Diversity {entropart} | R Documentation |

## Hill number of a community

### Description

Calculates the HCDT (generalized) diversity of order `q`

of a probability vector.

### Usage

```
Diversity(NorP, q = 1, ...)
bcDiversity(Ns, q = 1, Correction = "Best", CheckArguments = TRUE)
## S3 method for class 'ProbaVector'
Diversity(NorP, q = 1, ...,
CheckArguments = TRUE, Ps = NULL)
## S3 method for class 'AbdVector'
Diversity(NorP, q = 1, Correction = "Best", Level = NULL,
PCorrection="Chao2015", Unveiling="geom", RCorrection="Rarefy", ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'integer'
Diversity(NorP, q = 1, Correction = "Best", Level = NULL,
PCorrection="Chao2015", Unveiling="geom", RCorrection="Rarefy", ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'numeric'
Diversity(NorP, q = 1, Correction = "Best", 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 ( |

`q` |
A number: the order of diversity. Default is 1. |

`Correction` |
A string containing one of the possible asymptotic estimators: |

`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). |

`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

`Diversity`

calls `Tsallis`

to calculate entropy and transforms it into diversity by calculating its deformed exponential.

Bias correction requires the number of individuals to estimate sample `Coverage`

.
See `Tsallis`

for details.

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

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 `bcDiversity`

is called.

Diversity 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.
See `Tsallis`

for details.

### Value

A named number equal to the calculated diversity. The name is that of the bias correction used.

### References

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.

Marcon, E., Scotti, I., Herault, B., Rossi, V. and Lang, G. (2014). Generalization of the partitioning of Shannon diversity. *PLOS One* 9(3): e90289.

### See Also

`Tsallis`

, `expq`

, `AbdVector`

, `ProbaVector`

### 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)
# Calculate diversity of order 1, i.e. Shannon's diversity
Diversity(Ps, q=1)
# Calculate it with estimation bias correction (asymptotic estimator)
Diversity(Ns, q=1)
# Extrapolate it up to 99.9% sample coverage (close to the asymptotic estimator)
Diversity(Ns, q=1, Level=0.999)
# Rarefy it to half the sample size
Diversity(Ns, q=1, Level=sum(Ns)/2)
```

*entropart*version 1.6-13 Index]