richness | R Documentation |
richness()
returns sample richness.
composition()
returns asymptotic species richness.
richness(object, ...)
composition(object, ...)
index_ace(x, ...)
index_ice(x, ...)
index_chao1(x, ...)
index_chao2(x, ...)
index_margalef(x, ...)
index_menhinick(x, ...)
## S4 method for signature 'matrix'
richness(object, method = c("count", "margalef", "menhinick"))
## S4 method for signature 'data.frame'
richness(object, method = c("count", "margalef", "menhinick"))
## S4 method for signature 'matrix'
composition(
object,
method = c("chao1", "ace", "chao2", "ice"),
unbiased = FALSE,
improved = FALSE,
k = 10
)
## S4 method for signature 'data.frame'
composition(
object,
method = c("chao1", "ace", "chao2", "ice"),
unbiased = FALSE,
improved = FALSE,
k = 10
)
## S4 method for signature 'numeric'
index_margalef(x, na.rm = FALSE, ...)
## S4 method for signature 'numeric'
index_menhinick(x, na.rm = FALSE, ...)
## S4 method for signature 'numeric'
index_ace(x, k = 10, ...)
## S4 method for signature 'numeric'
index_chao1(x, unbiased = FALSE, improved = FALSE, ...)
## S4 method for signature 'matrix'
index_ice(x, k = 10, ...)
## S4 method for signature 'matrix'
index_chao2(x, unbiased = FALSE, improved = FALSE, ...)
object |
A |
... |
Further arguments to be passed to internal methods. |
x |
A |
method |
A |
unbiased |
A |
improved |
A |
k |
A length-one |
na.rm |
A |
richness()
returns a RichnessIndex object.
composition()
returns a CompositionIndex object.
index_*()
return a numeric
vector.
The number of different taxa, provides an instantly comprehensible
expression of diversity. While the number of taxa within a sample
is easy to ascertain, as a term, it makes little sense: some taxa
may not have been seen, or there may not be a fixed number of taxa
(e.g. in an open system; Peet 1974). As an alternative, richness
(S
) can be used for the concept of taxa number (McIntosh 1967).
It is not always possible to ensure that all sample sizes are equal
and the number of different taxa increases with sample size and
sampling effort (Magurran 1988). Then, rarefaction
(E(S)
) is the number of taxa expected if all samples were of a
standard size (i.e. taxa per fixed number of individuals).
Rarefaction assumes that imbalances between taxa are due to sampling and
not to differences in actual abundances.
The following richness measures are available for count data:
count
Returns the number of observed taxa/types.
margalef
Margalef richness index.
menhinick
Menhinick richness index.
The following measures are available for count data:
ace
Abundance-based Coverage Estimator.
chao1
(improved/unbiased) Chao1 estimator.
The following measures are available for replicated incidence data:
ice
Incidence-based Coverage Estimator.
chao2
(improved/unbiased) Chao2 estimator.
N. Frerebeau
Chao, A. (1984). Nonparametric Estimation of the Number of Classes in a Population. Scandinavian Journal of Statistics, 11(4), 265-270.
Chao, A. (1987). Estimating the Population Size for Capture-Recapture Data with Unequal Catchability. Biometrics 43(4), 783-791. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2531532")}.
Chao, A. & Chiu, C.-H. (2016). Species Richness: Estimation and Comparison. In Balakrishnan, N., Colton, T., Everitt, B., Piegorsch, B., Ruggeri, F. & Teugels, J. L. (Eds.), Wiley StatsRef: Statistics Reference Online. Chichester, UK: John Wiley & Sons, Ltd., 1-26. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/9781118445112.stat03432.pub2")}
Chao, A. & Lee, S.-M. (1992). Estimating the Number of Classes via Sample Coverage. Journal of the American Statistical Association, 87(417), 210-217. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.1992.10475194")}.
Chiu, C.-H., Wang, Y.-T., Walther, B. A. & Chao, A. (2014). An improved nonparametric lower bound of species richness via a modified good-turing frequency formula. Biometrics, 70(3), 671-682. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/biom.12200")}.
Magurran, A. E. (1988). Ecological Diversity and its Measurement. Princeton, NJ: Princeton University Press. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-94-015-7358-0")}.
Kintigh, K. W. (1989). Sample Size, Significance, and Measures of Diversity. In Leonard, R. D. and Jones, G. T., Quantifying Diversity in Archaeology. New Directions in Archaeology. Cambridge: Cambridge University Press, p. 25-36.
Magurran, A E. & Brian J. McGill (2011). Biological Diversity: Frontiers in Measurement and Assessment. Oxford: Oxford University Press.
Margalef, R. (1958). Information Theory in Ecology. General Systems, 3, 36-71.
Menhinick, E. F. (1964). A Comparison of Some Species-Individuals Diversity Indices Applied to Samples of Field Insects. Ecology, 45(4), 859-861. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/1934933")}.
McIntosh, R. P. (1967). An Index of Diversity and the Relation of Certain Concepts to Diversity. Ecology, 48(3), 392-404. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/1932674")}.
plot()
Other diversity measures:
heterogeneity()
,
occurrence()
,
rarefaction()
,
similarity()
,
simulate()
,
turnover()
## Data from Magurran 1988, p. 128-129
trap <- matrix(data = c(9, 3, 0, 4, 2, 1, 1, 0, 1, 0, 1, 1,
1, 0, 1, 0, 0, 0, 1, 2, 0, 5, 3, 0),
nrow = 2, byrow = TRUE, dimnames = list(c("A", "B"), NULL))
## Margalef and Menhinick index
richness(trap, method = "margalef") # 2.55 1.88
richness(trap, method = "menhinick") # 1.95 1.66
## Data from Chao & Chiu 2016
brazil <- matrix(
data = rep(x = c(1:21, 23, 25, 27, 28, 30, 32, 34:37, 41,
45, 46, 49, 52, 89, 110, 123, 140),
times = c(113, 50, 39, 29, 15, 11, 13, 5, 6, 6, 3, 4,
3, 5, 2, 5, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1,
0, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0)),
nrow = 1, byrow = TRUE
)
## Chao1-type estimators (asymptotic species richness)
composition(brazil, method = c("chao1"), unbiased = FALSE) # 461.625
composition(brazil, method = c("ace"), k = 10) # 445.822
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