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

ShannonBeta(NorP, NorPexp = NULL, ...)
bcShannonBeta(Ns, Nexp, Correction = "Best", CheckArguments = TRUE)
# S3 method for ProbaVector
ShannonBeta(NorP, NorPexp = NULL, ...,
CheckArguments = TRUE, Ps = NULL, Pexp = NULL)
# S3 method for AbdVector
ShannonBeta(NorP, NorPexp = NULL, Correction = "Best", ...,
CheckArguments = TRUE, Ns = NULL, Nexp = NULL)
# S3 method for integer
ShannonBeta(NorP, NorPexp = NULL, Correction = "Best", ...,
CheckArguments = TRUE, Ns = NULL, Nexp = NULL)
# S3 method for numeric
ShannonBeta(NorP, NorPexp = NULL, Correction = "Best", ...,
CheckArguments = TRUE, Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL)

## Arguments

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 (AbdVector) or a probability vector (ProbaVector). Contains either abundances or probabilities of the community.

NorPexp

A numeric vector, an integer vector, an abundance vector (AbdVector) or a probability vector (ProbaVector). Contains either abundances or probabilities of the metacommunity.

Correction

A string containing one of the possible corrections: currently, "ChaoShen" (Marcon et al., 2012) equivalent to "Best", and "ZhangGrabchak" (Zhang and Grabchak, 2014).

...

CheckArguments

Logical; if TRUE, the function arguments are verified. Should be set to FALSE to save time when the arguments have been checked elsewhere.

## Details

The derivation of Shannon beta entropy can be found in Marcon et al. (2012).

Bias correction requires the number of individuals to estimate sample Coverage. Use bcShannonBeta and choose the Correction.

The functions are designed to be used as simply as possible. ShannonBeta 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 bcShannonBeta is called. Explicit calls to bcShannonBeta (with bias correction) or to ShannonBeta.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 number equal to the calculated entropy.

## References

Marcon, E., Herault, B., Baraloto, C. and Lang, G. (2012). The Decomposition of Shannon's Entropy and a Confidence Interval for Beta Diversity. Oikos 121(4): 516-522.

Zhang, Z. and Grabchak M. (2014). Nonparametric Estimation of Kullback-Leibler Divergence. Neural computation 26(11): 2570-2593.

bcShannonBeta

## Examples

# 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])
# Shannon beta entropy of the plot
ShannonBeta(Ps1, Ps)
#>      None
#> 0.3499358

# 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 estimator of Shannon beta entropy of the plot
bcShannonBeta(Ns1, Ns)
#>      Best
#> 0.2949188