Generalized Simpson's Entropy

Estimate the Generalized Simpson's entropy of species from abundance or probability data.

Usage

ent_gen_simpson(x, ...)

# S3 method for class 'numeric'
ent_gen_simpson(
  x,
  k = 1,
  estimator = c("Zhang", "naive"),
  as_numeric = FALSE,
  ...,
  check_arguments = TRUE
)

# S3 method for class 'species_distribution'
ent_gen_simpson(
  x,
  k = 1,
  estimator = c("Zhang", "naive"),
  gamma = FALSE,
  as_numeric = FALSE,
  ...,
  check_arguments = TRUE
)

Arguments

x

An object, that may be a numeric vector containing abundances or probabilities, or an object of class abundances or probabilities.

...

Unused.

k

the order of Hurlbert's diversity.

estimator

An estimator of entropy.

as_numeric

if TRUE, a number or a numeric vector is returned rather than a tibble.

check_arguments

if TRUE, the function arguments are verified. Should be set to FALSE to save time when the arguments have been checked elsewhere.

gamma

if TRUE, \(\gamma\) diversity, i.e. diversity of the metacommunity, is computed.

Value

A tibble with the site names, the estimators used and the estimated entropy.

Details

The Generalized Simpson's Entropy (Zhang and Zhou 2010) of order \(k\) is, in the species accumulation curve,the probability for the individual sampled in rank \(k + 1\) to belong to a new species. It is a measure of diversity so long as \(k\) is lower than the number of species (Grabchak et al. 2017) .

Bias correction requires the number of individuals. It is limited to orders \(r\) less than or equal to the number of individuals in the community (Zhang and Grabchak 2016) .

Generalized Simpson's diversity cannot be estimated at a specified level of interpolation or extrapolation, and diversity partitioning is not available.

Note

The unbiased estimator is calculated by the EntropyEstimation::GenSimp.z function of the EntropyEstimation package.

See also

div_gen_simpson

#' @references Grabchak M, Marcon E, Lang G, Zhang Z (2017). “The Generalized Simpson's Entropy Is a Measure of Biodiversity.” Plos One, 12(3), e0173305. doi:10.1371/journal.pone.0173305 .

Zhang Z, Grabchak M (2016). “Entropic Representation and Estimation of Diversity Indices.” Journal of Nonparametric Statistics, 28(3), 563–575. doi:10.1080/10485252.2016.1190357 .

Zhang Z, Zhou J (2010). “Re-Parameterization of Multinomial Distributions and Diversity Indices.” Journal of Statistical Planning and Inference, 140(7), 1731–1738. doi:10.1016/j.jspi.2009.12.023 .

Examples

# Entropy of each community
ent_gen_simpson(paracou_6_abd, k = 50)
#> # A tibble: 4 × 5
#>   site      weight estimator order entropy
#>   <chr>      <dbl> <chr>     <dbl>   <dbl>
#> 1 subplot_1   1.56 Zhang        50   0.472
#> 2 subplot_2   1.56 Zhang        50   0.528
#> 3 subplot_3   1.56 Zhang        50   0.503
#> 4 subplot_4   1.56 Zhang        50   0.498
# gamma entropy
ent_gen_simpson(paracou_6_abd, k = 50, gamma = TRUE)
#> # A tibble: 1 × 3
#>   estimator order entropy
#>   <chr>     <dbl>   <dbl>
#> 1 Zhang        50   0.515