Ecology and Evolution · Unit 2: Genomes, development and diversification

Molecular Evolution

How can the differences between two species' genes tell you when they split, and whether selection or chance shaped those differences? This lesson treats sequence differences as historical evidence, dates a split with a fossil-calibrated molecular clock, sets out what the neutral and nearly neutral theories predict, and reads dN/dS and the McDonald-Kreitman test. Afterwards you can date a divergence from a calibration, state what the calibration assumes, and say what a test for positive selection can and cannot show.

Watch first Genes Date a Split Without Fossils · 3:01

Two living species may have left no fossil of the moment they split. Their genes can still tell you, roughly, when it happened, and whether selection or chance shaped what changed.

This lesson reads DNA and protein sequences the way a geologist reads layers of rock: as a record laid down over time. You will date a split from sequence differences, see why most of those differences are thought to be selectively neutral, and learn to tell, with caution, when selection has been at work.

The idea: sequences as a record of time

When one ancestral population splits into two lineages, each keeps acquiring mutations. Some spread until every member of the lineage carries them. A mutation that has reached fixation in a lineage is a substitution: the rate of substitution is the rate at which mutations arise and then fix. Compare the same gene in two species and you see the substitutions that built up on both branches since their common ancestor.

The gene must be orthologous: two copies descended from one gene in the common ancestor by speciation, rather than by duplication within a genome (the copies How Signaling Evolved traces through gene families are mostly the duplicated kind). How the sequences are obtained belongs to sequencing and genomes; here you start from an alignment.

Counting differences is like counting the scratches on two copies of a record that have been played for years. A new scratch over an old one goes unseen. In the same way, a site can change twice, or change and change back, so the observed proportion of differing sites, p, underestimates the true number of substitutions as sequences diverge. A corrected distance, d, estimates the real number. The simplest correction (Jukes and Cantor, assuming all four bases interchange at one rate) is:

d = -(3/4) x ln(1 - (4/3) x p)

If 30% of aligned sites differ (p = 0.30), then 1 - 0.40 = 0.60, ln 0.60 = -0.511, and d = 0.383 substitutions per site. More than a quarter more change happened than you can see. For small p the correction is tiny: p = 0.012 gives d = 0.0121.

The tree that relates the sequences is itself an inference with a stated support, as in reading phylogenetic trees.

The clock and its calibration

In the early 1960s Emile Zuckerkandl and Linus Pauling noticed that amino-acid differences between the hemoglobins of different mammals were roughly proportional to the time since their lineages split, as judged from fossils. That is the molecular clock: the expected number of changes on a branch is its rate times its duration.

Sequences alone cannot separate rate from time. A distance of 0.02 could mean a fast rate over a short time or a slow rate over a long one. You need a calibration: an age from outside the sequences. A fossil is the commonest. The oldest fossil that can be correctly assigned to a group shows the group existed by then, so it gives a minimum age; the actual split was earlier by an unknown margin. Sequences sampled at sufficiently different known dates, such as virus samples or ancient DNA, can also calibrate a tree.

Worked problem (illustrative data). Two species known from fossils to have split 3.0 million years ago differ by a corrected 0.012 substitutions per site in a gene. A second pair differs by 0.024 in the same gene. When did the second pair split? Assume both lineages in each pair evolve at the same constant rate, the calibration date is exact, and variation already present in the ancestral population adds negligible time.

  1. Set up the model. Substitutions accumulate along both branches from the common ancestor, so the distance between two tips is D = rt + rt = 2rt, where r is the rate per lineage and t the time since the split.
  2. Calibrate. r = 0.012 / (2 x 3,000,000 years) = 2.0 x 10^-9 substitutions per site per year.
  3. Date the target. t = 0.024 / (2 x 2.0 x 10^-9) = 0.024 / (4.0 x 10^-9) = 6.0 million years. Check: 2 x 2.0 x 10^-9 x 6,000,000 = 0.024 substitutions per site, the stated distance.

The commonest error is forgetting the factor 2 in step 3, which gives 0.024 / 2.0 x 10^-9 = 12 million years. And since the calibration is a minimum, both splits may be older than these figures.

Calibrating a molecular clock: D = 2rt⚙ original · interactive
  • D = 2rt, through the calibration
  • fossil calibration (3.0 million years)
  • target distance
  • date read from the line
1. Calibrate: r = D / (2t)
2. Date the target: t = D / (2r)

In this sketch: slider values other than 0.012 and 0.024 are illustrative; one constant rate on both lineages, the calibration date treated as exact, and ancestral polymorphism ignored. The fossil date is a minimum, so the dates may be older.

