Different Versions of the Dayhoff Rate Matrix

• In the PAM matrix articles, protein evolution models are only give in the form of probability matrices relating to specific levels of sequence divergence (our matrices), but many phylogenetic inference methods need to compute this probability matrix for any real evolutionary time as an instantaneous rate matrix (IRM) (pg 193)

• Markov model asserts one protein sequence is derived from another during evolution by a series of independent substitutions of one amino acid in the ancestral sequence to another in its descendant.
• Assumption: Independence of evolution at different sites (pg 194)
• Differences can underestimate the actual numbers of changes because multiple changes at a single site are observed as a single replacement; probability of multiple hits is reduced when closely related sequences are used, but that can be an inefficient use of data because divergent sequence pairs are discarded (pg 194)
• Assumption: n_ij = n_ji because the direction of evolutionary change cannot be determined from the observation of two contemporary sequences (pg 194)