Phylogenetics II

Maximum likelihood and tree topologies

Public Health Modeling Unit

2025-08-12

Barney Isaksen Potter

Series overview

  1. Trees, tree likelihoods, and models of evolution
  2. Rate heterogeneity and maximum likelihood
  3. Bayesian phylogenetics, Markov chain Monte Carlo, and summary trees
  4. Phylogeography and Kingman's coalescent

We will move rate heterogeneity to the final session

Textbooks

Snow
Forest
Mountains

Exercise 1:

solution

Kind of sucks, doesn't it?

Felsenstein's pruning algorithm

Felsenstein's pruning algorithm

Felsenstein's pruning algorithm

Felsenstein's pruning algorithm

Felsenstein's pruning algorithm

Felsenstein's pruning algorithm

Now we will pivot into inferring phylogenies

From now on we will be using log-likelihoods instead of regular likelihoods

  • Extremely small numbers can cause numerical errors because floating point arithmetic treats them as zeroes
  • Adding a bunch of negative numbers is far easier than multiplying a bunch of extremely small numbers

Recall: Substitution models

HKY: Hasegawa, Kishino, and Yano (1985)

Maximum likelihood (evol. rate)

Maximum likelihood (evol. rate)

Maximum likelihood (evol. rate)

Maximum likelihood (evol. rate)

Maximum likelihood (evol. rate)

Maximum likelihood (evol. rate)

Maximum likelihood (evol. rate)

What might we try to modify to get a more likely tree?

  • Evolutionary rate ($\mu$)
  • Substitution model parameters (e.g. $\kappa$)
  • Equlibrium base frequencies ($\pi$)
  • Branch lengths
  • Tree topology

Tree topologies

Tree topologies

Tree topologies

Tree topologies

Tree topologies

Tree topologies

How can we modify trees?

Prune and regraft

Prune and regraft

Prune and regraft

Prune and regraft

Exercise 2

On a piece of paper, draw all rooted, bifurcating tree topologies with five taxa.

Bonus: do it for six taxa

Check out phyloseminar!

FIN