entropart (version 1.4-4)

Originality.Species: Originality of species

Description

Calculates the originality of species according to the order of diversity.

Usage

Originality.Species(Tree, q = 2, CheckArguments = TRUE)

Arguments

Tree

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

q

A number: the order of diversity. Default is 2 for Rao quadratic entropy.

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 named vector of frequencies.

Details

The originality of species is their frequency resulting in the maximum value of generalized entropy of order $q$ (not that of similarity-based diversity) considering an ultrametric tree. Originality was introduced by Pavoine et al. (2005) for Rao quadratic entropy ($q=2$). It can be calculated exactly by originality. For other orders of diversity, numeric optimization is required. Leinster (2009) showed that the distribution maximizing Dqz does not depend of $q$. It can be calculated exactly using originality after transforming the similarity matrix into a distance matrix, supposing the distance matrix is ultrametric.

References

Leinster, T. (2009) A maximum entropy theorem with applications to the measurement of biodiversity. ArXiv 0910.0906: 1-26. Pavoine, S., Ollier, S. and Dufour, A.B. (2005). Is the originality of a species measurable? Ecology Letters 8: 579-586.

See Also

originality

Examples

data(Paracou618)
  # Calculate Originality of a species according to a simple functional tree, q=1
  (Frequencies <- Originality.Species(EightSpTree, 1))
  # Plot the result
  if (require(ade4, quietly = TRUE)) {
    dotchart.phylog(EightSpTree, Frequencies)
  }