Shannon's Entropy of a Community — ent

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

ent_shannon(x, ...)

# S3 method for 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 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,
  ...,
  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