Description Usage Arguments Value References Examples

`ChaoSpecies`

: Estimation of species richness in a single community based on five types of data:
Type (1) abundance data (datatype="abundance"), Type (1A) abundance-frequency counts

(datatype="abundance_freq_count"), Type (2) incidence-frequency data (datatype =
"incidence_freq"), Type (2A) incidence-frequency counts (datatype="incidence_freq_count"), and
Type (2B) incidence-raw data (datatype="incidence_raw"); see `SpadeR-package`

details for data input formats.

1 2 3 | ```
ChaoSpecies(data, datatype = c("abundance", "abundance_freq_count",
"incidence_freq", "incidence_freq_count", "incidence_raw"), k = 10,
conf = 0.95)
``` |

`data` |
a matrix/data.frame of species abundances/incidences. |

`datatype` |
type of input data, "abundance", "abundance_freq_count", "incidence_freq", "incidence_freq_count" or "incidence_raw". |

`k` |
the cut-off point (default = 10), which separates species into "abundant" and "rare" groups for abundance data for the estimator ACE; it separates species into "frequent" and "infrequent" groups for incidence data for the estimator ICE. |

`conf` |
a positive number |

a list of three objects:

`$Basic_data_information`

and `$Rare_species_group`

/`$Infreq_species_group`

for summarizing data information.

`$Species_table`

for showing a table of various species richness estimates, standard errors, and the associated confidence intervals.

Chao, A., and Chiu, C. H. (2012). Estimation of species richness and shared species richness. In N. Balakrishnan (ed). Methods and Applications of Statistics in the Atmospheric and Earth Sciences. p.76-111, Wiley, New York.

Chao, A., and Chiu, C. H. (2016). Nonparametric estimation and comparison of species richness. Wiley Online Reference in the Life Science. In: eLS. John Wiley and Sons, Ltd: Chichester. DOI: 10.1002/9780470015902.a0026329.

Chao, A., and Chiu, C. H. (2016). Species richness: estimation and comparison. Wiley StatsRef: Statistics Reference Online. 1-26.

Chiu, C. H., Wang Y. T., Walther B. A. and Chao A. (2014). An improved non-parametric lower bound of species richness via the Good-Turing frequency formulas. Biometrics, 70, 671-682.

Gotelli, N. G. and Chao, A. (2013). Measuring and estimating species richness, species diver- sity, and biotic similarity from sampling data. Encyclopedia of Biodiversity, 2nd Edition, Vol. 5, 195-211, Waltham, MA.

1 2 3 4 5 6 7 8 9 10 11 | ```
data(ChaoSpeciesData)
# Type (1) abundance data
ChaoSpecies(ChaoSpeciesData$Abu,"abundance",k=10,conf=0.95)
# Type (1A) abundance-frequency counts data
ChaoSpecies(ChaoSpeciesData$Abu_count,"abundance_freq_count",k=10,conf=0.95)
# Type (2) incidence-frequency data
ChaoSpecies(ChaoSpeciesData$Inci,"incidence_freq",k=10,conf=0.95)
# Type (2A) incidence-frequency counts data
ChaoSpecies(ChaoSpeciesData$Inci_count,"incidence_freq_count",k=10,conf=0.95)
# Type (2B) incidence-raw data
ChaoSpecies(ChaoSpeciesData$Inci_raw,"incidence_raw",k=10,conf=0.95)
``` |

```
(1) BASIC DATA INFORMATION:
Variable Value
Sample size n 1996
Number of observed species D 25
Coverage estimate for entire dataset C 0.998
CV for entire dataset CV 1.916
Cut-off point k 10
Variable Value
Number of observed individuals for rare group n_rare 53
Number of observed species for rare group D_rare 11
Estimate of the sample coverage for rare group C_rare 0.943
Estimate of CV for rare group in ACE CV_rare 0.629
Estimate of CV1 for rare group in ACE-1 CV1_rare 0.74
Number of observed individuals for abundant group n_abun 1943
Number of observed species for abundant group D_abun 14
NULL
(2) SPECIES RICHNESS ESTIMATORS TABLE:
Estimate s.e. 95%Lower 95%Upper
Homogeneous Model 25.660 0.954 25.082 30.295
Homogeneous (MLE) 25.000 0.975 25.000 28.500
Chao1 (Chao, 1984) 27.249 3.394 25.266 44.030
Chao1-bc 25.999 1.817 25.094 35.673
iChao1 (Chiu et al. 2014) 27.249 3.394 25.266 44.030
ACE (Chao & Lee, 1992) 26.920 2.367 25.292 37.639
ACE-1 (Chao & Lee, 1992) 27.399 3.163 25.336 42.153
1st order jackknife 27.998 2.449 25.739 37.171
2nd order jackknife 28.998 4.240 25.730 46.915
(3) DESCRIPTION OF ESTIMATORS/MODELS:
Homogeneous Model: This model assumes that all species have the same incidence or detection probabilities. See Eq. (3.2) of Lee and Chao (1994) or Eq. (12a) in Chao and Chiu (2016b).