Distance builds up on two branches, so D = 2rt: use the factor 2 when you find the rate and again when you find the date.

Real lineages do not run at one rate. Relaxed clocks let branch rates vary: in Drummond and colleagues’ 2006 method, each branch draws its own rate, and calibration uncertainty enters as a probability distribution on node ages. In their marsupial analysis the fastest branch of the most probable tree was estimated to evolve 2.7 times faster than the slowest. Even with abundant data, the dates such methods return stay sensitive to the assumptions about rates and times put in.

The neutral theory and what it predicts

Why would a protein change at a roughly steady rate? In 1968 Motoo Kimura argued that the substitution rate implied by protein comparisons was too high to be explained if each substitution had been driven by selection. His neutral theory holds that most substitutions that fix are neutral or nearly neutral, fixed by random drift, while most strongly harmful mutations are removed by selection before they spread. It does not say that all mutations are neutral, or that selection is unimportant for the traits organisms show.

The model makes a clean prediction. In an ideal diploid population of N individuals there are 2N copies of each site. If neutral mutations arise at rate mu per copy per generation:

new neutral mutations per generation = 2N x mu; fixation probability of each = 1/2N; so K = 2N x mu x 1/2N = mu

The neutral substitution rate K equals the neutral mutation rate and does not depend on population size: a large population makes more mutations, but each has a smaller chance of fixing. The derivation of the fixation probability belongs to population genetics. Note that mu is the neutral mutation rate, not the total; mutations removed by selection never become substitutions.

In 1973 Tomoko Ohta proposed the nearly neutral theory. Many mutations are slightly deleterious, with effects on fitness of the order of 1/Ne, where Ne, the effective population size, measures how strongly drift acts. In a small population drift can fix them; in a large one selection removes them. So for this class the substitution rate does depend on Ne.

Mutation input also varies. Bergeron and colleagues in 2023 sequenced 151 parent-offspring trios from 68 vertebrate species and found per-generation germline mutation rates differing 40-fold across species. The 36 mammals sampled averaged 7.97 x 10^-9 mutations per site per generation, and the four classes sampled did not differ significantly overall. That is a per-generation mutation rate; the clock rate above is a per-year substitution rate. Linking them takes assumptions about neutrality and generation time.

Reading selection in coding sequences

In a coding gene, a nonsynonymous change alters the amino acid and a synonymous change does not, because the genetic code has several codons for most amino acids. dN is nonsynonymous substitutions per nonsynonymous site; dS is synonymous substitutions per synonymous site. If synonymous changes are neutral, dS is a built-in control and their ratio omega = dN/dS reads selection on the protein:

  • omega below 1: most amino-acid changes were removed (purifying selection).
  • omega near 1: consistent with neutrality.
  • omega above 1: amino-acid changes fixed faster than silent ones (positive selection).

Worked problem, step 4. In the same gene from the second pair, dN = 0.004 and dS = 0.040 substitutions per site. Omega = 0.004 / 0.040 = 0.10. Amino-acid changes fixed at a tenth the rate of silent ones, so most were removed by purifying selection, even though the gene is still evolving.

A second signal comes from polymorphism. Under neutrality, variants within a species are transient stages on their way to fixation or loss, so the ratio of replacement to synonymous changes should be the same among polymorphisms as among fixed differences between species. In 1991 John McDonald and Martin Kreitman applied this to the Adh gene in three Drosophila species and found an excess of fixed replacement differences, which they suggested reflected adaptive fixation. The McDonald-Kreitman test uses each class of change as the control for the other, so it needs no clock.

When the signal misleads

Each of these tests is a model inference, and each model can fail.

A gene-wide omega averages over sites. If most codons are strongly constrained, a few positively selected sites barely lift the average, so the test has little power. Within a single population, omega near 1 can arise under selection and does not establish neutrality. Synonymous sites are not always neutral: Rahman and colleagues in 2021 found evidence of non-neutral synonymous substitutions in Enterobacterales, which undermines the denominator. And in 2018 Venkat, Hahn and Thornton showed with simulations based on mammal and fly alignments, containing no positive selection, that mutations changing several adjacent nucleotides at once can make the branch-site test report positive selection on a lineage.

Design problem

A branch-site test flags positive selection in an immune gene on one primate lineage. Before you believe it, what would you check?

One way to do it

Start with the data. Inspect the alignment around the flagged codons for errors, and confirm that every sequence is a true ortholog rather than a duplicated paralog or a misassembled copy.

Then test the model. Simulate alignments on the same tree with no positive selection but with realistic multinucleotide mutations and the observed base composition, and see how often the test fires; if it fires often, the empirical result is weak. Check codon-usage bias, since selection on synonymous sites changes dS.

