A problem in multivariate analysis of codon usage data and a possible solution

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Abstract
Multivariate analyses are often used to identify major trends of variation in synonymous codon usage among genes. These analyses need to be performed on properly normalized codon usage data to avoid biases masking this synonymous variation, i.e., gene length, amino acid usage, and codon degeneracy; however, previous studies have failed to do so. In this paper, we demonstrate that the use of alternative normalized data (called 'relative adaptiveness' in the literature) can avoid all these biases and furthermore, can identify more trends of variation among genes, including GC-ending codon usage, GT-ending codon usage, and gene expression level.