Abstract
Shape parameters, e.g. balance indices, of evolutionary trees have been extensively studied under the Yule model in phylogenetics. Independently, many of the same parameters have also been studied for random binary search trees in computer science, where they measure the running time of algorithms. In fact, under the Yule and binary search tree models, these parameters have the same distribution, resulting in many identical discoveries. In this survey, we explain these connections and introduce some of the tools that have been used in computer science to derive stochastic results for shape parameters.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.