Estimate actual probabilities of species from a sample
probabilities(x, ...)
# S3 method for numeric
probabilities(
x,
estimator = c("naive", "Chao2013", "Chao2015", "ChaoShen"),
unveiling = c("none", "uniform", "geometric"),
richness_estimator = c("jackknife", "iChao1", "Chao1", "rarefy", "naive"),
jack_alpha = 0.05,
jack_max = 10,
coverage_estimator = c("ZhangHuang", "Chao", "Turing", "Good"),
q = 0,
as_numeric = FALSE,
...,
check_arguments = TRUE
)
# S3 method for abundances
probabilities(
x,
estimator = c("naive", "Chao2013", "Chao2015", "ChaoShen"),
unveiling = c("none", "uniform", "geometric"),
richness_estimator = c("jackknife", "iChao1", "Chao1", "rarefy", "naive"),
jack_alpha = 0.05,
jack_max = 10,
coverage_estimator = c("ZhangHuang", "Chao", "Turing", "Good"),
q = 0,
...,
check_arguments = TRUE
)An object. It may be:
a numeric vector containing abundances. It may be named to track species names.
an object of class species_distribution.
Unused.
One of the estimators of a probability distribution: "naive" (the default value), or "Chao2013", "Chao2015", "ChaoShen" to estimate the probabilities of the observed species in the asymptotic distribution.
One of the possible unveiling methods to estimate the probabilities of the unobserved species: "none" (default, no species is added), "uniform" (all unobserved species have the same probability) or "geometric" (the unobserved species distribution is geometric).
An estimator of richness to evaluate the total number of species. "jackknife" is the default value. An alternative is "rarefy" to estimate the number of species such that the entropy of the asymptotic distribution rarefied to the observed sample size equals the actual entropy of the data.
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 order of diversity. Default is 0 for richness.
Used only to estimate asymptotic probability distributions when argument
richness_estimator is "rarefy". Then, the number of unobserved species is
fitted so that the entropy of order q of the asymptotic probability distribution
at the observed sample size equals the actual entropy of the data.
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.
probabilities() estimates a probability distribution from a sample.
If the estimator is not "naive", the observed abundance distribution is used
to estimate the actual probability distribution.
The list of species is changed:
zero-abundance species are cleared, and some unobserved species are added.
First, observed species probabilities are estimated following
Chao and Shen (2003)
, i.e. input probabilities are multiplied by
the sample coverage, or according to more sophisticated models:
Chao et al. (2013)
, a single-parameter model, or
Chao and Jost (2015)
, a two-parameter model.
The total probability of observed species equals the sample coverage.
Then, the distribution of unobserved species can be unveiled: their number
is estimated according to the richness_estimator.
The coverage deficit (1 minus the sample coverage) is shared by the unobserved
species equally (unveiling = "uniform", (Chao et al. 2013)
) or
according to a geometric distribution (unveiling = "geometric", (Chao and Jost 2015)
).
Chao A, Jost L (2015).
“Estimating Diversity and Entropy Profiles via Discovery Rates of New Species.”
Methods in Ecology and Evolution, 6(8), 873--882.
doi:10.1111/2041-210X.12349
.
Chao A, Shen T (2003).
“Nonparametric Estimation of Shannon's Index of Diversity When There Are Unseen Species in Sample.”
Environmental and Ecological Statistics, 10(4), 429--443.
doi:10.1023/A:1026096204727
.
Chao A, Wang Y, Jost L (2013).
“Entropy and the Species Accumulation Curve: A Novel Entropy Estimator via Discovery Rates of New Species.”
Methods in Ecology and Evolution, 4(11), 1091--1100.
doi:10.1111/2041-210x.12108
.
# Just transform abundances into probabilities
probabilities(paracou_6_abd)
#> # A tibble: 4 × 337
#> site weight Abarema_jupunba Abarema_mataybifolia Amaioua_guianensis
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 subplot_1 1 0.00212 0.00212 0.00106
#> 2 subplot_2 1 0.00229 0 0.00115
#> 3 subplot_3 1 0.00215 0.00215 0
#> 4 subplot_4 1 0.00501 0 0
#> # ℹ 332 more variables: Amanoa_congesta <dbl>, Amanoa_guianensis <dbl>,
#> # Ambelania_acida <dbl>, Amphirrhox_longifolia <dbl>, Andira_coriacea <dbl>,
#> # Apeiba_glabra <dbl>, Aspidosperma_album <dbl>, Aspidosperma_cruentum <dbl>,
#> # Aspidosperma_excelsum <dbl>, Bocoa_prouacensis <dbl>,
#> # Brosimum_guianense <dbl>, Brosimum_rubescens <dbl>, Brosimum_utile <dbl>,
#> # Carapa_surinamensis <dbl>, Caryocar_glabrum <dbl>, Casearia_decandra <dbl>,
#> # Casearia_javitensis <dbl>, Catostemma_fragrans <dbl>, …
# Estimate the distribution of probabilities from observed abundances (unveiled probabilities)
prob_unv <- probabilities(
paracou_6_abd,
estimator = "Chao2015",
unveiling = "geometric",
richness_estimator = "jackknife"
)
# Estimate entropy from the unveiled probabilities
ent_shannon(prob_unv)
#> # A tibble: 4 × 5
#> site weight estimator order entropy
#> <chr> <dbl> <chr> <dbl> <dbl>
#> 1 subplot_1 1 naive 1 4.57
#> 2 subplot_2 1 naive 1 4.73
#> 3 subplot_3 1 naive 1 4.65
#> 4 subplot_4 1 naive 1 4.55
# Identical to
ent_shannon(paracou_6_abd, estimator = "UnveilJ")
#> # 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