A neutral evolution test derived from a theoretical amino acid substitution model

•A mathematical model that explicitly considers nucleotides, codons, amino acids, and the degeneracy of the standard genetic code is elaborated.•The model is based on the neutral theory of molecular evolution.•A control for neutral evolution is derived and used as a neutrality test, which allows to measure selective pressures such as positive, negative, and neutral selection.•Our model and the neutrality test constitute a baseline to compare the evolution of any protein. A neutral evolution model that explicitly considers codons, amino acids, and the degeneracy of the genetic code is developed. The model is built from nucleotides up to amino acids, and it represents a refinement of the neutral theory of molecular evolution. The model is based on a stochastic process that leads to a stationary probability distribution of amino acids. The latter is used as a neutral test of evolution. We provide some examples for assessing the neutrality test for a small set of protein sequences. The Jukes-Cantor model is generalized to deal with amino acids and it is compared with our neutral model, along with the empirical BLOSUM62 substitution model. The neutral test provides a baseline to which the evolution of any protein can be analyzed, and it clearly helps in discerning putative amino acids with unexpected frequencies that might be under positive or negative selection. Our model and neutral test are as universal as the standard genetic code.