entropart (version 1.1.3)

AlphaEntropy: Unbiased alpha entropy of a metacommunity

Description

Calculates the unbiased total alpha entropy of order $q$ of communities.

Usage

AlphaEntropy(MC, q, Correction = "Best", Tree = NULL, Normalize = TRUE, 
  CheckArguments = TRUE)

Arguments

MC

A MetaCommunity object.

q

A number: the order of diversity.

Correction

A string containing one of the possible corrections: "ChaoShen", "Grassberger", "Holste", "Bonachela" or "Best", the default value.

Tree

An object of class hclust or phylog. The tree must be ultrametric.

Normalize

If TRUE (default), the entropy returned by the function is normalized by the height of the tree (it is the weighted average value of the entropy in each slice). If FALSE, it is the unnormalized weighted sum of the results.

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

• An MCentropy object containing entropy values of each community and of the metacommunity.

Details

If Tree is NULL, then generalized entropy is calculated by bcTsallis, else phylogenetic entropy is calculated by bcPhyloEntropy. The alpha entropy of each community is calculated and summed according to community weights. Correction techniques are from Chao and Shen (2003), Grassberger (1988), Holste et al. (1998), Bonachela et al. (2008). Currently, the "Best" correction is the max value of "ChaoShen" and "Grassberger" (Marcon et al., submitted).

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. Grassberger, P. (1988). Finite sample corrections to entropy and dimension estimates. Physics Letters A 128(6-7): 369-373. Holste, D., Grosse, I. and Herzel, H. (1998). Bayes' estimators of generalized entropies. Journal of Physics A: Mathematical and General 31(11): 2551-2566. Marcon, E., Scotti, I., Herault, B., Rossi, V. and Lang, G. (2014). Generalization of the partitioning of Shannon diversity. PLOS One 9(3): e90289. Marcon, E., Herault, B. (2014). Decomposing Phylodiversity. HAL hal-00946177(version 1).

See Also

bcTsallis

Examples

# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest)
  data(Paracou618)
  # Calculate Simpson alpha entropy
  summary(AlphaEntropy(Paracou618.MC, 2))
  # Compare without correction
  summary(AlphaEntropy(Paracou618.MC, 2, Correction = "None"))
  # Estimate phylogenetic Simpson alpha entropy
  summary(AlphaEntropy(Paracou618.MC, 2, Tree = Paracou618.Taxonomy) -> e)
  plot(e)