Chapter 17 What is Maximum Likelihood?

We are finally ready to try estimating trees using a true phylogenetic method. Maximum likelihood is a tree-searching method that attempts to find a tree that maximizes the likelihood of observing the data. Put another way, we want a tree that makes the data we see likely. If you’ve ever done any sort of statistical test (like a linear regression or a chi-square test), you’ve been doing maximum likelihood tests.

Essentially, for each possible DNA mutation you’ve seen in the data, you are finding a tree that recreates the most likely pattern of mutation that you see in your data. This includes limiting the amount of homoplasy or mutational reversals.

Maximum likelihood searches are tree-based searches (like parsimony). You supply a starting tree, and the algorithm estimates the likelihood of that tree given the data. (The likelihood value is often very small, so we transform it using to the loglikelihood for ease.) Then the algorithm permutates (or changes) the tree and calculates the likelihood of the new tree. If the new tree has a better likelihood, then it is kept and another permutation is tried. If the likelihood of the new tree is worse than the original tree, then the new tree is discarded and the algorithm tries a different permutation on the old tree.

The advent of the maximum likelihood method (published by Joe Felsenstein in 1981) revolutionized the field of evolutionary biology and really kickstarted the creation of phylogenetics as it exists today.