Nonbifurcating Phylogenetic Tree Inference via the Adaptive LASSO

Abstract

Phylogenetic tree inference using deep DNA sequencing is reshaping our understanding of rapidly evolving systems, such as the within-host battle between viruses and the immune system. Densely sampled phylogenetic trees can contain special features, including sampled ancestors in which we sequence a genotype along with its direct descendants, and polytomies in which multiple descendants arise simultaneously. These features are apparent after identifying zero-length branches in the tree. However, current maximum-likelihood based approaches are not capable of revealing such zero-length branches. In this article, we find these zero-length branches by introducing adaptive-LASSO-type regularization estimators for the branch lengths of phylogenetic trees, deriving their properties, and showing regularization to be a practically useful approach for phylogenetics. Supplementary materials for this article are available online.

Keywords:

• Adaptive LASSO
• Consistency
• ${\mathcal{l}}_1$ regularization
• Phylogenetics
• Model selection
• Sparsity

Acknowledgments

The authors would like to thank Vladimir Minin and Noah Simon for helpful discussions, and Sidney Bell for helping with the Dengue sequence data.

Additional information

Funding

This work supported by National Institutes of Health grants R01-GM113246, R01-AI120961, U19-AI117891, and U54-GM111274 as well as National Science Foundation grant CISE-1564137. The research of Frederick Matsen was supported in part by a Faculty Scholar grant from the Howard Hughes Medical Institute and the Simons Foundation.