Seek an independent signal. Build a McDonald-Kreitman table for the lineage from polymorphism data: replacement and synonymous changes, polymorphic and fixed. An excess of fixed replacements would support the inference by a different route.

Finally, test function. Reconstruct the ancestral and derived proteins, express both, and measure the property that matters, such as binding to a pathogen protein. Even then, report the result as a model inference supported by evidence, not as an observation of adaptation.

How we measure it

Fossil-calibrated molecular dating

Branch lengths estimated from sequences are converted to time with external age information: a fossil that sets a minimum age for a node, or sequences sampled at known, sufficiently different dates. Bayesian relaxed-clock methods let rates vary among branches and represent calibration uncertainty as a prior distribution on node ages.

Codon-model estimation of dN/dS

Aligned coding sequences are analysed on a phylogeny with a model that separates nonsynonymous from synonymous substitutions, each counted per available site. The ratio omega = dN/dS, estimated by maximum likelihood for a gene, a branch or a class of sites, measures how amino-acid changes have fared relative to silent ones.

McDonald-Kreitman test

Changes at one locus are sorted into a two-by-two table: replacement or synonymous, and polymorphic within species or fixed between species. Under neutrality the replacement to synonymous ratio is expected to be the same in both rows; an excess of fixed replacements suggests adaptive fixation, and an excess of replacement polymorphisms suggests weakly harmful variants.

Parent-offspring trio sequencing

The genomes of two parents and their offspring are sequenced at high coverage, and sites where both parents carry the reference base and the offspring is heterozygous are taken as candidate new mutations. Correcting for the callable part of the genome and for missed mutations gives a per-generation germline mutation rate.

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Evolution of Development

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Human deoxyhemoglobin — the protein the clock was first read from
Human deoxyhemoglobin — the protein the clock was first read from ● LIVE · RCSB PDB 2HHB
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Two alpha and two beta chains, each folded around a heme. Amino-acid differences between species fall mostly on the surface of the chains, while residues that contact the heme or the other subunits change much less often.

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Emile Zuckerkandl and Linus Pauling

Emile Zuckerkandl and Linus Pauling

Compared hemoglobin sequences across animals and proposed in the early 1960s that the number of amino-acid differences between two species grows roughly in proportion to the time since their lineages split, the idea later called the molecular clock.

In the late 1950s Emile Zuckerkandl joined Linus Pauling's laboratory at the California Institute of Technology, where Pauling had already shown that sickle-cell hemoglobin differs from normal hemoglobin as a molecule. Zuckerkandl studied hemoglobins from different animals. As partial amino-acid sequences of hemoglobin chains from several species became available, the two of them compared them and noticed a regularity: the more distantly two species were related, judging by the fossil record, the more amino-acid differences their hemoglobins showed, and the count rose roughly in proportion to the estimated time since the split. In papers of 1962 and 1965 they proposed that protein differences could be used to estimate when lineages diverged, and they argued that sequences are documents of evolutionary history. Other laboratories, comparing cytochrome c across species, were reaching related conclusions in the same years. The work made it possible to put dates on branches that have no fossil record, and it raised the question the neutral theory later tried to answer: why should a protein change at a roughly steady rate at all?

✓ verbatim Zuckerkandl & Pauling, Evolutionary divergence and convergence in proteins, in Bryson & Vogel (eds), Evolving Genes and Proteins, Academic Press (1965); Zuckerkandl & Pauling, Molecules as documents of evolutionary history, J. Theor. Biol. 8:357 (1965).
Motoo Kimura

Motoo Kimura

Argued in 1968 that the rate of molecular substitution inferred from protein comparisons was so high that many of the substitutions were probably neutral mutations fixed by random genetic drift, the founding argument of the neutral theory of molecular evolution.

Kimura was a population geneticist at the National Institute of Genetics in Mishima, Japan, and much of his earlier work was mathematics: how allele frequencies wander by chance in a finite population. In a short paper in Nature in February 1968 he turned that mathematics on the new protein data. He took published estimates of how fast amino acids are replaced in proteins such as hemoglobin, scaled them up to the whole genome of a mammal, and argued that the implied rate of nucleotide substitution was so high that it would be hard to explain if every substitution had been driven by selection. His alternative was that many of these substitutions were mutations with no effect on fitness that had reached fixation by drift. In a 1969 paper in PNAS he put the hypothesis more fully: a majority of the amino-acid substitutions in the homologous proteins examined, including mammal and carp hemoglobins, resulted from random fixation of neutral or nearly neutral mutations. He did not say that all mutations are neutral; harmful ones are removed. What the argument made possible was a null model for sequence evolution, against which selection can be tested.

