entropart (version 1.1.3)

Shannon: Shannon entropy of a community

Description

Calculates the Shannon entropy of a probability vector.

Usage

Shannon(Ps, CheckArguments = TRUE)
bcShannon(Ns, Correction = "Best", CheckArguments = TRUE)

Arguments

Ps

A probability vector, summing to 1.

Ns

A numeric vector containing species abundances.

Correction

A string containing one of the possible corrections: "None" (no correction), "ChaoShen", "Grassberger", "Grassberger2003", "Schurmann", "Holste", "Bonachela",

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

Bias correction requires the number of individuals to estimate sample Coverage. Use bcShannon and choose the Correction. Correction techniques are from Chao and Shen (2003), Grassberger (1988), Grassberger (2003), Schurmann (2003), Holste et al. (1998), Bonachela et al. (2008), Chao, Wang and Jost (2013). Using MetaCommunity mutual information, Chao, Wang and Jost (2013) calculate unbiased Shannon beta entropy (see the last example below) with better results than the Chao and Shen estimator, but community weights cannot be arbitrary: they must be proportional to the number of individuals.

References

Bonachela, J. A., Hinrichsen, H. and Munoz, M. A. (2008). Entropy estimates of small data sets. Journal of Physics A: Mathematical and Theoretical 41(202001): 1-9. Chao, A. and Shen, T. J. (2003). Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample. Environmental and Ecological Statistics 10(4): 429-443. Chao, A., Wang, Y. T. and Jost, L. (2013). Entropy and the species accumulation curve: a novel entropy estimator via discovery rates of new species. Methods in Ecology and Evolution 4(11):1091-1100. Grassberger, P. (1988). Finite sample corrections to entropy and dimension estimates. Physics Letters A 128(6-7): 369-373. Grassberger, P. (2003). Entropy Estimates from Insufficient Samplings. ArXiv Physics e-prints 0307138. Holste, D., Grosse, I. and Herzel, H. (1998). Bayes' estimators of generalized entropies. Journal of Physics A: Mathematical and General 31(11): 2551-2566. Shannon, C. E. (1948). A Mathematical Theory of Communication. The Bell System Technical Journal 27: 379-423, 623-656. Schurmann, T. (2004). Bias analysis in entropy estimation. Journal of Physics A: Mathematical and Theoretical 37(27): L295-L301. Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics 52(1): 479-487.

See Also

bcShannon, Tsallis

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 Shannon entropy
  Shannon(Ps)

  # Ns is the vector of abundances of the metacommunity
  Ns <- Paracou618.MC$Ns
  # Calculate an unbiased estimator of Shannon entropy
  bcShannon(Ns)
  
  # Use metacommunity data to calculate unbiased Shannon beta as mutual information
  (bcShannon(Paracou618.MC$Ns) + bcShannon(colSums(Paracou618.MC$Nsi))
    - bcShannon(Paracou618.MC$Nsi))
  # Compare with Chao and Shen correction (works for Tsallis entropy in general)
  summary(BetaEntropy(Paracou618.MC, 1))