Since the late '60s, various genome evolutionary models have been proposed to predict the evolution of a DNA sequence as the generations pass. Essentially, two main categories of such models can be found in the literature. The first one, based on nucleotides evolution, uses a mutation matrix of size 4x4. It encompasses for instance the well-known models of Jukes and Cantor, Kimura, and Tamura. In the second category, exclusively studied by Bahi and Michel, the evolution of trinucleotides is studied through a matrix of size 64x64. By essence, all of these models relate the evolution of DNA sequences to the computation of the successive powers of a mutation matrix. To make this computation possible, particular forms for the mutation matrix are assumed, which are not compatible with mutation rates that have been recently obtained experimentally on gene $ura3$ of the Yeast \textit{Saccharomyces cerevisiae}. Using this experimental study, authors of this paper have deduced a simple mutation matrice, compute the future evolution of the rate purine/pyrimidine for ura3, investigate the particular behavior of cytosines and thymines compared to purines, and simulate the evolution of each nucleotide.