Position Dependent and Independent Evolutionary Models Based on   Empirical Amino Acid Substitution Matrices
  Evolutionary models measure the probability of amino acid substitutions occurring over different evolutionary distances. We examine various evolutionary models based on empirically derived amino acid substitution matrices. The models are constructed using the PAM and BLOSUM amino acid substitution matrices. We rescale these matrices by raising them to powers to model substitution patterns that account for different evolutionary distances. We also examine models that account for the dissimilarity of substitution rates along a protein sequence. We compare the models by computing the likelihood of each model across different alignments. We also present a specific example to illustrate the subtle differences in the estimation of evolutionary distance computed using the different models. 
B. Barbiellini, Alexandra Portnova, Anna Chetoukhina, Chia-Hsin Lu and   Matteo Pellegrini