Different versions of the Dayhoff rate matrix

Area of Science:

• Computational Biology
• Evolutionary Biology
• Bioinformatics

Background:

• Phylogenetic inference commonly utilizes Markov models of sequence evolution.
• These models are often represented by instantaneous rate matrices (Q), but some, like the PAM model, were originally published as time-dependent probability matrices (P(t)).

Purpose of the Study:

• To address limitations in existing methods for deriving Q from P(t), specifically issues with large time values (t) affecting convergence.
• To introduce and validate simpler, more accurate methods for Q matrix derivation.

Main Methods:

• Developed two novel methods for deriving the Q matrix directly from P(t) information, avoiding eigen-decomposition and approximations.
• Analyzed the convergence of Q estimates with commonly used time values (t).
• Compared existing and new implementations of the Dayhoff model in current software.

Main Results:

• Demonstrated that commonly used time values (t) are often too large, leading to inaccurate Q matrix estimates.
• The new methods provide accurate Q matrix derivation without requiring approximations or eigen-decomposition.
• Identified variations in Dayhoff model implementations across software.

Conclusions:

• Existing methods for deriving Q from P(t) can be unreliable due to large time parameters.
• The newly proposed methods offer a simpler and more accurate standard for deriving Q matrices.
• Recommends adoption of a new standard method to ensure consistency in phylogenetic analyses using the Dayhoff model.