Calculates the phylogenetic diversity of order $$q$$ of a probability vector.

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

## Arguments

Ps

A probability vector, summing to 1.

q

A number: the order of diversity. Default is 1.

PhyloTree

An object of class hclust, phylo, 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 diversity is calculated following Chao et al. (2010). The result is identical to the total diversity calculated by PhyloDiversity but it is much faster. A single value is returned instead of a PhyloDiversity object, and no bias correction is available.

The Normalize arguments allows calculating either $$^{q}\bar{D}(T)$$ (if TRUE) or $$^{q}PD(T)$$ if FALSE.

Diversity can be calculated for non ultrametric trees following Chao et al. (2010) even though the meaning of the result is not so clear (Leinster and Cobold, 2011).

## Value

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

## References

Chao, A., Chiu, C.-H. and Jost, L. (2010). Phylogenetic diversity measures based on Hill numbers. Philosophical Transactions of the Royal Society B 365(1558): 3599-609.

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 <- Paracou618.MC$Ps # Calculate the phylogenetic Simpson diversity of the plot (ChaoPD(Paracou618.MC$Ps, 2, Paracou618.Taxonomy, Normalize=TRUE))
#>     None
#> 24.61698

# Calculate it using PhyloDiversity
# (more powerful but much slower if the tree has many periods)
PhyloDiversity(Paracou618.MC\$Ps, 2, Paracou618.Taxonomy, Normalize=TRUE) -> phyD
summary(phyD)
#> alpha or gamma phylogenetic or functional diversity of order 2 of distribution
#> -
#>  with correction: None
#> Phylogenetic or functional diversity was calculated according to the tree
#> Paracou618.Taxonomy
#>
#> Diversity is normalized
#>
#> Diversity equals: 24.61698