(This article was first published on Recology, and kindly contributed to R-bloggers)
I couldn't find any functions to calculate number of polytomies, and related metrics.
Here's a simple function that gives four metrics on a phylo tree object:
Here's output from the gist above:
`
dat $trsize [1] 15
$numpolys [1] 1
$numpolysbytrsize [1] 0.06666667
$proptipsdescpoly [1] 0.2
$propnodesdich [1] 12 `
To leave a comment for the author, please follow the link and comment on his blog: Recology.
R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

Zero Inflated Models and Generalized Linear Mixed Models with R.
Zuur, Saveliev, Ieno (2012).