Phylogenetic analysis

Phylogenetic analysis uses observations of phylogenetic characters to infer or test hypotheses about relationships produced by evolution. Its inputs, character definitions and inference rule matter: a phylogenetic tree is a proposed history supported to some extent by the data and model, rather than a direct photograph of ancestry.

For an illustrative four-organism example, suppose a binary phylogenetic character is 1 in A and B and 0 in C and D. On a phylogenetic tree separating A and B from C and D, one change explains the pattern; on a tree grouping A with C and B with D, at least two changes are needed. Maximum parsimony favors the first explanation for this character. Additional characters can conflict, and repeated changes can obscure ancestry.

An approach based on maximum likelihood estimation instead compares probabilities. With observed data $D$, tree $T$ and model parameters $\theta$, the likelihood function isA nucleotide substitution model assigns probabilities to sequence changes; unknown ancestral states are summed over using the phylogenetic pruning algorithm. Joseph Felsenstein's 1981 paper developed this approach for DNA sequences and discussed testing equal-rate hypotheses. Model choice and uncertainty therefore belong to the analysis alongside the displayed phylogenetic tree.^[ref]