Rao {entropart} | R Documentation |

## Rao Quadratic Entropy of a Community

### Description

Calculates Rao's quadratic entropy of a community described by a probability vector and a phylogenetic / functional tree.

### Usage

```
Rao(NorP, Tree, ...)
bcRao(Ns, Tree, Correction="Lande", CheckArguments = TRUE)
## S3 method for class 'ProbaVector'
Rao(NorP, Tree, ..., CheckArguments = TRUE, Ps = NULL)
## S3 method for class 'AbdVector'
Rao(NorP, Tree, Correction = "Lande", ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'integer'
Rao(NorP, Tree, Correction = "Lande", ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'numeric'
Rao(NorP, Tree, Correction = "Lande", ...,
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 ( |

`Tree` |
An object of class |

`Correction` |
A string containing one of the possible corrections accepted by |

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

`CheckArguments` |
Logical; if |

### Details

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

and choose the `Correction`

.

The unbiased estimator of Rao's entropy is identical to that of Simpson's entropy because Rao's entropy is a linear sum of Simson entropies, all of them calculated from the same number of individuals (Marcon and Herault, 2014). It equals the plug-in etimator multiplied by n/(n-1) where n is the total number of individuals.

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

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 `bcTsallis`

is called. Explicit calls to `bcTsallis`

(with bias correction) or to `Tsallis.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 entropy. The name is that of the bias correction used.

### References

Marcon, E., Herault, B. (2015). Decomposing Phylodiversity. *Methods in Ecology and Evolution* 6(3): 333-339.

Rao, C. R. (1982). Diversity and dissimilarity coefficients: a unified approach. *Theoretical Population Biology* 21: 24-43.

### See Also

### 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)
# Calculate Rao's quadratic entropy of the plot
Rao(Ps, Paracou618.Taxonomy)
```

*entropart*version 1.6-13 Index]