✓ verbatim Kimura, Evolutionary rate at the molecular level, Nature 217:624 (1968); Kimura, PNAS 63:1181 (1969).
Tomoko Ohta

Tomoko Ohta

Proposed in 1973 that many substitutions are slightly deleterious mutations whose fate depends on the balance between weak selection and drift, so that effective population size affects the substitution rate (the nearly neutral theory).

Ohta worked at the National Institute of Genetics in Mishima, where she collaborated with Kimura on the mathematics of neutral evolution. In a Nature paper in 1973 she proposed a change to the simple neutral picture. Between mutations that are strictly neutral and those that are clearly harmful, she argued, lies a large class of slightly deleterious mutations, whose effects on fitness are so small that drift and selection are of similar strength. The fate of such a mutation depends on the effective population size, Ne, which measures how strongly chance acts in a population. In a small population, drift can carry a slightly deleterious mutation to fixation; in a large one, selection removes it more reliably. The simple neutral model predicts that the substitution rate depends only on the neutral mutation rate; Ohta's model predicts that it also depends on Ne. That prediction gave researchers something new to test, by comparing species whose populations differ greatly in size, and the nearly neutral theory is now a standard framework for reading genome-wide patterns of constraint.

✓ verbatim Ohta, Slightly deleterious mutant substitutions in evolution, Nature 246:96 (1973).
John H. McDonald and Martin Kreitman

John H. McDonald and Martin Kreitman

Devised a test that compares the ratio of amino-acid-changing to silent differences among polymorphisms within species with the same ratio among fixed differences between species, and found an excess of fixed amino-acid replacements at the Adh locus of Drosophila.

The gene for alcohol dehydrogenase, Adh, had become one of the best-studied genes in Drosophila population genetics; in 1983 Kreitman had published a survey of its DNA sequence variation in D. melanogaster. In 1991 McDonald and Kreitman used Adh sequences to test a simple consequence of the neutral theory. If amino-acid changes and silent changes are both neutral, then the polymorphisms seen within a species are transient stages on the way to fixation or loss, and the ratio of replacement to synonymous changes among those polymorphisms should match the ratio among the differences that have become fixed between species. They compared Adh sequences from three species of the D. melanogaster subgroup and found more fixed amino-acid replacements between species than the polymorphism ratio predicted, which they suggested reflected adaptive fixation. The test needs no assumption about the substitution rate or the dates of the splits, because each class of change acts as the control for the other. It has since been extended to many genes at once to estimate what fraction of amino-acid substitutions might have been fixed by positive selection.

✓ verbatim McDonald & Kreitman, Adaptive protein evolution at the Adh locus in Drosophila, Nature 351:652 (1991).
Test yourself
Question 1 of 8 Score 0 / 0

For a gene compared between two species, dN = 0.006 and dS = 0.030 substitutions per site. What does omega suggest about amino-acid changes in this gene?
Sources & Integrity

Every structure, slide, simulation, and clip on this page is listed below with the source it came from. None of the 3D structures is drawn by hand or by AI: each one loads by accession ID from RCSB PDB or PubChem. This panel is generated from the lesson's own data file, so what it lists is what the page loads.

Molecular structures live data

  • Human deoxyhemoglobin — the protein the clock was first read from — RCSB PDB 2HHB · coordinates CC0 · Human deoxyhemoglobin, X-ray crystal structure (Fermi et al., J. Mol. Biol., 1984)

Simulations

  • Calibrating a molecular clock · Original interactive — Biochemistrypedia (Deppmann Lab).

Scientist profiles & quotes

  • Emile Zuckerkandl and Linus Pauling — Zuckerkandl & Pauling, Evolutionary divergence and convergence in proteins, in Bryson & Vogel (eds), Evolving Genes and Proteins, Academic Press (1965); Zuckerkandl & Pauling, Molecules as documents of evolutionary history, J. Theor. Biol. 8:357 (1965).
  • Motoo Kimura — Kimura, Evolutionary rate at the molecular level, Nature 217:624 (1968); Kimura, PNAS 63:1181 (1969).
  • Tomoko Ohta — Ohta, Slightly deleterious mutant substitutions in evolution, Nature 246:96 (1973).
  • John H. McDonald and Martin Kreitman — McDonald & Kreitman, Adaptive protein evolution at the Adh locus in Drosophila, Nature 351:652 (1991).

Quotes are verbatim from the cited source. Profile text is original to this site and was checked against the sources cited.

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Genes Date a Split Without Fossils · narration: an AI narrator voice (Gemini, Charon) reading narration written from this lesson's text · animation: AI-generated in code (Manim) by Claude, a schematic with no drawn molecular structures, plots computed from their equations · captions from the narration script.

