Two isolated populations of the same species have the same per-site neutral mutation rate μ, but one population has N=500 individuals and the other has N=500,000. Under neutral theory, which population accumulates neutral substitutions faster?
AThe large population, because it generates far more new mutations per generation
BThe small population, because each new mutation has a much higher probability of drifting to fixation
CBoth populations accumulate neutral substitutions at the same rate
DThe large population, but only at synonymous sites; the small population is faster at nonsynonymous sites
The neutral substitution rate K = 2Nμ × 1/(2N) = μ for diploids, canceling population size entirely. The large population generates 1000× more mutations per generation, but each has 1/1000 the probability of drifting to fixation. These effects exactly cancel, yielding the same substitution rate μ regardless of N. This counterintuitive result — that neutral evolution proceeds at the same pace in small and large populations — is the foundational insight of Kimura's neutral theory and the theoretical basis of the molecular clock.
Question 2 Multiple Choice
A researcher compares substitution rates at synonymous versus nonsynonymous sites in a protein-coding gene and finds that the nonsynonymous rate is far below the synonymous rate. What does this indicate?
ANonsynonymous mutations are less likely to occur because the genetic code is structured to make them rare
BPurifying selection removes most nonsynonymous mutations before they can fix, because amino acid changes tend to be deleterious
CPositive selection is driving rapid amino acid evolution at these sites
DThe gene has a low GC content, which reduces nonsynonymous mutation rates
When K_nonsynonymous << K_synonymous ≈ 2μ, it means most amino acid changes are eliminated by purifying selection before reaching fixation. Synonymous sites are approximately neutral (same amino acid regardless of nucleotide), so they serve as the neutral baseline (K ≈ 2μ). The ratio dN/dS = K_nonsynonymous / K_synonymous < 1 indicates constraint. If positive selection were driving amino acid evolution, we'd expect K_nonsynonymous > K_synonymous (dN/dS > 1), which is rare and localized.
Question 3 True / False
A large population accumulates neutral substitutions faster per generation than a small population because it generates more new mutations per generation.
TTrue
FFalse
Answer: False
This is the central misconception about neutral substitution rates. While a large population generates more mutations per generation (2Nμ vs. 2nμ for smaller n), each individual mutation has a proportionally lower probability of fixing by drift (1/2N vs. 1/2n). The two effects cancel exactly, yielding K = 2Nμ × 1/(2N) = μ for all population sizes. This independence from N is precisely what makes the molecular clock work across organisms of vastly different population sizes.
Question 4 True / False
The molecular clock hypothesis is theoretically grounded in the neutral theory finding that the substitution rate at neutral sites equals the neutral mutation rate.
TTrue
FFalse
Answer: True
If K = μ (neutral substitution rate equals per-site mutation rate), and μ is approximately constant per generation across lineages, then the number of neutral differences accumulated between two species is proportional to the number of generations since divergence. This proportionality — neutral differences accumulate like a clock ticking at rate μ — is the theoretical foundation. By comparing neutral or near-neutral sequence differences (synonymous sites, pseudogenes, intergenic regions) between species with known divergence times (from fossils), we can calibrate μ and then use it to date other divergences.
Question 5 Short Answer
Explain why neutral substitution rate is independent of population size, showing how the two population-size-dependent factors cancel in the derivation.
Think about your answer, then reveal below.
Model answer: In a diploid population of size N, there are 2N gene copies. Each generation produces 2Nμ new mutations across all copies (mutation rate per copy per generation is μ). Each new neutral mutation has probability 1/(2N) of eventually drifting to fixation by genetic drift, since it starts as a single copy out of 2N. The substitution rate is the product of these: K = (2Nμ) × (1/2N) = μ. Population size N appears in both the numerator and denominator and cancels exactly. The result is that neutral evolution proceeds at a rate set only by the mutation rate, independent of how large or small the population is.
The cancellation is exact under ideal Wright-Fisher conditions. In reality, variation in population size, generation length, and mutation rate create noise in the molecular clock. But the theoretical independence from N is what makes the clock concept viable at all — otherwise, we would need to know historical population sizes (which are very difficult to estimate) to use sequence divergence as a time measure.