CherryML: scalable maximum likelihood estimation of phylogenetic models

Phylogenetic models of molecular evolution are central to numerous biological applications spanning diverse timescales, from hundreds of millions of years involving orthologous proteins to just tens of days relating to single cells within an organism. A fundamental problem in these applications is estimating model parameters, for which maximum likelihood estimation is typically employed. Unfortunately, maximum likelihood estimation is a computationally expensive task, in some cases prohibitively so. To address this challenge, we here introduce CherryML, a broadly applicable method that achieves several orders of magnitude speedup by using a quantized composite likelihood over cherries in the trees. The massive speedup offered by our method should enable researchers to consider more complex and biologically realistic models than previously possible. Here we demonstrate CherryML’s utility by applying it to estimate a general 400 × 400 rate matrix for residue–residue coevolution at contact sites in three-dimensional protein structures; we estimate that using current state-of-the-art methods such as the expectation-maximization algorithm for the same task would take >100,000 times longer.