Maximum likelihood is a method of phylogenetic analysis that has become widely-used in molecular phylogenetics. In contrast to maximum parsimony, which finds the simplest tree to fit the data set, maximum likelihood finds the tree that is most likely to have given rise to data set on hand. While parsimony treats all changes as more or less equal, likelihood constructs an a priori model of the relative probabilities of the mutations involved. Because such models are usually not available or calculable for morphological characters, likelihood is not widely used in morphological phylogenetics. Maximum likelihood differs from Bayesian analysis in that the model is calculated a priori rather than a posteriori.
The model used in the analysis may either be derived from general principles about the mutations involved (for instance, assuming that transitions are about three times more likely than transversions), which runs the risk that the taxa being analysed may violate the usual rates, or may be calculated from the character set on hand, which is dependent on the data set accurately reflecting the correct rates.
While maximum likelihood does generally give more reliable results than strict parsimony (assuming that the correct model has been adopted), it has the potential disadvantage that it requires a lot more calculation than parsimony and so can take much longer. As a result, even if the primary analysis is conducted using likelihood, tests of support such as bootstrapping may be done using parsimony in order to keep time required within feasible limits. Also, likelihood is less conducive than parsimony for mapping individual character changes onto the resulting tree - as likelihood is dependent on the tree as a whole rather than individual changes, there may not be a simple one-to-one relationship with each mutation mapping to a single branch.