Methods for reconstruction of phylogenies
Maximum parsimony: Given a tree, count the number of character changes that must have occurred during evolution if the tree is correct. The most parsimonious tree is the one that postulates the fewest such changes among all possible trees.
Maximum likelihood: Given a tree and a model of molecular evolution, compute the probability that the sequences actually observed in the extant species have evolved. The maximum likelihood tree is the one for which this probability is largest among all possible trees.