Skip to contents

Shannon's Entropy of a Community

Source: R/ent_shannon.R
ent_shannon.Rd

Estimate the entropy (Shannon 1948) of species from abundance or probability data. Several estimators are available to deal with incomplete sampling.

Usage

ent_shannon(x, ...)

# S3 method for class 'numeric'
ent_shannon(
  x,
  estimator = c("UnveilJ", "ChaoJost", "ChaoShen", "GenCov", "Grassberger", "Marcon",
    "UnveilC", "UnveiliC", "ZhangGrabchak", "naive", "Bonachela", "Grassberger2003",
    "Holste", "Miller", "Schurmann", "ZhangHz"),
  level = NULL,
  probability_estimator = c("Chao2015", "Chao2013", "ChaoShen", "naive"),
  unveiling = c("geometric", "uniform", "none"),
  richness_estimator = c("jackknife", "iChao1", "Chao1", "naive"),
  jack_alpha = 0.05,
  jack_max = 10,
  coverage_estimator = c("ZhangHuang", "Chao", "Turing", "Good"),
  as_numeric = FALSE,
  ...,
  check_arguments = TRUE
)

# S3 method for class 'species_distribution'
ent_shannon(
  x,
  estimator = c("UnveilJ", "ChaoJost", "ChaoShen", "GenCov", "Grassberger", "Marcon",
    "UnveilC", "UnveiliC", "ZhangGrabchak", "naive", "Bonachela", "Grassberger2003",
    "Holste", "Miller", "Schurmann", "ZhangHz"),
  level = NULL,
  probability_estimator = c("Chao2015", "Chao2013", "ChaoShen", "naive"),
  unveiling = c("geometric", "uniform", "none"),
  richness_estimator = c("jackknife", "iChao1", "Chao1", "naive"),
  jack_alpha = 0.05,
  jack_max = 10,
  coverage_estimator = c("ZhangHuang", "Chao", "Turing", "Good"),
  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.

estimator

An estimator of entropy.

level

the level of interpolation or extrapolation. It may be a sample size (an integer) or a sample coverage (a number between 0 and 1). If not NULL, the asymptotic estimator is ignored.

probability_estimator

a string containing one of the possible estimators of the probability distribution (see probabilities). Used only for extrapolation.

unveiling

a string containing one of the possible unveiling methods to estimate the probabilities of the unobserved species (see probabilities). Used only for extrapolation.

richness_estimator

an estimator of richness to evaluate the total number of species, see div_richness. used for interpolation and extrapolation.

jack_alpha

the risk level, 5% by default, used to optimize the jackknife order.

jack_max

the highest jackknife order allowed. Default is 10.

coverage_estimator

an estimator of sample coverage used by coverage.

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

Bias correction requires the number of individuals.

See div_hill for non-specific estimators. Shannon-specific estimators are from Miller (1955) , Grassberger (2003) , Schürmann (2004) and Zhang (2012) . More estimators can be found in the entropy package.

Entropy can be estimated at a specified level of interpolation or extrapolation, either a chosen sample size or sample coverage (Chao et al. 2014) , rather than its asymptotic value. See accum_tsallis for details.

References

Chao A, Gotelli NJ, Hsieh TC, Sander EL, Ma KH, Colwell RK, Ellison AM (2014). “Rarefaction and Extrapolation with Hill Numbers: A Framework for Sampling and Estimation in Species Diversity Studies.” Ecological Monographs, 84(1), 45–67. doi:10.1890/13-0133.1 .

Grassberger P (2003). “Entropy Estimates from Insufficient Samplings.” arXiv Physics e-prints, 0307138(v2).

Miller GA (1955). “Note on the Bias of Information Estimates.” In Quastler H (ed.), Information Theory in Psychology: Problems and Methods, 95–100. Free Press, Glencoe, Ill.

Schürmann T (2004). “Bias Analysis in Entropy Estimation.” Journal of Physics A: Mathematical and General, 37(27), L295–L301. doi:10.1088/0305-4470/37/27/L02 .

Shannon CE (1948). “A Mathematical Theory of Communication.” The Bell System Technical Journal, 27(3), 379–423, 623–656. doi:10.1002/j.1538-7305.1948.tb01338.x .

Zhang Z (2012). “Entropy Estimation in Turing's Perspective.” Neural Computation, 24(5), 1368–1389. doi:10.1162/NECO_a_00266 .

Examples

# Entropy of each community
ent_shannon(paracou_6_abd)
#> # A tibble: 4 × 5
#>   site      weight estimator order entropy
#>   <chr>      <dbl> <chr>     <dbl>   <dbl>
#> 1 subplot_1   1.56 UnveilJ       1    4.57
#> 2 subplot_2   1.56 UnveilJ       1    4.73
#> 3 subplot_3   1.56 UnveilJ       1    4.65
#> 4 subplot_4   1.56 UnveilJ       1    4.55
# gamma entropy
ent_shannon(paracou_6_abd, gamma = TRUE)
#> # A tibble: 1 × 4
#>   site          estimator order entropy
#>   <chr>         <chr>     <dbl>   <dbl>
#> 1 Metacommunity UnveilJ       1    4.71

# At 80% coverage
ent_shannon(paracou_6_abd, level = 0.8)
#> # A tibble: 4 × 6
#>   site      weight estimator     order level entropy
#>   <chr>      <dbl> <chr>         <dbl> <dbl>   <dbl>
#> 1 subplot_1   1.56 Interpolation     1   304    4.10
#> 2 subplot_2   1.56 Interpolation     1   347    4.27
#> 3 subplot_3   1.56 Interpolation     1   333    4.23
#> 4 subplot_4   1.56 Interpolation     1   303    4.10