• richness() returns sample richness.

• composition() returns asymptotic species richness.

Usage

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 matrix
richness(object, method = c("count", "margalef", "menhinick"))

# S4 method for data.frame
richness(object, method = c("count", "margalef", "menhinick"))

# S4 method for matrix
composition(
object,
method = c("chao1", "ace", "chao2", "ice"),
unbiased = FALSE,
improved = FALSE,
k = 10
)

# S4 method for data.frame
composition(
object,
method = c("chao1", "ace", "chao2", "ice"),
unbiased = FALSE,
improved = FALSE,
k = 10
)

# S4 method for numeric
index_margalef(x, na.rm = FALSE, ...)

# S4 method for numeric
index_menhinick(x, na.rm = FALSE, ...)

# S4 method for numeric
index_ace(x, k = 10, ...)

# S4 method for numeric
index_chao1(x, unbiased = FALSE, improved = FALSE, ...)

# S4 method for matrix
index_ice(x, k = 10, ...)

# S4 method for matrix
index_chao2(x, unbiased = FALSE, improved = FALSE, ...)

Arguments

object

A $$m \times p$$ numeric matrix or data.frame of count data (absolute frequencies).

...

Further arguments to be passed to internal methods.

x

A numeric vector or matrix of count data (absolute frequencies).

method

A character string or vector of strings specifying the index to be computed (see details). Any unambiguous substring can be given.

unbiased

A logical scalar. Should the bias-corrected estimator be used? Only used with "chao1" or "chao2" (improved) estimator.

improved

A logical scalar. Should the improved estimator be used? Only used with "chao1" or "chao2".

k

A length-one numeric vector giving the threshold between rare/infrequent and abundant/frequent species. Only used if method is "ace" or "ice".

na.rm

A numeric scalar: should missing values (including NaN) be removed?

Value

• richness() returns a RichnessIndex object.

• composition() returns a CompositionIndex object.

• index_*() return a numeric vector.

Details

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.

Richness Measures

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.

Asymptotic Species Richness

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.

References

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()

N. Frerebeau

Examples

## 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
#> [1] 2.551432 1.949356
richness(trap, method = "menhinick") # 1.95 1.66
#> [1] 1.876630 1.664101

## 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
#> [1] 461.6254
composition(brazil, method = c("ace"), k = 10) # 445.822
#> [1] 445.8224

## Rarefaction
rarefaction(trap, sample = 13) # 6.56 6.00
#>   1        2      3        4        5        6        7        8        9
#> A 1 1.818182 2.5048 3.095765 3.616393 4.084312 4.511693 4.906919 5.275811
#> B 1 1.820513 2.5000 3.069930 3.555556 3.976690 4.348485 4.682984 4.986014
#>         10       11       12       13
#> A 5.622502 5.950041 6.260802 6.556735
#> B 5.269231 5.538462 6.000000 6.000000