Optimization Over a Class of Tree Shape Statistics

Tree shape statistics quantify some aspect of the shape of a phylogenetic tree. They are commonly used to compare reconstructed trees to evolutionary models and to find evidence of tree reconstruction bias. Historically, to find a useful tree shape statistic, formulas have been invented by hand and then evaluated for utility. This paper presents the first method which is capable of optimizing over a class of tree shape statistics, called binary recursive tree shape statistics (BRTSS). After defining the BRTSS class, a set of algebraic expressions is defined which can be used in the recursions. The set of tree shape statistics definable using these expressions in the BRTSS is very general and includes many of the statistics with which phylogenetic researchers are already familiar. We then present a practical genetic algorithm which is capable of performing optimization over BRTSS given any objective function. The chapter concludes with a successful application of the methods to find a new statistic which indicates a significant difference between two distributions on trees which were previously postulated to have similar properties.