Mathematical relations between codon bias indexes and their applications

Codon Adaptation Index (CAI), Effective Number of Codons as well as its modifications , can be used to measure gene codon bias. In this article, we prove is more efficient and unbiased than and by revisiting correlations of them with CAI in the level of individual amino acid’s codon bias. Correlations are studied by mathematical expressions rather than statistic methods, because the latter unavoidably depend on the data set used. Additionally, the immediate cause of correlations of with CAI (as well as those of RSCU with CAI) are also described in mathematical language. Perhaps, mathematics provides us a new way to study correlations between biological indexes.