. DOI: 10.1007/978-94-015-7358-0.

Robinson, W. S. (1951). A Method for Chronologically Ordering Archaeological Deposits. American Antiquity, 16(04), 293-301. DOI: 10.2307/276978.

See also

Other diversity: diversity, richness, turnover

Examples

# Data from Huntley 2008 ceramics <- CountMatrix( data = c(16, 9, 3, 0, 1, 13, 3, 2, 0, 0, 9, 5, 2, 5, 0, 14, 12, 3, 0, 0, 0, 26, 4, 0, 0, 1, 26, 4, 0, 0, 0, 11, 3, 13, 0, 0, 0, 17, 0, 16, 0, 0, 18, 0, 14), nrow = 9, byrow = TRUE, dimnames = list(c("Atsinna", "Cienega", "Mirabal", "PdMuertos", "Hesh", "LowPesc", "BoxS", "Ojo Bon", "S170"), c("DLH-1", "DLH-2a", "DLH-2b", "DLH-2c", "DLH-4")) ) # Brainerd-Robinson measure (count data) C <- similarity(ceramics, "brainerd") plot_spot(C)
# Data from Magurran 1988, p. 166 birds <- CountMatrix( data = c(1.4, 4.3, 2.9, 8.6, 4.2, 15.7, 2.0, 50, 1, 11.4, 11.4, 4.3, 13.0, 14.3, 8.6, 7.1, 10.0, 1.4, 2.9, 5.7, 1.4, 11.4, 2.9, 4.3, 1.4, 2.9, 0, 0, 0, 2.9, 0, 0, 0, 10, 0, 0, 5.7, 2.5, 5.7, 8.6, 5.7, 2.9, 0, 0, 2.9, 0, 0, 5.7, 0, 2.9, 0, 2.9) * 10, nrow = 2, byrow = TRUE, dimnames = list(c("unmanaged", "managed"), NULL) ) # Jaccard measure (presence/absence data) similarity(birds, "jaccard") # 0.46
#> 2 x 2 (dis)similarity matrix (jaccard): #> (39dc0461-7b97-4d1b-964f-007e99265551) #> unmanaged managed #> unmanaged 1.0000000 0.4615385 #> managed 0.4615385 1.0000000
# Sorenson measure (presence/absence data) similarity(birds, "sorenson") # 0.63
#> 2 x 2 (dis)similarity matrix (sorenson): #> (0be1f695-04a6-424b-aaf5-c682014ba207) #> unmanaged managed #> unmanaged 1.0000000 0.6315789 #> managed 0.6315789 1.0000000
# Jaccard measure (Bray's formula ; count data) similarity(birds, "bray") # 0.44
#> 2 x 2 (dis)similarity matrix (bray): #> (248b1947-2c6a-4b7c-8de8-fa04c746d3c0) #> unmanaged managed #> unmanaged 1.0000000 0.4442754 #> managed 0.4442754 1.0000000
# Morisita-Horn measure (count data) similarity(birds, "morisita") # 0.81
#> 2 x 2 (dis)similarity matrix (morisita): #> (77860f05-3c45-48fb-9f1c-d9c9591f81f6) #> unmanaged managed #> unmanaged 1.0000000 0.8134497 #> managed 0.8134497 1.0000000