div_hill: Hill number of a Community

In divent: Entropy Partitioning to Measure Diversity

Hill number of a Community

Description

Estimate the diversity sensu stricto, i.e. the \insertCiteHill1973;textualdivent number of species from abundance or probability data.

Usage

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

## S3 method for class 'numeric'
div_hill(
  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", "naive"),
  jack_alpha = 0.05,
  jack_max = 10,
  coverage_estimator = c("ZhangHuang", "Chao", "Turing", "Good"),
  q_threshold = 10,
  sample_coverage = NULL,
  as_numeric = FALSE,
  ...,
  check_arguments = TRUE
)

## S3 method for class 'species_distribution'
div_hill(
  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", "naive"),
  jack_alpha = 0.05,
  jack_max = 10,
  coverage_estimator = c("ZhangHuang", "Chao", "Turing", "Good"),
  q_threshold = 10,
  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.
q	a number: the order of diversity.
...	Unused.
estimator	an estimator of asymptotic diversity.
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.
q_threshold	the value of q above which diversity is computed directly with the naive estimator (\sum{p_s^q}^{\frac{1}{(1-q)}}, without computing entropy. When q is great, the exponential of entropy goes to 0^{\frac{1}{(1-q)}}, causing rounding errors while the naive estimator of diversity is less and less biased.
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.

Details

Several estimators are available to deal with incomplete sampling.

Bias correction requires the number of individuals.

Estimation techniques are from \insertCiteChao2003;textualdivent, \insertCiteGrassberger1988;textualdivent,\insertCiteHolste1998;textualdivent, \insertCiteBonachela2008;textualdivent, \insertCiteMarcon2014a;textualdivent which is actually the max value of "ChaoShen" and "Grassberger", \insertCiteZhang2014a;textualdivent, \insertCiteChao2014c;textualdivent, \insertCiteChao2015;textualdivent and \insertCiteMarcon2015a;textualdivent.

The ChaoJost estimator \insertCiteChao2013,Chao2015divent contains an unbiased part concerning observed species, equal to that of \insertCiteZhang2014a;textualdivent, and a (biased) estimator of the remaining bias based on the estimation of the species-accumulation curve. It is very efficient but slow if the number of individuals is more than a few hundreds.

The unveiled estimators rely on \insertCiteChao2014c;textualdivent, completed by \insertCiteMarcon2015a;textualdivent. The actual probabilities of observed species are estimated and completed by a geometric distribution of the probabilities of unobserved species. The number of unobserved species is estimated by the Chao1 estimator (UnveilC), following \insertCiteChao2014c;textualdivent, or by the iChao1 (UnveiliC) or the jackknife (UnveilJ). The UnveilJ estimator often has a lower bias but a greater variance \insertCiteMarcon2015adivent. It is a good first choice thanks to the versatility of the jackknife estimator of richness.

Estimators by \insertCiteBonachela2008;textualdivent and \insertCiteHolste1998;textualdivent are rarely used.

To estimate \gamma diversity, the size of a metacommunity (see metacommunity) is unknown so it has to be set according to a rule which does not ensure that its abundances are integer values. Then, classical bias-correction methods do not apply. Providing the sample_coverage argument allows applying the ChaoShen and Grassberger estimators to estimate quite well the entropy.

Diversity can be estimated at a specified level of interpolation or extrapolation, either a chosen sample size or sample coverage \insertCiteChao2014divent, rather than its asymptotic value. See accum_hill for details.

Value

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

References

\insertAllCited

Examples

# Diversity of each community
div_hill(paracou_6_abd, q = 2)
# gamma diversity
div_hill(paracou_6_abd, q = 2, gamma = TRUE)

# At 80% coverage
div_hill(paracou_6_abd, q = 2, level = 0.8)

divent documentation built on April 3, 2025, 7:40 p.m.