apTreeshape (version 1.5-0.1)

maxlik.betasplit: 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 can also be provided.

Usage

maxlik.betasplit(phylo, up = 10, remove.outgroup = FALSE,
confidence.interval = "none", conf.level = 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*.

conf.level

numeric. Probability associated with the confidence interval

size.bootstrap

number. Number of bootsrap replicates

Value

max_lik

The Beta value that maximizes the likelihood

conf_interval

A confidence interval for max_lik

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", a confidence interval is found with a resampling technique. Shall be used when the number of tips is small (<50).

When confidence.interval="profile", a confidence interval is found with a profile likelihood technique. Shall be used when the number of tips is large (>50).

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, colless.test

Examples

# NOT RUN {
tree.pda<-rtreeshape(n=1, tip.number=50, model="pda")[[1]]
maxlik.betasplit(tree.pda,confidence.interval="none")
##bootstrap example is commented because it is too slow to run
##maxlik.betasplit(tree.pda,confidence.interval="bootstrap")
maxlik.betasplit(tree.pda,confidence.interval="profile")
# }