Rapid maximum likelihood ancestral state reconstruction of continuous characters: A rerooting-free algorithm.

Area of Science:

• Computational Biology
• Evolutionary Biology
• Phylogenetics

Background:

• Ancestral state reconstruction is crucial for understanding evolutionary trajectories of quantitative traits on phylogenies.
• Existing methods for univariate Brownian motion models are inefficient for large phylogenies and lack generalization to complex models.
• Current phylogenetic comparative R packages often use slow tree rerooting and full traversals, hindering large-scale analyses.

Purpose of the Study:

• To develop a computationally efficient method for fast maximum likelihood ancestral state reconstruction of continuous characters.
• To generalize ancestral state reconstruction to complex evolutionary models beyond simple univariate Brownian motion.
• To overcome the computational limitations of existing methods for large phylogenies.

Main Methods:

• Developed a novel algorithm with linear complexity relative to the number of species.
• Implemented the algorithm in R functions 'anc.recon' and 'phylopars' within the 'Rphylopars' package.
• Algorithm designed for maximum likelihood estimation of ancestral states for continuous characters.

Main Results:

• The new algorithm achieves linear complexity, outperforming existing R implementations by orders of magnitude.
• Capable of reconstructing ancestral states on a 1,000,000-species phylogeny in under 2 seconds on a standard laptop.
• Demonstrates generalizability to complex models including multivariate trait evolution and non-Brownian motion.

Conclusions:

• The developed method drastically alleviates computational burdens in phylogenetic comparative studies.
• Enables fast, repeated computations on phylogenies of virtually any size, facilitating tasks like phylogenetic imputation and Bayesian estimation.
• The efficient algorithm supports advanced evolutionary modeling and analysis of large-scale phylogenetic data.