This Markov chain needs to be estimated from aligned sequences. Inhomogeneity in the degree of divergence inside the alignment data is the major obstacle to this goal. We briefly review all three procedure and evaluate their performance by means of extensive simulations. The focus is on the capability of the methods to recover accurately the Markov chain underlying the simulations. The maximum likelihood method as well as the resolvent method outperform Dayhoff's method clearly.
Maximum likelihood is the method of choice in the case of small sets of input data.
The resolvent method is computationally much less demanding while it performs only slightly worse than the maximum likelihood. Therefor it is perfectly appropriate for large scale applications.