`Diversity.Rd`

Calculates the HCDT (generalized) diversity of order \(q\) of a probability vector.

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

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 |

`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.

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

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.

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) # 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)#> None #> 113.98# Calculate it with estimation bias correction (asymptotic estimator) Diversity(Ns, q=1)#> UnveilJ #> 138.1078# Extrapolate it up to 99.9% sample coverage (close to the asymptotic estimator) Diversity(Ns, q=1, Level=0.999)#> Best #> 127.3298#> Interp #> 100.016