Heterogeneity and Evenness

• heterogeneity() computes an heterogeneity or dominance index.

• evenness() computes an evenness measure.

Usage

heterogeneity(object, ...)

evenness(object, ...)

# S4 method for class 'matrix'
heterogeneity(
  object,
  ...,
  method = c("berger", "boone", "brillouin", "mcintosh", "shannon", "simpson")
)

# S4 method for class 'data.frame'
heterogeneity(
  object,
  ...,
  method = c("berger", "boone", "brillouin", "mcintosh", "shannon", "simpson")
)

# S4 method for class 'matrix'
evenness(
  object,
  ...,
  method = c("shannon", "brillouin", "mcintosh", "simpson")
)

# S4 method for class 'data.frame'
evenness(
  object,
  ...,
  method = c("shannon", "brillouin", "mcintosh", "simpson")
)

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 specifying the index to be computed (see details). Any unambiguous substring can be given.

evenness

A logical scalar: should an evenness measure be computed instead of an heterogeneity/dominance index?

Value

• heterogeneity() returns an HeterogeneityIndex object.

• evenness() returns an EvennessIndex object.

Details

Diversity measurement assumes that all individuals in a specific taxa are equivalent and that all types are equally different from each other (Peet 1974). A measure of diversity can be achieved by using indices built on the relative abundance of taxa. These indices (sometimes referred to as non-parametric indices) benefit from not making assumptions about the underlying distribution of taxa abundance: they only take relative abundances of the species that are present and species richness into account. Peet (1974) refers to them as indices of heterogeneity.

Diversity indices focus on one aspect of the taxa abundance and emphasize either richness (weighting towards uncommon taxa) or dominance (weighting towards abundant taxa; Magurran 1988).

Evenness is a measure of how evenly individuals are distributed across the sample.

Heterogeneity and Evenness Measures

The following heterogeneity index and corresponding evenness measures are available (see Magurran 1988 for details):

berger

Berger-Parker dominance index.

boone

Boone heterogeneity measure.

brillouin

Brillouin diversity index.

mcintosh

McIntosh dominance index.

shannon

Shannon-Wiener diversity index.

simpson

Simpson dominance index.

The berger, mcintosh and simpson methods return a dominance index, not the reciprocal or inverse form usually adopted, so that an increase in the value of the index accompanies a decrease in diversity.

References

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

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 .

See also

index_berger(), index_boone(), index_brillouin(), index_mcintosh(), index_shannon(), index_simpson()

Other diversity measures: occurrence(), plot_diversity, plot_rarefaction, profiles(), rarefaction(), richness(), she(), similarity(), simulate(), turnover()

Author

N. Frerebeau

Examples

## Data from Conkey 1980, Kintigh 1989
data("cantabria")

## Shannon diversity index
(h <- heterogeneity(cantabria, method = "shannon"))
#> [1] 3.269200 2.955298 2.491683 2.485604 2.329187
(e <- evenness(cantabria, method = "shannon"))
#> [1] 0.8987278 0.8966760 0.8462335 0.9178574 0.9373336

plot(h)

as.data.frame(h)
#>                  observed singleton doubleton size    index
#> Altamira               38        13         4  152 3.269200
#> Cueto de la Mina       27        13         6   69 2.955298
#> El Juyo                19        10         4   53 2.491683
#> El Cierro              15         6         5   35 2.485604
#> La Paloma              12         6         3   23 2.329187