Phylogenetic Entropy of a Community

Calculates the phylogenetic diversity of order \(q\) of a probability vector.

Usage

AllenH(Ps, q = 1, PhyloTree, Normalize = TRUE, Prune = FALSE, CheckArguments = TRUE)

Arguments

Ps: A probability vector, summing to 1.
q: A number: the order of entropy. Default is 1.
PhyloTree: An object of class hclust, "phylo" (see read.tree), phylog or PPtree. The tree is not necessarily ultrametric.
Normalize: If TRUE (default), diversity is not affected by the height of the tree.
If FALSE, it is proportional to the height of the tree.
Prune: What to do when somes species are in the tree but not in Ps?
If TRUE, the tree is pruned to keep species of Ps only. The height of the tree may be changed if a pruned branch is related to the root.
If FALSE (default), species with probability 0 are added in Ps.
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 phylogenetic entropy is calculated following Allen et al. (2009) for order \(q=1\) and Leinster and Cobold (2011) for other orders.The result is identical to the total entropy calculated by PhyloEntropy but it is much faster. A single value is returned instead of a PhyloEntropy object, and no bias correction is available.

The Normalize argument allows normalizing entropy by the height of the tree, similarly to ChaoPD.

Diversity can be calculated for non ultrametric trees following Leinster and Cobold (2011) even though the meaning of the result is not so clear.

Value

A named number equal the entropy of the community. The name is "None" to recall that no bias correction is available.

References

Allen, B., Kon, M. and Bar-Yam, Y. (2009). A New Phylogenetic Diversity Measure Generalizing the Shannon Index and Its Application to Phyllostomid Bats. American Naturalist 174(2): 236-243.

Leinster, T. and Cobbold, C. (2011). Measuring diversity: the importance of species similarity. Ecology 93(3): 477-489.

Examples

# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest
#      and their taxonomy)
data(Paracou618)
# Ps is the vector of probabilities
Ps <- as.ProbaVector(Paracou618.MC$Ns)

# Calculate the phylogenetic Shannon diversity of the plot
AllenH(Ps, 1, Paracou618.Taxonomy, Normalize=TRUE)
#>     None 
#> 3.919941 

# Calculate it using PhyloEntropy: more powerful but much slower is the tree has many periods
PhyloEntropy(Ps, 1, Paracou618.Taxonomy, Normalize=TRUE) -> phyE
summary(phyE)
#> alpha or gamma phylogenetic or functional entropy of order 1 of distribution -
#>  with correction: None
#> Phylogenetic or functional entropy was calculated according to the tree 
#> Paracou618.Taxonomy 
#> 
#> Entropy is normalized
#> 
#> Entropy equals: 3.919941