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"), ...)

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

... | Further arguments to be passed to internal methods. |

method | A |

`similarity`

returns a symmetric matrix of class
SimilarityMatrix.

\(\beta\)-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.

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.

Other diversity: `heterogeneity-index`

,
`richness-index`

,
`turnover-index`

# 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#> <SimilarityMatrix: dfab2aea-e5f7-435f-9625-403e4f182d0f> #> 2 x 2 (dis)similarity matrix (jaccard): #> unmanaged managed #> unmanaged 1.0000000 0.4615385 #> managed 0.4615385 1.0000000# Sorenson measure (presence/absence data) similarity(birds, "sorenson") # 0.63#> <SimilarityMatrix: 4102f66b-f785-46b7-976a-84e01fcaf5f5> #> 2 x 2 (dis)similarity matrix (sorenson): #> unmanaged managed #> unmanaged 1.0000000 0.6315789 #> managed 0.6315789 1.0000000# Jaccard measure (Bray's formula ; count data) similarity(birds, "bray") # 0.44#> <SimilarityMatrix: e872fdaa-235a-47d3-9431-651069bfb3c8> #> 2 x 2 (dis)similarity matrix (bray): #> unmanaged managed #> unmanaged 1.0000000 0.4442754 #> managed 0.4442754 1.0000000# Morisita-Horn measure (count data) similarity(birds, "morisita") # 0.81#> <SimilarityMatrix: 772aa2a6-655f-472e-9011-3588dc602e50> #> 2 x 2 (dis)similarity matrix (morisita): #> unmanaged managed #> unmanaged 1.0000000 0.8134497 #> managed 0.8134497 1.0000000