Phylogenetic Trees and Multiple Alignments

Evolution

A tree is an undirected acyclic connected graph. A leaf is an exterior node with degree one. Interior nodes have a degree greater than one.

A phylogenetic tree is a tree, where the leaves are labelled 1..n (with objects, OTUs, species, sequences). One speaks of a tree over n objects. Usually the issue is a binary tree, i.e. every inner node has degree three. Sometimes there are weights on the edges which then represent a distance. A particular edge or node can be highlighted to be the root, the tree is rooted (hierarchy, dendrogram).

Path metric of a weighted tree: if there are positive weights on the edges of a tree over n objects given, the path metric is the metric that results from adding up the weights along a path between to leaves.

When one wants to stress that a tree has no weights attached to the edges one frequently speaks of the topology of the tree.

Regarding a weighted phylogenetic tree, whereat the weights of the edges represent an estimate of the evolutionary distance between the nodes, relies on Darwin's theory of Evolution:

Starting with a set of n known present-day objects a phylogenetic tree may be constructed by first assigning each object a leaf of the tree and then assigning ancestral and unknown objects to the interior nodes.

In the 1960ies Zuckerkandl and Pauling assigned protein sequences to the leaves of a phylogenetic tree being a trace of molecular evolution:

Evolutionary time is reflected in the distances between the leaves or sequences respectively. The time has passed during evolution of different species or sequences starting from a common ancestor. Thus, assuming that the studied present-day sequences have evolved from a common ancestor at equal rate, the corresponding phylogenetic tree would be ultrametric, which implies the existance of a root, and the same length of all paths from the root to the leaves.