# A surrogate function for one-dimensional phylogenetic likelihoods

## TL;DR

This paper introduces a four-parameter surrogate function for one-dimensional phylogenetic likelihoods, enabling efficient approximation across various models and improving Bayesian sampling performance.

## Contribution

It presents a novel surrogate function for likelihood approximation that is versatile, easy to fit, and enhances Bayesian sampling in phylogenetics.

## Key findings

- Effective across diverse models and trees
- Improves likelihood computation efficiency
- Enhances Bayesian sampling performance

## Abstract

Phylogenetics has seen an steady increase in substitution model complexity, which requires increasing amounts of computational power to compute likelihoods. This model complexity motivates strategies to approximate the likelihood functions for branch length optimization and Bayesian sampling. In this paper, we develop an approximation to the one-dimensional likelihood function as parametrized by a single branch length. This new method uses a four-parameter surrogate function abstracted from the simplest phylogenetic likelihood function, the binary symmetric model. We show that it offers a surrogate that can be fit over a variety of branch lengths, that it is applicable to a wide variety of models and trees, and that it can be used effectively as a proposal mechanism for Bayesian sampling. The method is implemented as a stand-alone open-source C library for calling from phylogenetics algorithms; it has proven essential for good performance of our online phylogenetic algorithm sts.