entropart (version 1.2.0)

Tsallis: Tsallis Entropy of a community

Description

Calculates the HCDT, also known as Tsallis entropy of order $q$ of a probability vector.

Usage

Tsallis(Ps, q = 1, CheckArguments = TRUE)
bcTsallis(Ns, q = 1, Correction = "Best", CheckArguments = TRUE)

Arguments

Ps

A probability vector, summing to 1.

Ns

A numeric vector containing species abundances.

q

A number: the order of entropy. Some corrections allow only a positive number. Default is 1 for Shannon entropy.

Correction

A string containing one of the possible corrections: "None" (no correction), "ChaoShen", "Grassberger", "Holste", "Bonachela", "ZhangGrabchak" or "Best", the defaul

CheckArguments

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

Value

• A number equal to the calculated entropy.

Details

Tsallis (Havrda and Charvat, 1967; Daroczy, 1970; Tsallis, 1988) generalized entropy is a generalized measure of diversity (Jost, 2006). Bias correction requires the number of individuals to estimate sample Coverage. Use bcTsallis and choose the Correction. Correction techniques are from Chao and Shen (2003), Grassberger (1988), Holste et al. (1998), Bonachela et al. (2008) and Zhang and Grabchak (2014). Currently, the "Best" correction is the max value of "ChaoShen" and "Grassberger" (Marcon et al., 2014).

References

Havrda, J. and Charvat, F. (1967). Quantification method of classification processes. Concept of structural a-entropy. Kybernetika 3(1): 30-35. Daroczy, Z. (1970). Generalized information functions. Information and Control 16(1): 36-51. Marcon, E., Scotti, I., Herault, B., Rossi, V. and Lang, G. (2014). Generalization of the partitioning of Shannon diversity. PLOS One 9(3): e90289. Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics 52(1): 479-487. Jost, L. (2006). Entropy and diversity. Oikos 113(2): 363-375. Zhang, Z. and Grabchak M. (2014). Entropic Representation and Estimation of Diversity Indices. arXiv 1403.3031(v. 1): 1-12.

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 <- Paracou618.MC$Ps
  # Calculate Tsallis entropy of order 2, i.e. Simpson's index of diversity
  Tsallis(Ps, 2) 

  # Ns is the vector of abundances of the metacommunity
  Ns <- Paracou618.MC$Ns
  # Calculate an unbiased estimator of Tsallis entropy of order 2, i.e. Simpson's index
  bcTsallis(Ns, 2)