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Im doing a computational biology project in which I simulate evolution under different inheritance rulesets and I am generating phylogenetic trees (beautifully visualised in python with ete3, which I recommend and can be found here: http://etetoolkit.org/download/

My question is: Can someone point me in the right direction to find and test out some simple metrics that can describe these trees in terms of 'branchy-ness' (you can tell i'm not a bioinformatician or phylogeneticist!). I'm looking for kind of mean-field descriptors of the trees. Kind of like degree distribution for networks...

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In Natural Language Processing the terms "bushy" and "straggly" are used to describe tree structure of sentence grammar parses. "Bushy" trees are flatter rather than deeper. "Straggly" trees branch deeply to the right or left. As far as metrics, you could use tree depth as well as straggliness which has be quantified as by Belay et al.:

We calculate the straggliness of a sentence to be the maximum depth of the tree (calculated by counting the maximum stack depth of the parse trees) divided by the number of phrases in the sentence (as determined by the number of lines in the parse tree). In addition, we took the average and standard deviation of the bushiness and straggliness of each sentence and used those as features as well.

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