= Phylogenetic analysis
\b[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> is
$$
L(T,\theta)=\Pr(D\mid T,\theta).
$$
A <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>.<Evolutionary trees from DNA sequences: a maximum likelihood approach by Joseph Felsenstein>[Journal of Molecular Evolution 17 (1981), pp. 368–376: likelihood calculation and tests of evolutionary-rate hypotheses.]{ref}
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