Number of Species of a Community — div

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

div_richness(x, ...)

# S3 method for numeric
div_richness(
  x,
  estimator = c("jackknife", "iChao1", "Chao1", "rarefy", "naive"),
  jack_alpha = 0.05,
  jack_max = 10,
  level = NULL,
  probability_estimator = c("Chao2015", "Chao2013", "ChaoShen", "naive"),
  unveiling = c("geometric", "uniform", "none"),
  coverage_estimator = c("ZhangHuang", "Chao", "Turing", "Good"),
  as_numeric = FALSE,
  ...,
  check_arguments = TRUE
)

# S3 method for species_distribution
div_richness(
  x,
  estimator = c("jackknife", "iChao1", "Chao1", "rarefy", "naive"),
  jack_alpha = 0.05,
  jack_max = 10,
  level = NULL,
  probability_estimator = c("Chao2015", "Chao2013", "ChaoShen", "naive"),
  unveiling = c("geometric", "uniform", "none"),
  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. The metacommunity if built by combining the community abundances with respect to their weight.
estimator: An estimator of richness to evaluate the total number of species.
jack_alpha: The risk level, 5% by default, used to optimize the jackknife order.
jack_max: The highest jackknife order allowed. Default is 10.
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). The asymptotic estimator is used in extrapolation (i.e. a level greater than the sample size).
probability_estimator: A string containing one of the possible estimators of the probability distribution (see probabilities). Used only by the estimator of richness "rarefy".
unveiling: A string containing one of the possible unveiling methods to estimate the probabilities of the unobserved species (see probabilities). Used only by the estimator of richness "rarefy".
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 numbers of species.

Details

Bias correction requires the number of individuals. Chao's correction techniques are from Chao et al. (2014) and Chiu et al. (2014) . The Jackknife estimator is calculated by a straight adaptation of the code by Ji-Ping Wang (jackknife in package SPECIES). The optimal order is selected according to Burnham and Overton (1978); Burnham and Overton (1979) . Many other estimators are available elsewhere, the ones implemented here are necessary for other entropy estimations.

Richness can be estimated at a specified level of interpolation or extrapolation, either a chosen sample size or sample coverage (Chiu et al. 2014) , rather than its asymptotic value. Extrapolation relies on the estimation of the asymptotic richness. If probability_estimator is "naive", then the asymptotic estimation of richness is made using the chosen estimator, else the asymptotic distribution of the community is derived and its estimated richness adjusted so that the richness of a sample of this distribution of the size of the actual sample has the richness of the actual sample.

References

Burnham KP, Overton WS (1978). “Estimation of the Size of a Closed Population When Capture Probabilities Vary among Animals.” Biometrika, 65(3), 625--633. doi:10.2307/2335915 .

Burnham KP, Overton WS (1979). “Robust Estimation of Population Size When Capture Probabilities Vary among Animals.” Ecology, 60(5), 927--936. doi:10.2307/1936861 .

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 .

Chiu C, Wang Y, Walther BA, Chao A (2014). “An Improved Nonparametric Lower Bound of Species Richness via a Modified Good-Turing Frequency Formula.” Biometrics, 70(3), 671--682. doi:10.1111/biom.12200 , 24945937.

Examples

# Diversity of each community
div_richness(paracou_6_abd)
#> # A tibble: 4 × 5
#>   site      weight estimator   order diversity
#>   <chr>      <dbl> <chr>       <dbl>     <dbl>
#> 1 subplot_1   1.56 Jackknife 3     0       355
#> 2 subplot_2   1.56 Jackknife 2     0       348
#> 3 subplot_3   1.56 Jackknife 2     0       315
#> 4 subplot_4   1.56 Jackknife 2     0       296
# gamma diversity
div_richness(paracou_6_abd, gamma = TRUE)
#> # A tibble: 1 × 4
#>   site          estimator   order diversity
#>   <chr>         <chr>       <dbl>     <dbl>
#> 1 Metacommunity Jackknife 2     0       473

# At 80% coverage
div_richness(paracou_6_abd, level = 0.8)
#> # A tibble: 4 × 6
#>   site      weight estimator order level diversity
#>   <chr>      <dbl> <chr>     <dbl> <dbl>     <dbl>
#> 1 subplot_1   1.56 SAC           0   304      106.
#> 2 subplot_2   1.56 SAC           0   347      125.
#> 3 subplot_3   1.56 SAC           0   333      117.
#> 4 subplot_4   1.56 SAC           0   303      109.