Researcher A builds an ML tree using Jukes-Cantor (log-likelihood = −10,500). Researcher B uses GTR+Γ on the same alignment (log-likelihood = −9,800). What is the most appropriate interpretation?
AResearcher A's tree is more reliable because Jukes-Cantor is more conservative and avoids overfitting
BThe two likelihoods cannot be meaningfully compared because different substitution models were used
CGTR+Γ fits the data better; a likelihood ratio test or information criterion can assess whether the improvement justifies the additional parameters
DResearcher B's tree is always preferable because more parameters always improve likelihood
Higher log-likelihood means the model assigns greater probability to the observed data, which is evidence of better fit. GTR+Γ allows different substitution rates and rate variation across sites — capturing real features of molecular evolution that Jukes-Cantor ignores. Model comparison tests (likelihood ratio test for nested models, AIC/BIC for non-nested) formalize whether the improvement is statistically justified. The correct approach is model selection, not blanket preference for simpler or more complex models.
Question 2 Multiple Choice
Why do ML phylogenetic programs like RAxML use heuristic search strategies rather than evaluating every possible tree topology?
AHeuristic methods are provably more accurate than exhaustive search for biological data
BThe number of possible unrooted tree topologies grows super-exponentially with the number of taxa, making exhaustive search computationally infeasible even for modest datasets
CML likelihood calculations can only be performed for trees with branch lengths below a certain threshold
DExhaustive search does not allow simultaneous optimization of branch lengths
For N taxa, the number of distinct unrooted tree topologies is (2N−5)!! — a super-exponential function. For 20 sequences, this exceeds 10²⁰ trees; for 50 sequences, the number is astronomically larger. Evaluating every tree is impossible. Heuristics like nearest-neighbor interchange (NNI) and subtree pruning-regrafting (SPR) start from an initial tree and improve it incrementally, but they cannot guarantee finding the global ML optimum.
Question 3 True / False
In ML phylogenetics, the likelihood of a tree at a single alignment site is calculated by summing over all possible ancestral nucleotide states at internal nodes, weighted by the substitution probabilities defined by the evolutionary model.
TTrue
FFalse
Answer: True
This is the Felsenstein pruning algorithm. At each internal node, you cannot observe the ancestral sequence directly, so you must average over all possible ancestral states. Each path through the tree — assigning specific nucleotides to all internal nodes — has a probability determined by the substitution model's rate matrix and the branch lengths. Summing these probabilities over all possible ancestral assignments gives the marginal likelihood of observing the tip nucleotides at that site, given the tree and model.
Question 4 True / False
The ML tree returned by phylogenetic software is very likely to be the tree with the highest possible likelihood across most possible topologies for the given alignment.
TTrue
FFalse
Answer: False
There is no guarantee. Heuristic search explores only a fraction of tree space, moving from tree to tree by local rearrangements. It can get trapped in local optima — regions where no simple branch swap improves the likelihood, even though a better tree exists elsewhere in tree space. The returned tree has the highest likelihood found during the search, not the highest possible. This is why researchers often run multiple searches from different starting trees.
Question 5 Short Answer
What role does the substitution model play in ML phylogenetics, and why does using a more realistic model typically produce a higher likelihood even without changing the tree topology?
Think about your answer, then reveal below.
Model answer: The substitution model defines a matrix of probabilities for each nucleotide changing into another over a given branch length. It is used to calculate the probability of observing the actual sequence data at the tips, given the tree and branch lengths. A more realistic model (e.g., GTR allows unequal rates for all six substitution types; Γ allows rate variation across sites) better matches the true patterns of molecular evolution. Because the model more accurately predicts the data-generating process, it assigns higher probability to the observed alignment — producing a higher likelihood — even with the same tree topology. The improvement comes from a better statistical description of how sequences evolve, not from a different evolutionary history.
This is why model selection is a critical step in ML phylogenetics. An underfitting model (e.g., treating all substitutions as equally likely when they are not) systematically mispredicts data patterns, reducing the likelihood. Choosing a well-fitting model improves both the likelihood and the accuracy of the inferred tree.