maxlik.betasplit {apTreeshape}R Documentation

Maximum likelihood of beta in the Beta-splitting model

Description

The function finds the beta value that maximizes the likelihood in the Beta-splitting model. Beta=0 corresponds to Yule trees, Beta<0 corresponds to trees more unbalanced than Yule trees and Beta>0 corresponds to trees more balanced than Yule trees. Confidence intervals may also be provided.

Usage

maxlik.betasplit(phylo, up = 10, remove.outgroup = FALSE, confidence.interval = "none", prob.conf.inter = 0.95, size.bootstrap = 100)

Arguments

phylo An object of class '"treeshape"' or '"phylo"' on which the likelihood is computed.
up numeric. The Beta value that maximizes the likelihood is searched between -2 and up
remove.outgroup logical. Should one or two outgroups be removed before computing the likelihood
confidence.interval The method to be used for computing confidence intervals. See *Details*.
prob.conf.inter numeric. Probability associated with the confidence interval
size.bootstrap number. Number of bootsrap replicates

Details

The beta-splitting model has been introduced by Aldous to simulate trees with different tree balance.

Beta=0 corresponds to Yule trees.

Beta<0 corresponds to trees more unbalanced than Yule trees, Beta=-3/2 corresponds to the PDA model.

Beta>0 corresponds to trees more balanced than Yule trees.

By default, confidence.interval='"none"' and no confidence interval is computed.

When confidence.interval=bootstrap_param, parametric bootstraping is performed to compute a confidence interval. Shall be used when the number of tips is small (<50).

When confidence.interval=chi_square, a chi-square approximatiom is used for computing a confidence interval. Shall be used when the number of tips is large (>50).

Value

max_lik The Beta value that maximizes the likelihood
conf_interval A confidence interval for max_lik

Author(s)

michael.blum@imag.fr

References

Aldous, D. J. (1996) Probability Distributions on Cladograms pp.1-18 of Random Discrete Structures eds D. Aldous and R. Pemantle, IMA Volumes Math. Appl. 76.

Aldous, D. J. (2001) Stochastic Models and Descriptive Statistics for Phylogenetic Trees, from Yule to Today. Statistical Science, *16*, 23 - 24.

Blum, M.G.B. and Francois, O. Which random processes describe the Tree of Life? A large-scale study of phylogenetic tree imbalance. Systematic Biology *55*, 685-691, 2006.

See Also

sackin,sackin.test,colless,link{colless.test}

Examples

library(ape)
library(Bhat)
tree.pda<-rpda(50)
maxlik.betasplit(tree.pda,confidence.interval="none")
maxlik.betasplit(tree.pda,confidence.interval="chi_square")
maxlik.betasplit(tree.pda,confidence.interval="bootstrap_param")

[Package apTreeshape version 1.4-1 Index]