The main concern of this paper is the models for genotype diversity.Genotypes are represented as finite sequences (s_1.s_2 s_n).where the entries s_i are drawn from a finite alphabet.The mutation matrix is given in terms of Hamming distances.It is proved that the long time behavior of a class of genotype evolution models is governed by the principal eigenvectors of sum of mutation and fitness matrices.It is proved that the components of principal eigenvectors are symmetric and monotonely decreasing in terms of Hamming distances.