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 m x p |
... |
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. 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. 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. 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. doi: 10.1111/biom.12200.
Magurran, A. E. (1988). Ecological Diversity and its Measurement. Princeton, NJ: Princeton University Press. 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. 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. doi: 10.2307/1932674.
plot_diversity()
Other diversity measures:
heterogeneity()
,
occurrence()
,
plot_diversity
,
rarefaction()
,
similarity()
,
simulate()
,
turnover()
## Richness ## Margalef and Menhinick index ## 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)) richness(trap, method = "margalef") # 2.55 1.88 richness(trap, method = "menhinick") # 1.95 1.66 ## Asymptotic species richness ## Chao1-type estimators ## 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 ) composition(brazil, method = c("chao1"), unbiased = FALSE) # 461.625 composition(brazil, method = c("ace"), k = 10) # 445.822 ## Rarefaction rarefaction(trap, sample = 13) # 6.56 6.00
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.