Richness {entropart} | R Documentation |

## Number of species of a community

### Description

Calculates the number of species from probability vector. The name is that of the estimator (the bias correction) used.

### Usage

```
Richness(NorP, ...)
bcRichness(Ns, Correction = "Best", Alpha = 0.05, JackOver = FALSE, JackMax = 10,
CheckArguments = TRUE)
## S3 method for class 'ProbaVector'
Richness(NorP, ..., CheckArguments = TRUE, Ps = NULL)
## S3 method for class 'AbdVector'
Richness(NorP, Correction = "Best", Alpha = 0.05,
JackOver = FALSE, JackMax = 10,
Level = NULL, PCorrection = "Chao2015", Unveiling = "geom", RCorrection = "Rarefy",
..., CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'integer'
Richness(NorP, Correction = "Best", Alpha = 0.05,
JackOver = FALSE, JackMax = 10,
Level = NULL, PCorrection = "Chao2015", Unveiling = "geom", RCorrection = "Rarefy",
..., CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'numeric'
Richness(NorP, Correction = "Best", Alpha = 0.05,
JackOver = FALSE, JackMax = 10,
Level = NULL, PCorrection = "Chao2015", Unveiling = "geom", RCorrection = "Rarefy",
..., CheckArguments = TRUE, Ps = NULL, Ns = NULL)
```

### Arguments

`Ps` |
A probability vector, summing to 1. |

`Ns` |
A numeric vector containing species abundances. |

`NorP` |
A numeric vector, an integer vector, an abundance vector ( |

`Correction` |
A string containing one of the possible corrections: |

`Alpha` |
The risk level, 5% by default, used to optimize the jackknife order. |

`JackOver` |
If |

`JackMax` |
The highest jackknife order allowed. Default is 10. Allowed values are between 1 and 10. |

`Level` |
The level of interpolation or extrapolation. It may be an a chosen sample size (an integer) or a sample coverage (a number between 0 and 1). Richness extrapolation require its asymptotic estimation depending on the choice of |

`PCorrection` |
A string containing one of the possible corrections to estimate a probability distribution in |

`Unveiling` |
A string containing one of the possible unveiling methods to estimate the probabilities of the unobserved species in |

`RCorrection` |
A string containing a correction recognized by |

`...` |
Additional arguments. Unused. |

`CheckArguments` |
Logical; if |

### Details

Bias correction requires the number of individuals. Use `bcRichness`

and choose the `Correction`

.

Chao correction techniques are from Chao (1984) and Chiu *et al.* (2015). The Jackknife estimator is calculated by a straight adaptation of the code by Ji-Ping Wang (`jackknife`

in CRAN-archived package `SPECIES`

). The optimal order is selected according to Burnham and Overton (1978; 1979). The argument `JackOver`

allows selecting one order over the optimal one.
Many other estimators are available elsewhere, the ones implemented here are necessary for other entropy estimations.

The functions are designed to be used as simply as possible. `Richness`

is a generic method. If its first argument is an abundance vector, an integer vector or a numeric vector which does not sum to 1, the bias corrected function `bcRichness`

is called.

Richness can be estimated at a specified level of interpolation or extrapolation, either a chosen sample size or sample coverage (Chao et al., 2014), rather than its asymptotic value.
Extrapolation relies on the estimation of the asymptotic richness. If `PCorrection`

is "None", then the asymptotic estimation of richness is made using the chosen `Correction`

, else the asymtpotic distribution of the community is derived and its estimated richness adjusted so that the entropy of a sample of this distribution of the size of the actual sample has the entropy of the actual sample.

### Value

A named number equal to the estimated number of species.
The name is the `Correction`

, except for "SAC" (Species Accumulation Curve) for interpolation.

### References

Burnham, K. P., and Overton,W. S. (1978), Estimation of the Size of a Closed Population When Capture Probabilities Vary Among Animals. *Biometrika*, 65: 625-633.

Burnham, K. P., and Overton,W. S. (1979), Robust Estimation of Population Size When Capture Probabilities Vary Among Animals. *Ecology* 60:927-936.

Chao, A. (1984) Nonparametric estimation of the number of classes in a population. *Scandinavian Journal of Statistics* 11: 265-270.

Chao, A., Gotelli, N. J., Hsieh, T. C., Sander, E. L., Ma, K. H., Colwell, R. K., Ellison, A. M (2014). Rarefaction and extrapolation with Hill numbers: A framework for sampling and estimation in species diversity studies. *Ecological Monographs*, 84(1): 45-67.

Chiu, C.-H., Wang, Y.-T., Walther, B. A., Chao, A. (2014) An Improved Nonparametric Lower Bound of Species Richness via a Modified Good-Turing Frequency Formula. *Biometrics* 70(3): 671-682.

### Examples

```
# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest)
data(Paracou618)
# Ns is the total number of trees per species
Ns <- as.AbdVector(Paracou618.MC$Ns)
# Species probabilities
Ps <- as.ProbaVector(Paracou618.MC$Ns)
# Whittaker plot
plot(Ns)
# Number of observed species
Richness(Ps)
# Estimate the actual number of species
bcRichness(Ns, Correction = "Chao1")
bcRichness(Ns, Correction = "iChao1")
bcRichness(Ns, Correction = "Jackknife")
bcRichness(Ns, Correction = "Jackknife", JackOver=TRUE)
```

*entropart*version 1.6-13 Index]