Calculates the Simpson beta entropy of a community belonging to a metacommunity.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
SimpsonBeta(NorP, NorPexp = NULL, Correction = "Best", CheckArguments = TRUE,
Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL)
bcSimpsonBeta(Ns, Nexp, Correction = "Best", CheckArguments = TRUE)
## S3 method for class 'ProbaVector'
SimpsonBeta(NorP, NorPexp = NULL, Correction = "Best", CheckArguments = TRUE,
Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL)
## S3 method for class 'AbdVector'
SimpsonBeta(NorP, NorPexp = NULL, Correction = "Best", CheckArguments = TRUE,
Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL)
## S3 method for class 'integer'
SimpsonBeta(NorP, NorPexp = NULL, Correction = "Best", CheckArguments = TRUE,
Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL)
## S3 method for class 'numeric'
SimpsonBeta(NorP, NorPexp = NULL, Correction = "Best", CheckArguments = TRUE,
Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL)
``` |

`Ps` |
The probability vector of species of the community. |

`Pexp` |
The probability vector of species of the metacommunity. |

`Ns` |
A numeric vector containing species abundances of the community. |

`Nexp` |
A numeric vector containing species abundances of the metacommunity. |

`NorP` |
A numeric vector, an integer vector, an abundance vector ( |

`NorPexp` |
A numeric vector, an integer vector, an abundance vector ( |

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

`CheckArguments` |
Logical; if |

The derivation of Tsallis beta entropy (Simpson is Tsallis of order 2) can be found in Marcon et al. (2014).

Bias correction requires the number of individuals to estimate sample `Coverage`

. Use `bcSimpsonBeta`

and choose the `Correction`

.

Note that Simpson beta entropy value is related to Simpson alpha entropy value and cannot be compared accross communities (Jost, 2007). Beta entropy of a community is not meaningful in general, do rather calculate the `BetaDiversity`

of order 2 of the metacommunity.

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

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 `bcSimpsonBeta`

is called. Explicit calls to `bcSimpsonBeta`

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

Eric Marcon <Eric.Marcon@ecofog.gf>

Jost (2007), Partitioning diversity into independent alpha and beta components. *Ecology* 88(10): 2427-2439.

Marcon, E., Scotti, I., Herault, B., Rossi, V. and Lang, G. (2014). Generalization of the partitioning of Shannon diversity. *PLOS One* 9(3): e90289.

`Simpson`

, `bcSimpsonBeta`

, `BetaDiversity`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest)
data(Paracou618)
# Ps is the vector of probabilities
Ps <- as.ProbaVector(Paracou618.MC$Ps)
# Probability distribution of the first plot
Ps1 <- as.ProbaVector(Paracou618.MC$Psi[, 1])
# Simpson beta entropy of the plot
SimpsonBeta(Ps1, Ps)
# Transform into diversity
expq(SimpsonBeta(Ps1, Ps)/(1-Simpson(Ps1)), 2)
# Ns is the vector of abundances of the metacommunity
Ns <- as.AbdVector(Paracou618.MC$Ns)
# Abundances in the first plot
Ns1 <- as.AbdVector(Paracou618.MC$Nsi[, 1])
# Reduced-bias Shannon beta entropy of the plot
bcSimpsonBeta(Ns1, Ns)
``` |

Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.

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