Phylogenetic tree

A phylogenetic tree, also called a phylogeny, is a diagram that maps the evolutionary history of a group of species or other taxa over a given period. It uses a branching structure to show how these entities are related, based on shared physical traits or genetic data. In evolutionary biology, all life on Earth is thought to belong to one vast phylogenetic tree, reflecting a single common ancestor. The study of these trees is called phylogenetics, and the main challenge is finding the tree that best represents the evolutionary ancestry among a set of species. Computational phylogenetics, or phylogeny inference, focuses on the algorithms used to search for this optimal tree.

Phylogenetic trees can be either rooted or unrooted. In a rooted tree, each internal node (a taxonomic unit) represents the inferred most recent common ancestor of its descendants, and the lengths of the branches may indicate time. Internal nodes are often called hypothetical taxonomic units because they cannot be directly observed. Rooted trees are useful in fields like bioinformatics, systematics, and phylogenetics. Unrooted trees, by contrast, only show how the leaf nodes are related, without needing to know or infer a common ancestor.

The concept of a tree of life has ancient roots, evolving from earlier ideas of a ladder-like progression from lower to higher life forms, such as the Great Chain of Being. Early branching diagrams include a "paleontological chart" in Edward Hitchcock's 1840 book *Elementary Geology*. Charles Darwin included a diagrammatic evolutionary tree in his 1859 *On the Origin of Species*, and biologists still use such diagrams because they effectively convey how speciation occurs through the splitting of lineages. The word "phylogenetic" comes from the ancient Greek *phûlon* (race, lineage) and *génesis* (origin, source).

A rooted phylogenetic tree is a directed tree with a single root node, which represents the imputed most recent common ancestor of all leaf entities. The root has no parent but is the parent of all other nodes; it has a degree of 2, while other internal nodes have a minimum degree of 3. The most common way to root a tree is by using an uncontroversial outgroup—close enough for inference but distant enough to be a clear outgroup. Other methods include midpoint rooting or using a non-stationary substitution model.

Unrooted trees show leaf-node relatedness without assumptions about ancestry. They can be turned into rooted trees by inserting a root, which requires identifying ancestry—usually by including an outgroup in the data or by using assumptions about evolutionary rates, such as the molecular clock hypothesis.

Both rooted and unrooted trees can be bifurcating or multifurcating. A rooted bifurcating tree has exactly two descendants from each interior node (forming a binary tree), while an unrooted bifurcating tree has exactly three neighbors at each internal node. A rooted multifurcating tree can have more than two children at some nodes, and an unrooted multifurcating tree can have more than three neighbors.

Trees can also be labeled or unlabeled. A labeled tree has specific values assigned to its leaves, while an unlabeled tree (or tree shape) defines only a topology. Some sequence-based trees, like Phylotree, label internal nodes with inferred ancestral haplotypes.

The number of possible trees for a given number of leaf nodes depends on the tree type. There are always more labeled than unlabeled trees, more multifurcating than bifurcating trees, and more rooted than unrooted trees. The last distinction is biologically significant because an unrooted tree can have the root placed in many positions. For bifurcating labeled trees, the total number of rooted trees for \(n \geq 2\) is given by \((2n-3)!! = \frac{(2n-3)!}{2^{n-2}(n-2)!}\).