Questions: DNA Sequence Divergence and Phylogenetic Distance

Question 1

Two distantly related species have a p-distance (raw proportion of different sites) of 0.45 at a given gene locus. A researcher concludes that approximately 45% of sites have undergone substitution since their common ancestor. What is wrong with this interpretation?

• A. Nothing — the p-distance directly measures the true number of substitutions
• B. The p-distance overestimates true divergence because sequencing errors inflate the count
• C. The p-distance underestimates true divergence because multiple hits and back mutations cause some substitutions to go undetected
• D. The p-distance is only meaningful for protein sequences, not DNA sequences

Answer: (C)

At high divergence levels, many sites will have experienced multiple substitutions (multiple hits) or substituted and then returned to the original base (back mutations). Both events make sites appear unchanged or falsely identical, so the raw count of differences underestimates the true number of substitutions. The p-distance also saturates — as sequences diverge further, it approaches a ceiling (~0.75 for equal-rate models) even as true substitutions continue to accumulate. Statistical corrections like Jukes-Cantor or Kimura's two-parameter model are required to estimate the true evolutionary distance.

Question 2

Why does Kimura's two-parameter model generally give more accurate evolutionary distance estimates than the simpler Jukes-Cantor model?

• A. Kimura's model accounts for the fact that transitions (purine-to-purine or pyrimidine-to-pyrimidine changes) occur more frequently than transversions
• B. Kimura's model uses amino acid sequences rather than nucleotide sequences
• C. Kimura's model corrects for gene duplication events that inflate apparent sequence differences
• D. Kimura's model only applies to non-coding regions where mutation rates are higher

Answer: (A)

The Jukes-Cantor model assumes all substitution types (A↔G, A↔C, A↔T, etc.) occur at equal rates. But empirically, transitions (A↔G, purine-to-purine; C↔T, pyrimidine-to-pyrimidine) occur more frequently than transversions (A↔C, A↔T, G↔C, G↔T) — often by a ratio of 2:1 or higher. If you ignore this asymmetry, you incorrectly weight different types of differences, leading to biased distance estimates. Kimura's two-parameter model estimates separate rates for transitions (κ) and transversions, producing better-calibrated distances for most real datasets.

Question 3

As two DNA sequences diverge over longer and longer evolutionary time, the observed p-distance continues to increase proportionally with time and rarely plateaus.

• T. True
• F. False

Answer: False

The p-distance saturates. Because there are only four nucleotide states, sites that have already changed can change again (multiple hits) or revert (back mutations). As divergence increases, an ever-larger fraction of observed differences are erased by subsequent substitutions, while an ever-larger fraction of identical-looking sites are actually sites that changed multiple times and returned to their original state. The p-distance approaches a theoretical maximum near 0.75 (for equal base frequencies and equal rates), after which additional true substitutions produce no increase in observed differences. This is why corrections are necessary for ancient divergences.

Question 4

Applying the Jukes-Cantor correction to a p-distance always gives an estimated true distance larger than the raw p-distance value.

• T. True
• F. False

Answer: True

The Jukes-Cantor correction formula d = −(3/4)ln(1 − 4p/3) always produces d ≥ p for valid values of p (0 ≤ p < 0.75). This makes biological sense: the correction inflates the estimate to account for the multiple hits and back mutations that the raw p-distance cannot see. The larger the p-distance, the more the correction diverges from the raw value, because at high divergence levels the probability of undetected multiple hits grows. The correction approaches infinity as p → 0.75, reflecting the complete loss of phylogenetic signal at saturation.

Question 5

Explain why the same nucleotide position can appear identical in two distantly related species even though two substitutions have occurred at that site since their common ancestor.

Model answer: If the ancestral state at a site is A, and one lineage substitutes A→G independently in both lineages, both modern sequences show G at that site — they look identical, but two substitutions have occurred (one in each lineage). Alternatively, in one lineage a site might change A→G and then later G→A (a back mutation), again appearing identical to the unchanged other lineage despite two events. In both cases, the site contributes zero to the p-distance count, even though it accumulated two substitutions. This is the 'multiple hits' problem, and it causes p-distance to systematically underestimate the true number of substitutions.

The problem worsens with evolutionary distance because the probability of multiple events at the same site increases with time. For closely related sequences it is negligible, but for ancient divergences it can be severe, which is why increasingly complex substitution models — Jukes-Cantor, Kimura, GTR — are necessary for accurate evolutionary inference across deep time.