Dqz {entropart} | R Documentation |

## Similarity-based diversity of a community

### Description

Calculates the diversity of order `q`

of a probability vector according to a similarity matrix.

### Usage

```
Dqz(NorP, q = 1, Z = diag(length(NorP)), ...)
bcDqz(Ns, q = 1, Z = diag(length(Ns)), Correction = "Best", CheckArguments = TRUE)
## S3 method for class 'ProbaVector'
Dqz(NorP, q = 1, Z = diag(length(NorP)), ...,
CheckArguments = TRUE, Ps = NULL)
## S3 method for class 'AbdVector'
Dqz(NorP, q = 1, Z = diag(length(NorP)), Correction = "Best", ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'integer'
Dqz(NorP, q = 1, Z = diag(length(NorP)), Correction = "Best", ...,
CheckArguments = TRUE, Ns = NULL)
## S3 method for class 'numeric'
Dqz(NorP, q = 1, Z = diag(length(NorP)), Correction = "Best", ...,
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. |

`Z` |
A relatedness matrix, |

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

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

`CheckArguments` |
Logical; if |

### Details

Diversity is calculated following Leinster and Cobbold (2012): it is the reciprocal of the (generalized) average (of order `q`

) of the community species ordinariness.

A similarity matrix is used (as for `Dqz`

), not a distance matrix as in Ricotta and Szeidl (2006). See the example.

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

and choose the `Correction`

.
Correction techniques are from Marcon *et al.* (2014).

Currently, the `"Best"`

correction is the max value of `"HorvitzThomson"`

and `"MarconZhang"`

.

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

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 `bcDqz`

is called. Explicit calls to `bcDqz`

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

### References

Leinster, T. and Cobbold, C. (2012). Measuring diversity: the importance of species similarity. *Ecology* 93(3): 477-489.

Marcon, E., Zhang, Z. and Herault, B. (2014). The decomposition of similarity-based diversity and its bias correction. *HAL* hal-00989454(version 3).

### See Also

### Examples

```
# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest)
data(Paracou618)
# Prepare the similarity matrix
DistanceMatrix <- as.matrix(Paracou618.dist)
# Similarity can be 1 minus normalized distances between species
Z <- 1 - DistanceMatrix/max(DistanceMatrix)
# Calculate diversity of order 2
Dqz(Paracou618.MC$Ns, 2, Z)
```

*entropart*version 1.6-13 Index]