Questions: Bayesian Phylogenetics

Question 1

A Bayesian phylogenetic analysis assigns a posterior probability of 0.95 to a particular clade. What does this value mean?

• A. The clade appeared in 95% of bootstrap replicates when the sequence data were resampled
• B. There is a 95% probability that this clade is correct, given the data and the prior model
• C. The maximum likelihood tree supports this clade with a likelihood ratio of 0.95
• D. If the analysis were repeated 100 times with different random seeds, the clade would appear in 95 of them

Answer: (B)

Posterior probability has a direct probabilistic interpretation: given the data and the prior distributions you specified, there is a 95% probability that the clade is correct. This is more intuitive than a bootstrap value (option A), which is a frequentist measure of how often a clade appears under data resampling — not a direct probability that the clade is real. Options C and D confuse Bayesian posterior probability with likelihood ratios and repeated-sampling logic respectively. The Bayesian posterior integrates over uncertainty in tree topology, branch lengths, and model parameters.

Question 2

Why is Markov chain Monte Carlo (MCMC) sampling necessary in Bayesian phylogenetics rather than simply evaluating all possible trees?

• A. MCMC speeds up the calculation of maximum likelihood scores for each candidate tree
• B. MCMC corrects for substitution rate heterogeneity across sites in the alignment
• C. The number of possible tree topologies grows super-exponentially with the number of taxa, making exhaustive evaluation impossible — MCMC samples trees in proportion to their posterior probability
• D. MCMC allows the analysis to be run without specifying prior distributions on model parameters

Answer: (C)

For even modest numbers of taxa, the number of possible unrooted tree topologies is astronomically large — for 50 species, more than the number of atoms in the observable universe. No computer could evaluate all possible trees, let alone integrate over all parameter values at each topology. MCMC solves this by constructing a random walk through tree space that, at convergence, visits trees in proportion to their posterior probability. The resulting sample of trees approximates the full posterior distribution without requiring exhaustive enumeration.

Question 3

In Bayesian phylogenetics, the prior distribution on model parameters can influence the posterior when sequence data are sparse.

• T. True
• F. False

Answer: True

By Bayes' theorem, the posterior is proportional to the likelihood times the prior. When data are abundant and informative, the likelihood dominates and the prior has little effect — Bayesian and maximum likelihood analyses converge on similar results. But when data are sparse (few taxa, short sequences, rapidly evolving regions), the likelihood surface is flat and the prior exerts substantial influence on the posterior. This is why sensitivity analysis — running analyses under different prior specifications and checking whether conclusions change — is essential practice in Bayesian phylogenetics.

Question 4

Bayesian phylogenetics and maximum likelihood phylogenetics answer the same fundamental question: which single tree topology is best supported by the sequence data.

• T. True
• F. False

Answer: False

Maximum likelihood finds the single tree topology (and parameter values) that maximizes the probability of observing the data — it produces a point estimate. Bayesian phylogenetics estimates the full posterior probability distribution over all possible tree topologies, branch lengths, and model parameters. Instead of one best tree, you get a distribution of trees, each with a posterior probability. This distributional answer directly quantifies uncertainty about the tree, whereas ML treats uncertainty indirectly through bootstrapping — resampling the data to ask how often a clade appears, not what its probability is.

Question 5

What is the fundamental difference between a maximum likelihood phylogenetic analysis and a Bayesian one, in terms of what each produces and how each handles uncertainty?

Model answer: Maximum likelihood finds the single tree topology and parameter values that maximize P(data|tree, parameters) — it produces a point estimate, one best tree. Uncertainty is assessed indirectly through bootstrapping: the data are resampled, the tree is re-estimated each time, and the frequency with which a clade appears across replicates is used as a support measure. Bayesian phylogenetics instead estimates the posterior probability distribution P(tree, parameters|data) ∝ P(data|tree, parameters) × P(prior). MCMC samples from this distribution, producing a collection of trees visited in proportion to their posterior probability. Uncertainty is expressed directly as posterior probabilities on clades — the probability, given the data and prior, that each clade is real.

The practical consequence is that Bayesian posterior probabilities are more intuitively interpretable than bootstrap values, and Bayesian analyses naturally integrate over model parameter uncertainty rather than fixing parameters at their ML estimates. The tradeoff is that Bayesian analyses require specifying prior distributions, which introduces assumptions that can influence results when data are limited.