Correcting the bias of empirical frequency parameter estimators in codon models

Area of Science:

• Computational Biology
• Evolutionary Genetics
• Bioinformatics

Background:

• Markov models of codon substitution are key for studying natural selection and amino acid preferences.
• Current methods often estimate equilibrium distributions using observed nucleotide frequencies, a practice rooted in historical convention.

Purpose of the Study:

• To identify bias in standard nucleotide frequency estimators used in codon substitution models.
• To propose and validate a corrected empirical estimator that accounts for stop codon nucleotide composition.

Main Methods:

• Demonstration of bias in popular nucleotide frequency estimators.
• Development of a corrected empirical estimator incorporating stop codon frequencies.
• Simulation studies to compare corrected and standard estimators.
• Evaluation on curated sequence alignments to assess goodness of fit and parameter estimation.

Main Results:

• Standard nucleotide frequency estimators are shown to be biased, negatively impacting goodness of fit and substitution rate estimates.
• The corrected empirical estimator provides more accurate frequency estimates and improves the estimation of other evolutionary model parameters.
• Significant improvements in goodness of fit were observed using the corrected estimators on sequence alignments.

Conclusions:

• The corrected empirical estimator offers a statistically and computationally sound alternative to standard methods.
• There is limited justification for the continued use of traditional, biased nucleotide frequency estimators.
• Maximum likelihood estimation is a viable alternative, though computationally more intensive.