Random Tree-Puzzle Leads to the Yule-Harding Distribution

Approaches to reconstruct phylogenies abound and are widely used in the study of molecular evolution. Partially through extensive simulations, we are beginning to understand the potential pitfalls as well as the advantages of different methods. However, little work has been done on possible biases introduced by the methods if the input data are random and do not carry any phylogenetic signal. Although Tree-Puzzle (Strimmer K, von Haeseler A. 1996. Quartet puzzling: a quartet maximum-likelihood method for reconstructing tree topologies. Mol Biol Evol. 13:964-969; Schmidt HA, Strimmer K, Vingron M, von Haeseler A. 2002. Tree-Puzzle: maximum likelihood phylogenetic analysis using quartets and parallel computing. Bioinformatics 18:502-504) has become common in phylogenetics, the resulting distribution of labeled unrooted bifurcating trees when data do not carry any phylogenetic signal has not been investigated. Our note shows that the distribution converges to the well-known Yule-Harding distribution. However, the bias of the Yule-Harding distribution will be diminished by a tiny amount of phylogenetic information.