Chao2 (Chao, 1987): This approach uses the frequencies of uniques and duplicates to estimate the number of undetected species; see Chao (1987) or Eq. (11a) in Chao and Chiu (2016b).
Chao2-bc: A bias-corrected form for the Chao2 estimator; see Chao (2005).
iChao2: An improved Chao2 estimator; see Chiu et al. (2014).
ICE (Incidence-based Coverage Estimator): A non-parametric estimator originally proposed by Lee and Chao (1994) in the context of capture-recapture data analysis. The observed species are separated as frequent and infrequent species groups; only data in the infrequent group are used to estimate the number of undetected species. The estimated CV for species in the infrequent group characterizes the degree of heterogeneity among species incidence probabilities. See Eq. (12b) of Chao and Chiu (2016b), which is an improved version of Eq. (3.18) in Lee and Chao (1994). This model is also called Model(h) in capture-recapture literature where h denotes "heterogeneity".
ICE-1: A modified ICE for highly-heterogeneous cases.
1st order jackknife: It uses the frequency of uniques to estimate the number of undetected species; see Burnham and Overton (1978).
2nd order jackknife: It uses the frequencies of uniques and duplicates to estimate the number of undetected species; see Burnham and Overton (1978).
95% Confidence interval: A log-transformation is used for all estimators so that the lower bound of the resulting interval is at least the number of observed species. See Chao (1987).
(1) BASIC DATA INFORMATION:
Variable Value
Sample size n 1008
Number of observed species D 188
Coverage estimate for entire dataset C 0.94
CV for entire dataset CV 1.567
Cut-off point k 10
Variable Value
Number of observed individuals for rare group n_rare 515
Number of observed species for rare group D_rare 167
Estimate of the sample coverage for rare group C_rare 0.882
Estimate of CV for rare group in ACE CV_rare 0.715
Estimate of CV1 for rare group in ACE-1 CV1_rare 0.891
Number of observed individuals for abundant group n_abun 493
Number of observed species for abundant group D_abun 21
NULL
(2) SPECIES RICHNESS ESTIMATORS TABLE:
Estimate s.e. 95%Lower 95%Upper
Homogeneous Model 210.438 6.323 201.053 226.572
Homogeneous (MLE) 188.910 0.969 188.165 193.011
Chao1 (Chao, 1984) 241.104 17.849 215.967 288.836
Chao1-bc 238.783 17.099 214.716 284.530
iChao1 (Chiu et al. 2014) 254.136 10.632 236.358 278.448
ACE (Chao & Lee, 1992) 245.828 15.195 222.850 283.957
ACE-1 (Chao & Lee, 1992) 265.366 22.736 232.012 323.998
1st order jackknife 248.939 11.037 230.852 274.661
2nd order jackknife 274.923 19.105 244.787 321.050
(3) DESCRIPTION OF ESTIMATORS/MODELS:
Homogeneous Model: This model assumes that all species have the same incidence or detection probabilities. See Eq. (3.2) of Lee and Chao (1994) or Eq. (12a) in Chao and Chiu (2016b).
Chao2 (Chao, 1987): This approach uses the frequencies of uniques and duplicates to estimate the number of undetected species; see Chao (1987) or Eq. (11a) in Chao and Chiu (2016b).
Chao2-bc: A bias-corrected form for the Chao2 estimator; see Chao (2005).
iChao2: An improved Chao2 estimator; see Chiu et al. (2014).
ICE (Incidence-based Coverage Estimator): A non-parametric estimator originally proposed by Lee and Chao (1994) in the context of capture-recapture data analysis. The observed species are separated as frequent and infrequent species groups; only data in the infrequent group are used to estimate the number of undetected species. The estimated CV for species in the infrequent group characterizes the degree of heterogeneity among species incidence probabilities. See Eq. (12b) of Chao and Chiu (2016b), which is an improved version of Eq. (3.18) in Lee and Chao (1994). This model is also called Model(h) in capture-recapture literature where h denotes "heterogeneity".
ICE-1: A modified ICE for highly-heterogeneous cases.
1st order jackknife: It uses the frequency of uniques to estimate the number of undetected species; see Burnham and Overton (1978).
2nd order jackknife: It uses the frequencies of uniques and duplicates to estimate the number of undetected species; see Burnham and Overton (1978).
