Evolution is often described as 'random', but this need not mean that all evolutionary changes are equally probable. Some mutations between bases (and hence acids) are, in fact, far more probable than others.
Simple Markov models, representing the frequency with which each type of mutation can occur, have been widely used for reconstructing evolutionary trees and searching for related sequences. However, these models typically assume that the pattern of substitution (i.e. the elements in the transition matrix) are constant for all species, whereas differences in the frequencies of particular 'symbols' in genes and proteins demonstrate that the matrix varies.
In this talk, I outline some of the common models that have been widely used for sequence evolution, describing their plausiblity in terms of biological mechanisms. I also discuss sources of sequence and mutation data that, excitingly, may now be sufficiently complete to test these models against each other and to reveal the evolutionary lineages in which the pattern of mutation has changed.