Estimate the diversity sensu stricto, i.e. the Hill1973;textualdivent number of species from abundance or probability data.
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"),
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"),
gamma = FALSE,
...,
check_arguments = TRUE
)An object, that may be a numeric vector containing abundances or probabilities, or an object of class abundances or probabilities.
The order of diversity.
Unused.
An estimator of asymptotic diversity.
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.
A string containing one of the possible estimators of the probability distribution (see probabilities). Used only for extrapolation.
A string containing one of the possible unveiling methods to estimate the probabilities of the unobserved species (see probabilities). Used only for extrapolation.
An estimator of richness to evaluate the total number of species, see div_richness. Used for interpolation and extrapolation.
The risk level, 5% by default, used to optimize the jackknife order.
The highest jackknife order allowed. Default is 10.
An estimator of sample coverage used by coverage.
The sample coverage of x calculated elsewhere.
Used to calculate the gamma diversity of meta-communities, see details.
If TRUE, a number or a numeric vector is returned rather than a tibble.
If TRUE, the function arguments are verified.
Should be set to FALSE to save time when the arguments have been checked elsewhere.
If TRUE, \(\gamma\) diversity, i.e. diversity of the metacommunity, is computed.
A tibble with the site names, the estimators used and the estimated diversity.
Several estimators are available to deal with incomplete sampling.
Bias correction requires the number of individuals.
Estimation techniques are from Chao2003;textualdivent, Grassberger1988;textualdivent,Holste1998;textualdivent, Bonachela2008;textualdivent, Marcon2014a;textualdivent which is actually the max value of "ChaoShen" and "Grassberger", Zhang2014a;textualdivent, Chao2014c;textualdivent, Chao2015;textualdivent and Marcon2015a;textualdivent.
The ChaoJost estimator Chao2013,Chao2015;textualdivent contains
an unbiased part concerning observed species, equal to that of
Zhang2014a;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 Chao2014c;textualdivent,
completed by Marcon2015a;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 Chao2014c;textualdivent, or by the iChao1 (UnveiliC)
or the jackknife (UnveilJ).
The UnveilJ correction often has a lower bias but a greater variance
Marcon2015adivent.
It is a good first choice thanks to the versatility of the jackknife
estimator of richness.
Estimators by Bonachela2008;textualdivent and Holste1998;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 corrections 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 Chao2014divent, rather than its asymptotic value. See accum_hill for details.
# Diversity of each community
div_hill(paracou_6_abd, q = 2)
#> # A tibble: 4 × 5
#> site weight estimator order diversity
#> <chr> <dbl> <chr> <dbl> <dbl>
#> 1 subplot_1 1.56 UnveilJ 2 42.3
#> 2 subplot_2 1.56 UnveilJ 2 44.6
#> 3 subplot_3 1.56 UnveilJ 2 48.8
#> 4 subplot_4 1.56 UnveilJ 2 36.0
# gamma diversity
div_hill(paracou_6_abd, q = 2, gamma = TRUE)
#> # A tibble: 1 × 4
#> site estimator order diversity
#> <chr> <chr> <dbl> <dbl>
#> 1 Metacommunity UnveilJ 2 46.5
# At 80% coverage
div_hill(paracou_6_abd, q = 2, level = 0.8)
#> # A tibble: 4 × 6
#> site weight estimator order level diversity
#> <chr> <dbl> <chr> <dbl> <dbl> <dbl>
#> 1 subplot_1 1.56 Chao2014 2 304 37.2
#> 2 subplot_2 1.56 Chao2014 2 347 39.6
#> 3 subplot_3 1.56 Chao2014 2 333 42.7
#> 4 subplot_4 1.56 Chao2014 2 303 32.3