Consistency and convergence rate of phylogenetic inference via regularization

Area of Science:

• Computational Biology
• Evolutionary Biology
• Phylogenetics

Background:

• Reconstructing accurate gene trees is challenging due to limited sequence data.
• Gene trees can deviate from species trees due to various genetic processes.
• Incorporating species tree information can enhance gene tree accuracy.

Purpose of the Study:

• To develop a statistically consistent method for gene tree reconstruction using species tree information.
• To analyze the convergence rates of the proposed method.
• To improve the accuracy of estimating both gene tree structure and edge lengths.

Main Methods:

• Proposed a penalized maximum likelihood estimator for gene tree reconstruction.
• Utilized the squared Billera-Holmes-Vogtmann geodesic distance as a penalty term.
• Derived theoretical guarantees for consistency and convergence rates.

Main Results:

• The penalized maximum likelihood estimator is proven to be statistically consistent.
• Derived convergence rates for simultaneous estimation of gene tree structure and edge lengths.
• The method demonstrates 'adaptive fast convergence,' reconstructing long edges efficiently.

Conclusions:

• The proposed method significantly improves gene tree reconstruction accuracy.
• The approach is robust, not requiring an exact species tree.
• This provides a powerful tool for phylogenetic analysis in computational biology.