tabula (version 1.0.0)

beta-diversity: \(\beta\)-diversity

Description

Measures differenciation diversity. similarity returns a similarity matrix. turnover returns the degree of turnover in taxa composition along a grandient or transect.

Usage

turnover(object, ...)
similarity(object, ...)
# S4 method for CountMatrix
turnover(object, method = c("whittaker", "cody",
  "routledge1", "routledge2", "routledge3", "wilson"), simplify = FALSE,
  ...)
# S4 method for IncidenceMatrix
turnover(object, method = c("whittaker",
  "cody", "routledge1", "routledge2", "routledge3", "wilson"),
  simplify = FALSE, ...)
# S4 method for CountMatrix
similarity(object, method = c("brainerd", "bray",
  "jaccard", "morisita", "sorenson"), ...)
# S4 method for IncidenceMatrix
similarity(object, method = c("jaccard",
  "sorenson"), ...)

Arguments

object

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

...

Further arguments passed to other methods.

method

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

simplify

A logical scalar: should the result be simplified to a matrix? The default value, FALSE, returns a list.

Value

similarity returns a \(m \times m\) symetric matrix.

If simplify is FALSE, turnover returns a list (default), else returns a matrix.

Turnover

The following methods can be used to acertain the degree of turnover in taxa composition along a gradient (\(\beta\)-diversity) on qualitative (presence/absence) data. This assumes that the order of the matrix rows (from 1 to \(n\)) follows the progression along the gradient/transect.

whittaker

Whittaker measure.

cody

Cody measure.

routledge1

Routledge first measure.

routledge2

Routledge second measure.

routledge3

Routledge third measure. This is the exponential form of the second measure.

wilson

Wilson measure.

Similarity

\(\beta\)-diversity can also be measured by addressing similarity between pairs of sites. This provides a scale of similarity from 0-1 where 1 is perfect similarity and 0 is no similarity (with the exception of the Brainerd-Robinson index which is scaled between 0 and 200):

brainerd

Brainerd-Robinson quantitative index. This is a city-block metric of similarity.

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.

Cody, M. L. (1975). Towards a theory of continental species diversity: Bird distributions over Mediterranean habitat gradients. In M. L. Cody & J. M. Diamond (Eds.), Ecology and Evolution of Communities. Cambridge, MA: Harvard University Press, p. 214<U+2013>257.

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.

Routledge, R. D. (1977). On Whittaker<U+2019>s Components of Diversity. Ecology, 58(5), 1120-1127. DOI: 10.2307/1936932.

Whittaker, R. H. (1960). Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30(3), 279-338. DOI: 10.2307/1943563.

Wilson, M. V., & Shmida, A. (1984). Measuring Beta Diversity with Presence-Absence Data. The Journal of Ecology, 72(3), 1055-1064. DOI: 10.2307/2259551.

See Also

richness rarefaction diversity evenness

Examples

# NOT RUN {
# Degree of turnover
# Data from Magurran 1988, p. 162
trees <- IncidenceMatrix(
  data = c(1, 1, 1, 0, 0, 0,
           1, 1, 1, 1, 1, 1,
           0, 0, 1, 0, 1, 0,
           0, 0, 0, 1, 1, 1,
           0, 0, 0, 0, 1, 1,
           0, 0, 0, 1, 0, 1),
  nrow = 6, byrow = FALSE,
  dimnames = list(c("1", "2", "3", "4", "5", "6"),
                  c("Birch", "Oak", "Rowan", "Beech", "Hazel", "Holly"))
)

## Whittaker's measure
turnover(trees, "whittaker") # 1

## Cody's measure
turnover(trees, "cody") # 3

## Routledge's measures
turnover(trees, "routledge1") # 0.29
turnover(trees, "routledge2") # 0.56
turnover(trees, "routledge3") # 1.75

## Wilson and Shmida's measure
turnover(trees, "wilson") # 1

# Similarity measures
# 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

## Sorenson measure
## (presence/absence data)
similarity(birds, "sorenson") # 0.63

## Jaccard measure (Bray's formula)
## (count data)
similarity(birds, "bray") # 0.44

## Morisita-Horn measure
## (count data)
similarity(birds, "morisita") # 0.81
# }