Description Usage Arguments Value References Examples

`ChaoShared`

: Estimation of shared species richness between two communities/assemblages based on
three types of data: Type (1) abundance data (datatype="abundance"), Type (2) incidence-frequency
data (datatype="incidence_freq"), and Type (2B) incidence-raw data (datatype="incidence

_raw"); see `SpadeR-package`

details for data input formats.

1 2 | ```
ChaoShared(data, datatype = c("abundance", "incidence_freq", "incidence_raw"),
units, se = TRUE, nboot = 200, conf = 0.95)
``` |

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

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

`units` |
number of sampling units in each community. For |

`se` |
a logical variable to calculate the bootstrap standard error and the associated confidence interval. |

`nboot` |
an integer specifying the number of bootstrap replications. |

`conf` |
a positive number |

a list of two objects:

`$Basic_data_information`

for summarizing data information.

`$Estimation_results`

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

Chao, A., Hwang, W.-H., Chen, Y.-C. and Kuo. C.-Y. (2000). Estimating the number of shared species in two communities. Statistica Sinica, 10, 227-246.

Pan, H.-Y., Chao, A. and Foissner, W. (2009). A non-parametric lower bound for the number of species shared by multiple communities. Journal of Agricultural, Biological and Environmental Statistics, 14, 452-468.

1 2 3 4 5 6 7 | ```
data(ChaoSharedData)
# Type (1) abundance data
ChaoShared(ChaoSharedData$Abu,"abundance",se=TRUE,nboot=200,conf=0.95)
# Type (2) incidence-frequency data
ChaoShared(ChaoSharedData$Inci,"incidence_freq",se=TRUE,nboot=200,conf=0.95)
# Type (2B) incidence-raw data
ChaoShared(ChaoSharedData$Inci_raw,"incidence_raw",units=c(16,17),se=TRUE,nboot=200,conf=0.95)
``` |

```
(1) BASIC DATA INFORMATION:
Sample size in Community 1 n1 = 85867
Sample size in Community 2 n2 = 59646
Number of observed species in Community 1 D1 = 155
Number of observed species in Community 2 D2 = 140
Number of observed shared species D12 = 111
Bootstrap replications for s.e. estimate 200
"Entire" Shared Species Group:
Some statistics:
---------------------------------------------------------------------------
f[11] = 4 ; f[1+] = 10 ; f[+1] = 15 ; f[2+] = 2 ; f[+2] = 7 ; f[22] = 0
---------------------------------------------------------------------------
"Rare" Shared Species Group: (Both frequencies can only up to 10)
Some statistics:
-------------------------------------------------------------------
f[1+]_rare = 8 ; f[+1]_rare = 9 ; f[2+]_rare = 1 ; f[+2]_rare = 4
-------------------------------------------------------------------
Number of observed individuals in Community 1 n1_rare = 3358
Number of observed individuals in Community 2 n2_rare = 558
Number of observed shared species D12_rare = 21
Estimated sample coverage C12_rare = 0.86
Estimated CCVs CCV_1 = 0.733
CCV_2 = 1.007
CCV_12 = 0.457
(2) ESTIMATION RESULTS OF THE NUMBER OF SHARED SPECIES:
Estimate s.e. 95%Lower 95%Upper
Homogeneous 114.429 6.682 110.524 147.459
Heterogeneous(ACE-shared) 133.921 18.155 116.378 199.717
Chao1-shared 142.125 18.364 121.329 201.090
Chao1-shared-bc 142.125 18.364 121.329 201.090
(3) DESCRIPTION OF MODELS FOR ESTIMATING SHARED SPECIES RICHNESS:
Homogeneous: This model assumes that the shared species in each community have the same discovery probabilities; see the Eq. (3.11a) of Chao et al. (2000).
Heterogeneous (ACE-shared): This model allows for heterogeneous discovery probabilities among shared species; see Eq. (3.11b) of Chao et al. (2000). It is an extension of the ACE estimator to two communities. It is replaced by Chao1-shared when the estimated sample coverage for rare shared species group (C12_rare in the output) is zero.
Chao1-shared: An extension of the Chao1 estimator to estimate shared species richness between two communities. It provides a lower bound of shared species richness. See Eq. (3.6) of Pan et al. (2009). It is replaced by Chao1-shared-bc for the case f[2+]=0 or f[+2]=0.
Chao1-shared-bc: A bias-corrected form of Chao1-shared estimator; See Pan et al. (2009).
(1) BASIC DATA INFORMATION:
Number of sampling units in Community 1 T1 = 16
Number of sampling units in Community 2 T2 = 17
Number of total incidences in Community 1 U1 = 1958
Number of total incidences in Community 2 U2 = 2215
Number of observed species in Community 1 D1 = 223
Number of observed species in Community 2 D2 = 223
Number of observed shared species in two communities D12 = 196
Bootstrap replications for s.e. estimate 200
Some statistics:
--------------------------------------------------------------------------
Q[11] = 5 ; Q[1+] = 16 ; Q[+1] = 11 ; Q[2+] = 16 ; Q[+2] = 6 ; Q[22] = 2
--------------------------------------------------------------------------
(2) ESTIMATION RESULTS OF THE NUMBER OF SHARED SPECIES:
Estimate s.e. 95%Lower 95%Upper
Chao2-shared 215.748 12.000 202.581 255.253
Chao2-shared-bc 211.483 9.245 201.246 241.697
(3) DESCRIPTION OF MODELS FOR ESTIMATING SHARED SPECIES RICHNESS:
Chao2-shared: An extension of the Chao2 estimator to estimate shared species richness between two communities. It provides a lower bound of shared species richness. See Pan et al. (2009). It is replaced by Chao2-shared-bc for the case Q[2+]=0 or Q[+2]=0.
Chao2-shared-bc: A bias-corrected form of Chao2-shared. See Pan et al. (2009).
(1) BASIC DATA INFORMATION:
Number of sampling units in Community 1 T1 = 16
Number of sampling units in Community 2 T2 = 17
Number of total incidences in Community 1 U1 = 1958
Number of total incidences in Community 2 U2 = 2215
Number of observed species in Community 1 D1 = 223
Number of observed species in Community 2 D2 = 223
Number of observed shared species in two communities D12 = 196
Bootstrap replications for s.e. estimate 200
Some statistics:
--------------------------------------------------------------------------
Q[11] = 5 ; Q[1+] = 16 ; Q[+1] = 11 ; Q[2+] = 16 ; Q[+2] = 6 ; Q[22] = 2
--------------------------------------------------------------------------
(2) ESTIMATION RESULTS OF THE NUMBER OF SHARED SPECIES:
Estimate s.e. 95%Lower 95%Upper
Chao2-shared 215.748 12.000 202.581 255.253
Chao2-shared-bc 211.483 9.245 201.246 241.697
(3) DESCRIPTION OF MODELS FOR ESTIMATING SHARED SPECIES RICHNESS:
Chao2-shared: An extension of the Chao2 estimator to estimate shared species richness between two communities. It provides a lower bound of shared species richness. See Pan et al. (2009). It is replaced by Chao2-shared-bc for the case Q[2+]=0 or Q[+2]=0.
Chao2-shared-bc: A bias-corrected form of Chao2-shared. See Pan et al. (2009).
```

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