Fast likelihood calculation for multivariate Gaussian phylogenetic models with shifts.

Area of Science:

• Evolutionary Biology
• Phylogenetics
• Computational Biology

Background:

• Phylogenetic comparative methods (PCMs) are crucial for studying quantitative trait evolution across diverse organisms.
• Traditional Gaussian phylogenetic models (e.g., Brownian motion, Ornstein-Uhlenbeck) face computational challenges with large phylogenetic trees and struggle with evolutionary heterogeneity.
• Existing methods often restrict evolutionary shifts to specific parameters due to slow likelihood calculations.

Purpose of the Study:

• To introduce and explore the G_LInv sub-family of Gaussian phylogenetic models.
• To develop an efficient, linear-time algorithm for calculating likelihoods within the G_LInv family, suitable for large phylogenetic trees.
• To enable the modeling of evolutionary heterogeneity through shifts in model parameters or types within the G_LInv framework.

Main Methods:

• Exploration of the G_LInv family, characterized by linear expectation and invariant variance.
• Development of an efficient algorithm for likelihood calculation, linear in the number of nodes.
• Implementation of the algorithm in the R-package PCMBase, supporting missing data and various tree types (polytomies, non-ultrametric).

Main Results:

• The G_LInv family encompasses most commonly used Gaussian phylogenetic models.
• The developed algorithm provides a significant computational speed-up for likelihood calculations on large trees.
• The method effectively accommodates evolutionary shifts in parameters and model types across different parts of the phylogenetic tree.

Conclusions:

• The G_LInv models and the associated efficient likelihood calculation algorithm address key limitations of current PCMs for large datasets.
• PCMBase facilitates the integration of these advanced models into maximum likelihood and Bayesian inference frameworks.
• This work enables more robust and nuanced studies of trait evolution under heterogeneous evolutionary pressures.