What is phylogenetics?

“data”: sequence alignment

Sequence alignment is hard!

Sometimes it’s more or less impossible

Phylogenetic approach is best

Muscle vs PRANK

BAli-Phy

Co-estimate tree & alignment using Bayesian methods

Multiple sequence alignment: summary

• Use PRANK, perhaps through Wasabi
• If you need a faster algorithm and are happy with a less good result, try Muscle
• If you really care about alignments (and trees) use BAli-Phy.

Types of phylogenetic inference methods

• Distance-based
• Parsimony
• Likelihood-based
  • Maximum likelihood
  • Bayesian

Distance-based phylogenetics

Parsimony phylogenetics

Likelihood setup

• Come up with a statistical model of experiment
• Parametrize that model
• Evaluate likelihood under various parameter values

Example: flipping coins

Say that, after flipping a coin 20 times, we get 6 heads.

Model using the binomial distribution. Say \(p\) is the probability of getting a tail, and each draw is independent.

The likelihood of getting the observed result is \[ { {20} \choose 6} \, p^6 \, (1-p)^{20-6}. \] Recall: \({ {20} \choose 6}\) is the number of ways of choosing 6 items out of 20.

Exercise: likelihood surface

• Run Beta_binomial.R in R
• Change the number of heads and tails.
• The maximum likelihood estimate of the parameter of interest is the parameter value(s) that maximize the likelihood. Here it's marked with a dot.
• What do you notice about the ML value when the observations are rare?
• How does the shape of the likelihood surface change when we get more observations?

Likelihood recap

• Maximum likelihood is a way of inferring unknown parameters
• To apply likelihood, we need a model of the system under investigation
• In general, the “likelihood” is the likelihood of generating the data under the given parameters, written \(P(D | \theta),\) where \(D\) is the data and \(\theta\) are the parameters.

Setup for likelihood based phylogenetics

The phylogenetic likelihood of a tree is the likelihood of generating the observed data given that tree (under the sequence evolution model).

Note that the UW’s own Joe Felsenstein was the first to formalize this and develop efficient algorithms.

Sequence evolution models tell us the probability of seeing a certain mutation in some period of (evolutionary) time

Model hierarchy, from Posada and Crandall

Calculating likelihood of a single column

Likelihood of an alignment

The phylogenetic likelihood of a tree is the likelihood of generating the observed data given that tree (under the sequence evolution model)

Bayes is magic

\[ P(\theta \mid D) \propto P(D \mid \theta) P(\theta) \]

Exercise: the prior and the posterior

• Open Beta_binomial.R again.
• Return the number of heads and tails to zero, and click "Bayesian".
• Alpha and Beta are the parameters of the prior. Try changing them around.
• Make them such that the prior is peaked around 0.5.
• Now, what happens when you vary the number of heads and tails?

The posterior probability of a tree is the probability that the observed tree is correct (given the model and priors)

• Bayesians sample from this posterior
• If you can deal with a prior, it’s the statistically right thing to do
• Sometimes we aren’t actually interested in the tree, so we can integrate it out
• But! Short alignment, 100 taxa = hours

Markov chain Monte Carlo

Metropolis-Hastings algorithm

• If you jump to a better tree, accept that move
• If you jump to a worse tree, accept that move with a non-zero probability
• It’s all arranged so that you sample trees in proportion to their posterior probability

Subset to high probability nodes

Real tree spaces have bottlenecks

Likelihood phylogenetics recap

Crazy but typical model assumptions

• differences between sequences only appear by point mutation
• evolution happens on each column independently
• sequences are evolving according to reversible models (this excludes selection and directional evolution of base composition)
• the evolutionary process is identical on all branches of the tree

To read

• Inferring Phylogenies by Felsenstein
• The phylogenetic handbook edited by Lemey, Salemi, and Vandamme, chapters by the stars
• Bodega phylogenetics tutorials

Software

• FastTree – approximate ML
• RAxML and PhyML – somewhat less approximate ML
• BEAST – Bayesian
• MrBayes – Bayesian
• many others, but these are the ones I know …