Similarity
Usage
similarity(object, ...)
index_jaccard(x, y, ...)
index_sorenson(x, y, ...)
index_bray(x, y, ...)
index_morisita(x, y, ...)
index_brainerd(x, y, ...)
index_binomial(x, y, ...)
# S4 method for matrix
similarity(
object,
method = c("brainerd", "bray", "jaccard", "morisita", "sorenson", "binomial")
)
# S4 method for data.frame
similarity(
object,
method = c("brainerd", "bray", "jaccard", "morisita", "sorenson", "binomial")
)
# S4 method for character,character
index_jaccard(x, y)
# S4 method for logical,logical
index_jaccard(x, y)
# S4 method for numeric,numeric
index_jaccard(x, y)
# S4 method for logical,logical
index_sorenson(x, y)
# S4 method for numeric,numeric
index_sorenson(x, y)
# S4 method for numeric,numeric
index_bray(x, y)
# S4 method for numeric,numeric
index_morisita(x, y)
# S4 method for numeric,numeric
index_brainerd(x, y)
# S4 method for numeric,numeric
index_binomial(x, y)
Value
similarity()
returns a stats::dist object.index_*()
return anumeric
vector.
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 measures:
heterogeneity()
,
occurrence()
,
plot_diversity
,
rarefaction()
,
richness()
,
simulate()
,
turnover()
Examples
## Data from Huntley 2004, 2008
data("pueblo")
## Brainerd-Robinson measure
(C <- similarity(pueblo, "brainerd"))
#> Atsinna Cienega Mirabal PdMuertos Hesh LowPesc BoxS
#> Cienega 164.36782
#> Mirabal 152.38095 138.09524
#> PdMuertos 179.31034 150.57471 152.38095
#> Hesh 82.75862 55.55556 66.66667 103.44828
#> LowPesc 89.21023 62.00717 73.11828 109.89989 193.54839
#> BoxS 82.75862 55.55556 114.28571 102.17114 103.70370 103.70370
#> Ojo Bon 27.58621 22.22222 19.04762 20.68966 26.66667 25.80645 22.22222
#> S170 27.58621 22.22222 19.04762 20.68966 26.66667 25.80645 22.22222
#> Ojo Bon
#> Cienega
#> Mirabal
#> PdMuertos
#> Hesh
#> LowPesc
#> BoxS
#> Ojo Bon
#> S170 190.53030
plot_spot(C)
## Data from Magurran 1988, p. 166
birds <- matrix(
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),
nrow = 2, byrow = TRUE
)
rownames(birds) <- c("unmanaged", "managed")
## Jaccard measure (presence/absence data)
similarity(birds, "jaccard") # 0.46
#> unmanaged
#> managed 0.4615385
## Sorenson measure (presence/absence data)
similarity(birds, "sorenson") # 0.63
#> unmanaged
#> managed 0.6315789
# Jaccard measure (Bray's formula ; count data)
similarity(birds, "bray") # 0.44
#> unmanaged
#> managed 0.4442754
# Morisita-Horn measure (count data)
similarity(birds, "morisita") # 0.81
#> unmanaged
#> managed 0.8134497