95% Confidence interval: A log-transformation is used for all estimators so that the lower bound of the resulting interval is at least the number of observed species. See Chao (1987).
(1) BASIC DATA INFORMATION:
Variable Value
Number of observed species D 34
Number of sampling units T 121
Total number of incidences U 461
Coverage estimate for entire dataset C 0.994
CV for entire dataset CV 1.162
Variable Value
Cut-off point k 10
Total number of incidences in infrequent group U_infreq 115
Number of observed species for infrequent group D_infreq 23
Estimated sample coverage for infrequent group C_infreq 0.974
Estimated CV for infrequent group in ICE CV_infreq 0.384
Estimated CV1 for infrequent group in ICE-1 CV1_infreq 0.412
Number of observed species for frequent group D_freq 11
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
Incidence freq. counts 3 2 3 3 1 5 1 1 3 1
(2) SPECIES RICHNESS ESTIMATORS TABLE:
Estimate s.e. 95%Lower 95%Upper
Homogeneous Model 34.609 0.880 34.076 38.878
Chao2 (Chao, 1987) 36.231 3.370 34.263 52.900
Chao2-bc 34.992 1.805 34.093 44.606
iChao2 (Chiu et al. 2014) 36.723 2.403 34.615 46.053
ICE (Lee & Chao, 1994) 35.064 1.371 34.153 41.398
ICE-1 (Lee & Chao, 1994) 35.132 1.473 34.161 41.966
1st order jackknife 36.975 2.434 34.731 46.103
2nd order jackknife 37.975 4.193 34.730 55.652
(3) DESCRIPTION OF ESTIMATORS/MODELS:
Homogeneous Model: This model assumes that all species have the same incidence or detection probabilities. See Eq. (3.2) of Lee and Chao (1994) or Eq. (12a) in Chao and Chiu (2016b).
Chao2 (Chao, 1987): This approach uses the frequencies of uniques and duplicates to estimate the number of undetected species; see Chao (1987) or Eq. (11a) in Chao and Chiu (2016b).
Chao2-bc: A bias-corrected form for the Chao2 estimator; see Chao (2005).
iChao2: An improved Chao2 estimator; see Chiu et al. (2014).
ICE (Incidence-based Coverage Estimator): A non-parametric estimator originally proposed by Lee and Chao (1994) in the context of capture-recapture data analysis. The observed species are separated as frequent and infrequent species groups; only data in the infrequent group are used to estimate the number of undetected species. The estimated CV for species in the infrequent group characterizes the degree of heterogeneity among species incidence probabilities. See Eq. (12b) of Chao and Chiu (2016b), which is an improved version of Eq. (3.18) in Lee and Chao (1994). This model is also called Model(h) in capture-recapture literature where h denotes "heterogeneity".
ICE-1: A modified ICE for highly-heterogeneous cases.
1st order jackknife: It uses the frequency of uniques to estimate the number of undetected species; see Burnham and Overton (1978).
2nd order jackknife: It uses the frequencies of uniques and duplicates to estimate the number of undetected species; see Burnham and Overton (1978).
95% Confidence interval: A log-transformation is used for all estimators so that the lower bound of the resulting interval is at least the number of observed species. See Chao (1987).
(1) BASIC DATA INFORMATION:
Variable Value
Number of observed species D 76
Number of sampling units T 18
Total number of incidences U 142
Coverage estimate for entire dataset C 0.71
CV for entire dataset CV 0.654
Variable Value
Cut-off point k 10
Total number of incidences in infrequent group U_infreq 142
Number of observed species for infrequent group D_infreq 76
Estimated sample coverage for infrequent group C_infreq 0.71
Estimated CV for infrequent group in ICE CV_infreq 0.662
Estimated CV1 for infrequent group in ICE-1 CV1_infreq 0.891
Number of observed species for frequent group D_freq 0
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
Incidence freq. counts 43 16 8 6 0 2 1 0 0 0
(2) SPECIES RICHNESS ESTIMATORS TABLE:
Estimate s.e. 95%Lower 95%Upper
Homogeneous Model 107.060 10.201 92.587 134.161
Chao2 (Chao, 1987) 130.571 22.753 100.899 195.605
Chao2-bc 126.167 20.718 99.048 185.193
iChao2 (Chiu et al. 2014) 139.901 15.602 115.874 178.408
ICE (Lee & Chao, 1994) 133.595 20.793 105.003 190.374
ICE-1 (Lee & Chao, 1994) 155.184 34.275 111.147 254.396
1st order jackknife 116.611 8.886 102.581 138.048
2nd order jackknife 141.448 14.872 118.160 177.598
(3) DESCRIPTION OF ESTIMATORS/MODELS:
Homogeneous Model: This model assumes that all species have the same incidence or detection probabilities. See Eq. (3.2) of Lee and Chao (1994) or Eq. (12a) in Chao and Chiu (2016b).
