LvD: A New Algorithm for Computing the Likelihood of a Phylogeny

TL;DR

The paper introduces LvD, a novel algorithm for phylogenetic likelihood computation that significantly improves speed by enabling updates in logarithmic time, benefiting large-scale and parallel phylogenetic analyses.

Contribution

LvD offers a new decomposition-based algorithm for likelihood calculation in phylogenetics, achieving worst-case logarithmic update times and enabling efficient parallel computation.

Findings

Achieves $O(\log n)$ likelihood update time for $n$ taxa.

Provides $O(\log n)$ parallel likelihood computation per site.

Demonstrates practical speed-up on simulated and empirical datasets.

Abstract

There are few, if any, algorithms in statistical phylogenetics which are used more heavily than Felsenstein's 1973 pruning method for computing the likelihood of a tree. We present LvD, (Likelihood via Decomposition), an alternative to Felsenstein's algorithm based on a different decomposition of the underlying phylogeny. It works for all standard nucleotide models. The new algorithm allows updates of the likelihood calculation in worst case $O(\log n)$ time with $n$ taxa, as opposed to worst case $O(n)$ time for existing methods. In practice this leads to appreciable improvements in likelihood calculations, the extent of speed-up depending on how balanced or unbalanced the trees are. We explore implications for parallel computing, and show that the approach allows likelihoods to be computed in $O(\log n)$ parallel time per site, compared to (worst case) $O(n)$ time. We implemented and applied the algorithm to large numbers of simulated and empirical data sets and showed that these theoretical advances lead to a significant practical speed-up, although the extent of the improvement depends on how balanced the phylogenies already are.