Character Based Methods

We will discuss the following problem:
 

The process of solving this problem is called inferring the phylogeny. The input is usually given as an $n \times m$ matrix M, where M_i,j represents the value of the jth character of the ith species. The state (value), of each character is taken from a known set A_j.

The input may also include other relevant parameters - e.g., the distribution of changes (mutations) in each character, weights representing relative importance of characters, etc. The goal will be to maximize some score over the possible phylogenetic trees and produce the best one.

We will make the following assumptions in attempting to infer phylogenies:

• Characters are mutually independent - that is, change in one character has no effect on the distribution of another character.
• After two species diverge in the tree, they continue to evolve independently.

None of these assumptions is necessarily (or even probably) correct, but they make our life much easier, simplifying the discussion considerably.