We’ve touched on how we must navigate an enormous landscape through tree space using phylogenetic algorithms.
We’ll now explore the two most widely used statistical frameworks for inferring evolutionary relationships, Maximum Likelihood (ML) and Bayesian phylogenetics.
Both of these methods explore the vast landscape of tree space, fundamentally they ask different questions.
Hunting for Treasure
Imagine we’re on a treasure hunt and the prize is hidden somewhere in tree space.
We take some kit with us, two different treasure finders; one based on Maximum Likelihood, the other Bayesian.
Running our ML treasure finder, it spits out a single location.
Next we run our Bayesian treasure finder, this tool does not give us a single location.
Instead it presents us with a map of the landscape, where each location is given a probability representing how plausible it is that the treasure may be there.
It’s our lucky day and the location identified by the ML finder lies in a high-probability region on our Bayesian map.
Taken together both methods directed us to the same region of tree space, though they arrived there with different approaches!
An Example With Sequences
In practice, if we start with a sequence alignment representing 20 different species, and we want to infer the evolutionary relationships between them we will often use both complementary methods.
We can run Maximum likelihood phylogenetics to ask which tree, out of a set of possible trees, best explains the sequence data in our alignment given an evolutionary model.
We can then run Bayesian phylogenetic analysis to ask how probable each tree is given our sequence data, an evolutionary model and prior knowledge.
Both methods can use similar tree rearrangement operations (eg. SPR) however they have different aims.
ML optimises, it searches for the single most likely tree.
Bayesian methods estimate a probability distribution over many possible trees, allowing us to quantify uncertainty.
Measuring tree support
Maximum likelihood and Bayesian phylogenetics use different measures of support for inferred relationships.
In ML analysis, tree support is often estimated using bootstrap analysis . Bootstrapping in phylogenetics involves repeated resampling of the sequence alignment and reconstructing trees from each resampled alignment.
The bootstrap value for a given node represents how often the relationship appears across all bootstrap trees.
In Bayesian phylogenetics we estimate posterior probabilities. These values represent the probability of a given relationship under the sequence data, evolutionary model and prior assumptions.
Rather than resampling the sequence alignment, this information comes from the posterior distribution of trees explored during analysis.
For our example alignment of 20 sequences, as in the treasure hunt, both approaches give us a measure of support for relationships in the tree, though in different ways.
We can compare clade support across both approaches and gauge the level of confidence.
For the ML tree we look at bootstrap values, for the Bayesian tree the posterior probabilities.
Posterior probabilities are estimated using a sampling algorithm, known as MCMC or Markov Chain Monte Carlo, which samples from the posterior distribution over tree space.
We’ll explore bootstrapping and MCMC methods in a future post.