Impact of bias discrepancy and amino acid usage on estimates of the effective number of codons used in a gene, and a test for selection on codon usage

The effective number of codons (Nc) used in a gene is one of the most commonly used measures of synonymous codon usage bias, owing much of its popularity to the fact that it is species independent and that simulation studies have shown that it is less dependent of gene length than other measures. In this paper I provide a clear and practically meaningful definition of bias discrepancy (BD; when the degree of codon bias varies within a degeneracy class). Moreover I evaluate the impact of BD and amino acid usage on estimates of Nc. It is shown that both factors have a significant effect on accuracy and precision. Both amino acid usage and BD influence accuracy considerably, especially in short genes. Finally, I demonstrate how the definition of bias discrepancy can be applied to investigate if codon usage is influenced by selection and I discuss this test in relation to the incongruous literature that exists for Buchnera sp. APS and Borrelia burgdorferi.