Hurlbert {entropart} | R Documentation |

## Hurlbert's Index and Explicit Diversity

### Description

Calculates the Hurlbert entropy of order `k`

of a probability or abundance vector, and its effective number of species.

### Usage

```
Hurlbert(NorP, k = 2, ...)
bcHurlbert(Ns, k = 2, CheckArguments = TRUE)
## S3 method for class 'ProbaVector'
Hurlbert(NorP, k = 2, ...,
CheckArguments = TRUE, Ps = NULL)
## S3 method for class 'AbdVector'
Hurlbert(NorP, k = 2, ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'integer'
Hurlbert(NorP, k = 2, ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'numeric'
Hurlbert(NorP, k = 2, ...,
CheckArguments = TRUE, Ps = NULL, Ns = NULL)
HurlbertD(NorP, k = 2, ...)
bcHurlbertD(Ns, k = 2, CheckArguments = TRUE)
## S3 method for class 'ProbaVector'
HurlbertD(NorP, k = 2, ...,
CheckArguments = TRUE, Ps = NULL)
## S3 method for class 'AbdVector'
HurlbertD(NorP, k = 2, ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'integer'
HurlbertD(NorP, k = 2, ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'numeric'
HurlbertD(NorP, k = 2, ...,
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 ( |

`k` |
A number: the order of diversity. Default is 2 for Simpson's diversity. |

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

`CheckArguments` |
Logical; if |

### Details

Hurlbert's index of diversity (1971) of order `k`

is the expected number of species in a sample of size `k`

.

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

. It is limited to orders `k`

less than or equal to the number of individuals in the community.

The effective number of species `HurlbertD`

(explicit diversity) has been derived by Dauby & Hardy (2012). It is calculated numerically. `bcHurlbertD`

calculates it from the bias-corrected index `bcHurlbert`

.

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

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 `bcHurlbert`

is called. Explicit calls to `bcHurlbert`

(with bias correction) or to `Hurlbert.ProbaVector`

(without correction) are possible to avoid ambiguity. The `.integer`

and `.numeric`

methods accept `Ps`

or `Ns`

arguments instead of `NorP`

for backward compatibility.

### Value

A named number equal to the calculated index or diversity. The name is either "Biased" or "Unbiased", depending on the estimator used.

### References

Dauby G. & Hardy O.J. (2012) Sampled-based estimation of diversity sensu stricto by transforming Hurlbert diversities into effective number of species. *Ecography* 35(7): 661-672.

Hurlbert (1971) The Nonconcept of Species Diversity: A Critique and Alternative Parameters. *Ecology* 52(4): 577-586.

### 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 Hurlbert entropy of order 2, equal to Simpson's index of diversity
Hurlbert(Ps, 2)
# Calculate an unbiased estimator of Hurlbert entropy of order 2
Hurlbert(Ns, 2)
```

*entropart*version 1.6-13 Index]