Phylogenetic tree

A phylogenetic tree represents a hypothesis of ancestral relationships among sampled lineages. Branch points indicate inferred common ancestry; a rooted tree specifies direction from ancestors toward descendants. Branch length may encode elapsed time or evolutionary change, but a cladogram need encode neither.

A gene tree follows sampled gene copies, whereas a species tree summarizes lineage relationships at the species level. Distinguishing these objects matters when incomplete lineage sorting or introgression produces different histories for different genomic regions. Computationally, inference over unknown ancestral states can use belief propagation on the tree.

A phylogenetic epoch is an interval between successive branching or merging events during which the number of extant ancestral branches is constant. Its expected duration with $k$ branches is denoted $E_k$.

A representation of the branching history of species lineages. Individual gene trees can differ, so a well-supported tree for one gene is not automatically a complete species history.

A phylogenetic tree describing the ancestry of sampled gene copies or a genomic region. It need not match a species tree, because lineage sorting, duplication or introgression can produce a different history.

The Felsenstein pruning algorithm computes a site likelihood function by sum-product belief propagation from leaves to root. For a finite-state Markov kernel $K$, the subtree likelihood function obeys $L_v(a)={\prod }_{w\text{ child of }v}{\sum }_{b}K(a,b)L_w(b)$, with observed-state indicators at leaves. Summing against the root probability distribution gives the site likelihood function. An outward pass gives edge posterior probabilities and expected transition counts for the expectation-maximization algorithm.