Chao2 (Chao, 1987): This approach uses the frequencies of uniques and duplicates to estimate the number of undetected species; see Chao (1987) or Eq. (11a) in Chao and Chiu (2016b).
Chao2-bc: A bias-corrected form for the Chao2 estimator; see Chao (2005).
iChao2: An improved Chao2 estimator; see Chiu et al. (2014).
ICE (Incidence-based Coverage Estimator): A non-parametric estimator originally proposed by Lee and Chao (1994) in the context of capture-recapture data analysis. The observed species are separated as frequent and infrequent species groups; only data in the infrequent group are used to estimate the number of undetected species. The estimated CV for species in the infrequent group characterizes the degree of heterogeneity among species incidence probabilities. See Eq. (12b) of Chao and Chiu (2016b), which is an improved version of Eq. (3.18) in Lee and Chao (1994). This model is also called Model(h) in capture-recapture literature where h denotes "heterogeneity".
ICE-1: A modified ICE for highly-heterogeneous cases.
1st order jackknife: It uses the frequency of uniques to estimate the number of undetected species; see Burnham and Overton (1978).
2nd order jackknife: It uses the frequencies of uniques and duplicates to estimate the number of undetected species; see Burnham and Overton (1978).
95% Confidence interval: A log-transformation is used for all estimators so that the lower bound of the resulting interval is at least the number of observed species. See Chao (1987).
(1) BASIC DATA INFORMATION:
Variable Value
Number of observed species D 76
Number of sampling units T 18
Total number of incidences U 142
Coverage estimate for entire dataset C 0.71
CV for entire dataset CV 0.654
Variable Value
Cut-off point k 10
Total number of incidences in infrequent group U_infreq 142
Number of observed species for infrequent group D_infreq 76
Estimated sample coverage for infrequent group C_infreq 0.71
Estimated CV for infrequent group in ICE CV_infreq 0.662
Estimated CV1 for infrequent group in ICE-1 CV1_infreq 0.891
Number of observed species for frequent group D_freq 0
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
Incidence freq. counts 43 16 8 6 0 2 1 0 0 0
(2) SPECIES RICHNESS ESTIMATORS TABLE:
Estimate s.e. 95%Lower 95%Upper
Homogeneous Model 106.946 10.179 92.511 133.999
Chao2 (Chao, 1987) 130.571 22.753 100.899 195.605
Chao2-bc 126.167 20.718 99.048 185.193
iChao2 (Chiu et al. 2014) 139.901 15.602 115.874 178.408
ICE (Lee & Chao, 1994) 133.661 20.827 105.028 190.539
ICE-1 (Lee & Chao, 1994) 155.450 34.410 111.250 255.071
1st order jackknife 116.611 8.886 102.581 138.048
2nd order jackknife 141.448 14.872 118.160 177.598
(3) DESCRIPTION OF ESTIMATORS/MODELS:
Homogeneous Model: This model assumes that all species have the same incidence or detection probabilities. See Eq. (3.2) of Lee and Chao (1994) or Eq. (12a) in Chao and Chiu (2016b).
Chao2 (Chao, 1987): This approach uses the frequencies of uniques and duplicates to estimate the number of undetected species; see Chao (1987) or Eq. (11a) in Chao and Chiu (2016b).
Chao2-bc: A bias-corrected form for the Chao2 estimator; see Chao (2005).
iChao2: An improved Chao2 estimator; see Chiu et al. (2014).
ICE (Incidence-based Coverage Estimator): A non-parametric estimator originally proposed by Lee and Chao (1994) in the context of capture-recapture data analysis. The observed species are separated as frequent and infrequent species groups; only data in the infrequent group are used to estimate the number of undetected species. The estimated CV for species in the infrequent group characterizes the degree of heterogeneity among species incidence probabilities. See Eq. (12b) of Chao and Chiu (2016b), which is an improved version of Eq. (3.18) in Lee and Chao (1994). This model is also called Model(h) in capture-recapture literature where h denotes "heterogeneity".
ICE-1: A modified ICE for highly-heterogeneous cases.
1st order jackknife: It uses the frequency of uniques to estimate the number of undetected species; see Burnham and Overton (1978).
2nd order jackknife: It uses the frequencies of uniques and duplicates to estimate the number of undetected species; see Burnham and Overton (1978).
95% Confidence interval: A log-transformation is used for all estimators so that the lower bound of the resulting interval is at least the number of observed species. See Chao (1987).
```

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