  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.
