`Dqz.Rd`

Calculates the diversity of order \(q\) of a probability vector according to a similarity matrix.

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

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 |

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.

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

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).

Eric Marcon <Eric.Marcon@ecofog.gf>

# 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)#> Best #> 1.48295