aka phylogeny

Inducing phylogenetic tree

A Tree (combinatorial structure)

Many algorithms don't find the root of the tree, but finding the root is important to find the time direction in the tree.

Phylogenetic trees are most often binary (aka bifurcating).

Edges can be labelled with time duration or amount of evolution. If the amount of evolution is proportional to time duration, we have a Molecular clock.

Enumerating trees..

Coelescent topologies. The time-ranking in time matters.

Combinatorics, Analytic combinatorics...

Principles for inference

Minimum parsimony

Minimum number of changes in letters in the sequence.

Maximum likelihood

Using some Probabilistic model