Calculates the Tsallis beta entropy of order \(q\) of a community belonging to a metacommunity.
TsallisBeta(NorP, NorPexp = NULL, q = 1, ...) bcTsallisBeta(Ns, Nexp = NULL, q, Correction = "Best", CheckArguments = TRUE) # S3 method for ProbaVector TsallisBeta(NorP, NorPexp = NULL, q = 1, ..., CheckArguments = TRUE, Ps = NULL, Pexp = NULL) # S3 method for AbdVector TsallisBeta(NorP, NorPexp = NULL, q = 1, Correction = "Best", ..., CheckArguments = TRUE, Ns = NULL, Nexp = NULL) # S3 method for integer TsallisBeta(NorP, NorPexp = NULL, q = 1, Correction = "Best", ..., CheckArguments = TRUE, Ns = NULL, Nexp = NULL) # S3 method for numeric TsallisBeta(NorP, NorPexp = NULL, q = 1, Correction = "Best", ..., CheckArguments = TRUE, Ps = NULL, Ns = NULL, Pexp = NULL, Nexp = NULL)
The probability vector of species of the community.
The probability vector of species of the metacommunity.
A numeric vector containing species abundances of the community.
A numeric vector containing species abundances of the metacommunity.
A number: the order of entropy. Default is 1 for Shannon entropy.
A string containing one of the possible corrections: currently, only
"Best" is the default value, it is equivalent to
Additional arguments. Unused.
TRUE, the function arguments are verified. Should be set to
FALSE to save time when the arguments have been checked elsewhere.
The derivation of Tsallis beta entropy can be found in Marcon et al. (2014).
Bias correction requires the number of individuals to estimate sample
bcTsallisBeta and choose the
Note that beta entropy value is related to alpha entropy (if \(q\) is not 1) and cannot be compared accross communities (Jost, 2007). Beta entropy of a community is not meaningful in general, do rather calculate the
BetaDiversity of the metacommunity.
The functions are designed to be used as simply as possible.
TsallisBeta 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
bcTsallisBeta is called. Explicit calls to
bcTsallisBeta (with bias correction) or to
TsallisBeta.ProbaVector (without correction) are possible to avoid ambiguity. The
.numeric methods accept
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.
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.
# 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 <- Paracou618.MC$Ps # Probability distribution of the first plot Ps1 <- Paracou618.MC$Psi[, 1] # Divergence of order 2 between plot 1 and the whole forest TsallisBeta(Ps1, Ps, 2) #> None #> 0.01004705 # Ns is the vector of abundances of the metacommunity Ns <- Paracou618.MC$Ns # Abundances in the first plot Ns1 <- Paracou618.MC$Nsi[, 1] # Divergence of order 2 between plot 1 and the whole forest, with bias correction bcTsallisBeta(Ns1, Ns, 2) #> Best #> 0.007566555