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Like I'm five

Every time a living thing has babies, its instructions get copied, and once in a while a letter is copied wrong. Over a very long time two kinds of animals that came from the same grandparents pile up more and more different letters. If you know how fast the letters change, you can count the differences and guess how long ago they split. Some letter changes break things and disappear, and some do nothing at all and just drift along.
High school

When two species split from a common ancestor, mutations keep arising in each line, and some spread until every member carries them. Comparing the same gene in both species shows how many changes have built up. If changes build up at a steady rate, and a fossil tells you when one pair of species split, you can work out the rate and use it to date other splits. The neutral theory says most of the changes that spread had no effect on survival or reproduction and spread by chance, while harmful ones were removed. Comparing changes that alter a protein with changes that do not shows where selection has acted.
College

Orthologous sequences diverge as substitutions accumulate on both lineages, so a corrected pairwise distance D = 2rt. A calibration (a fossil, which gives a minimum node age, or dated samples) breaks the confounding of rate and time, and relaxed-clock models let r vary among branches. Kimura's neutral theory holds that most substitutions that fix are neutral or nearly neutral, while strongly harmful mutations are removed; for neutral mutations the substitution rate K equals the neutral mutation rate mu, because 2N mu new copies arise per generation and each fixes with probability 1/2N. Ohta's nearly neutral theory adds slightly deleterious mutations whose fate depends on Ne. In coding sequences omega = dN/dS below 1 indicates purifying selection, near 1 is consistent with neutrality and above 1 suggests positive selection; the McDonald-Kreitman test compares the replacement to synonymous ratio among polymorphisms with that among fixed differences.
Graduate

Divergence dating is an inference under a model: sequence data alone confound rate with time, so even very large alignments leave date estimates sensitive to the priors on node ages and rates (Donoghue and Yang 2016), and an uncorrelated lognormal relaxed clock (Drummond et al. 2006) estimated a fastest-to-slowest branch-rate ratio of 2.7 in a marsupial data set. Mutation input itself varies: pedigree estimates across 68 vertebrate species (Bergeron et al. 2023) differed 40-fold per generation, with a mean of 7.97 x 10^-9 per site per generation across the 36 mammals sampled, and the four sampled classes did not differ significantly overall. Per-generation mutation rates, per-year substitution rates and fixed differences are different quantities, linked only by assumptions about neutrality and generation time. Codon-model tests inherit their assumptions. A gene-wide omega can hide a few positively selected sites under strong constraint elsewhere; omega near 1 in a single-population sample does not show neutrality (Kryazhimskiy and Plotkin 2008); synonymous sites are not always neutral (Rahman et al. 2021, Enterobacterales); and multinucleotide mutations produce false branch-site positives in simulations based on mammal and fly alignments (Venkat, Hahn and Thornton 2018). An open question is how much of the adaptive-substitution fraction estimated from McDonald-Kreitman-type data survives correction for slightly deleterious polymorphisms, demographic change and linked selection in a given species.
Molecules as documents

In a 1965 essay Zuckerkandl and Pauling sorted the molecules of a cell by how much history they carry. Molecules whose structure is read off genetic information, DNA, RNA and proteins, they called semantides, and they argued that comparing these across species could reconstruct the branching of lineages. The essay pointed toward what became routine decades later: building trees and dating splits directly from sequences.

— Zuckerkandl & Pauling, Molecules as documents of evolutionary history, J. Theor. Biol. 8:357 (1965).
Two papers, one argument

In 1969, Jack King and Thomas Jukes published a long article in Science titled Non-Darwinian evolution. Working from protein sequences and the structure of the genetic code, they argued independently that much of the amino-acid change seen between species reflects neutral mutations fixed by drift. The neutral theory therefore entered the literature from two directions at once, one built on population-genetic mathematics and one on the biochemistry of proteins and codons.

— King & Jukes, Non-Darwinian evolution, Science 164:788 (1969); Kimura, Nature 217:624 (1968).
A false alarm built into the model

The branch-site test assumes that a codon changes one nucleotide at a time. Venkat, Hahn and Thornton simulated coding sequences with no positive selection at all, but with mutations that sometimes change several adjacent nucleotides at once, at rates taken from real mammal and fly alignments. The test still reported positive selection in many simulated data sets. The result does not mean that published cases of adaptation are false, but it showed that an omitted mutation process can produce the signal the test credits to selection.

— Venkat, Hahn & Thornton, Nature Ecology & Evolution (2018), doi:10.1038/s41559-018-0584-5.

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