genAldousBetaTree {poweRbal}

Generation of rooted binary trees under Aldous' beta splitting model

Description

genAldousBetaTree - Generates a rooted binary tree in phylo format with the given number of n leaves under the Aldous beta model. The Aldous beta model is not a rate-based incremental evolutionary (tree) construction and thus cannot generate edge lengths, only a topology. Instead, the Aldous beta model works as follows: The idea is to start with the root and the set of its descendant leaves, i.e., all n leaves. Then, this set is partitioned into two subsets according to a density function dependent on the parameter beta. The two resulting subsets contain the leaves of the two maximal pending subtrees of the root, respectively. The same procedure is then applied to the root's children and their respective subsets, and so forth.
Due to the restrictions of the phylo or multiphylo format the number of leaves must be at least 2 since there must be at least one edge.

Usage

genAldousBetaTree(n, BETA)

Arguments

n

Integer value that specifies the desired number of leaves, i.e., vertices with in-degree 1 and out-degree 0.

BETA

Numeric value >=-2 which specifies how the leaf sets are partitioned. For certain choices of BETA the Aldous beta model coincides with known models:

• BETA = 0: Yule model
  

• BETA = -3/2: PDA model (all phylogenies equally probable)
  

• BETA = -2: Caterpillar with n leaves

Value

genAldousBetaTree A single tree of class phylo is returned.

Author(s)

Sophie Kersting

References

• D. Aldous. Probability Distributions on Cladograms. In Random Discrete Structures, pages 1–18. Springer New York, 1996.

Examples

genAldousBetaTree(n = 5, BETA = 1)