• richness() computes sample richness.

• composition() computes asymptotic species richness.

## Usage

richness(object, ...)

composition(object, ...)

# S4 method for class 'matrix'
richness(object, ..., method = c("count", "margalef", "menhinick"))

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

# S4 method for class 'matrix'
composition(object, ..., method = c("chao1", "ace", "squares", "chao2", "ice"))

# S4 method for class 'data.frame'
composition(object, ..., method = c("chao1", "ace", "squares", "chao2", "ice"))

## Arguments

object

A $$m \times p$$ numeric matrix or data.frame of count data (absolute frequencies giving the number of individuals for each category, i.e. a contingency table). A data.frame will be coerced to a numeric matrix via data.matrix().

...

Further arguments to be passed to internal methods (see below).

method

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

## 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

Number of observed taxa/types.

margalef
menhinick

## Asymptotic Species Richness

The following measures are available for count data:

ace
chao1

(improved/unbiased) Chao1 estimator.

squares

The following measures are available for replicated incidence data:

ice
chao2

(improved/unbiased) Chao2 estimator.

## References

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. (1988). Ecological Diversity and its Measurement. Princeton, NJ: Princeton University Press. doi:10.1007/978-94-015-7358-0 .

Magurran, A E. & Brian J. McGill (2011). Biological Diversity: Frontiers in Measurement and Assessment. Oxford: Oxford University Press.

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 .

Peet, R. K. (1974). The Measurement of Species Diversity. Annual Review of Ecology and Systematics, 5(1), 285-307. doi:10.1146/annurev.es.05.110174.001441 .

index_margalef(), index_menhinick(), index_ace(), index_chao1(), index_squares(), index_ice(), index_chao2()

plot()

Other diversity measures: heterogeneity(), occurrence(), profiles(), rarefaction(), she(), similarity(), simulate(), turnover()

N. Frerebeau

## Examples

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

## 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
#> [1] 461.6254
composition(brazil, method = c("ace"), k = 10) # 445.822
#> [1] 443.6836