Tsallis Entropy of a Community — ent

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

ent_tsallis(x, q = 1, ...)

# S3 method for numeric
ent_tsallis(
  x,
  q = 1,
  estimator = c("UnveilJ", "ChaoJost", "ChaoShen", "GenCov", "Grassberger", "Marcon",
    "UnveilC", "UnveiliC", "ZhangGrabchak", "naive", "Bonachela", "Holste"),
  level = NULL,
  probability_estimator = c("Chao2015", "Chao2013", "ChaoShen", "naive"),
  unveiling = c("geometric", "uniform", "none"),
  richness_estimator = c("jackknife", "iChao1", "Chao1", "rarefy", "naive"),
  jack_alpha = 0.05,
  jack_max = 10,
  coverage_estimator = c("ZhangHuang", "Chao", "Turing", "Good"),
  sample_coverage = NULL,
  as_numeric = FALSE,
  ...,
  check_arguments = TRUE
)

# S3 method for species_distribution
ent_tsallis(
  x,
  q = 1,
  estimator = c("UnveilJ", "ChaoJost", "ChaoShen", "GenCov", "Grassberger", "Marcon",
    "UnveilC", "UnveiliC", "ZhangGrabchak", "naive", "Bonachela", "Holste"),
  level = NULL,
  probability_estimator = c("Chao2015", "Chao2013", "ChaoShen", "naive"),
  unveiling = c("geometric", "uniform", "none"),
  richness_estimator = c("jackknife", "iChao1", "Chao1", "rarefy", "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.
q: The order of diversity.
...: 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.
sample_coverage: The sample coverage of x calculated elsewhere. Used to calculate the gamma diversity of meta-communities, see details.
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 estimators.

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 .

Examples

# Entropy of each community
ent_tsallis(paracou_6_abd, q = 2)
#> # A tibble: 4 × 5
#>   site      weight estimator order entropy
#>   <chr>      <dbl> <chr>     <dbl>   <dbl>
#> 1 subplot_1   1.56 UnveilJ       2   0.976
#> 2 subplot_2   1.56 UnveilJ       2   0.978
#> 3 subplot_3   1.56 UnveilJ       2   0.980
#> 4 subplot_4   1.56 UnveilJ       2   0.972
# gamma entropy
ent_tsallis(paracou_6_abd, q = 2, gamma = TRUE)
#> # A tibble: 1 × 4
#>   site          estimator order entropy
#>   <chr>         <chr>     <dbl>   <dbl>
#> 1 Metacommunity UnveilJ       2   0.979

# At 80% coverage
ent_tsallis(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