Testing Patterns of Nucleotide Substitution Rates at Multiple Genes

Abstract

Studying patterns of nucleotide substitution rates at multiple loci can help provide clues to the evolution and function of genes. The computational drawback of the maximum likelihood version of relative ratio tests becomes a concern when a large number of pairwise comparisons are performed among multiple genes. We propose a new version of relative ratio test, including four procedures, based on the use of pairwise sequence distances. The first is based on ANOVA two-way model and allows covariances between branch lengths. The second method applies generalized estimation equations (GEEs) to Poisson regression in a log-linear model. The third one is a nonparametric approach based on bootstrap percentile confidence intervals. The fourth method is based on weighted least squares estimation with covariances.

Simulation studies have been conducted to compare Type I errors and powers between the likelihood version of test and the first three proposed methods. The formula have been derived for the last method as well as the numerical steps. The ANOVA-based method is the least computationally expensive and it has desirable Type I errors in most cases as well as good powers. The bootstrap-based method is the slowest among the four methods, but with smallest Type I errors and powers similar to the ANOVA-based method. The Likelihood-based method is the second slowest and has more desirable Type I errors than those of the ANOVA-based method, but has less powers than the ANOVA-based method. The GEE-based method is suitable only for very long genes, but has good statistical properties.

The ANOVA-based method is applied to mtDNA sequences from a broad range of animal mitochondrial genomes. The results indicate that it is uncommon that branch lengths are conserved well among animal mitochondrial genes.