Evolutionary Biology: Chapter 6 — Selection in populations

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6.1 Dominance decides whether selection can see the allele #

6.1.1 Rare alleles, hidden or exposed #

Selection changes allele frequency only where genotypes differ in fitness, and dominance decides whether a rare allele is in a genotype that expresses it. An advantageous dominant is almost always heterozygous when rare, the heterozygote shows the favoured phenotype, and the allele increases at once. An advantageous recessive is hidden in heterozygotes until homozygotes, at frequency about q², become common enough to matter, so early spread is very slow. Once a recessive advantageous allele is common, the finish is fast, because the remaining alternative allele is exposed. A dominant advantageous allele does the opposite: fast at the start, slow at the finish, because the last copies of the unfavoured recessive are hidden and not selected against.

An additive allele, with an intermediate heterozygote, changes fastest at intermediate frequency. For weak selection the change per generation is on the order of (s/2) p(1 − p). There is no long hidden phase.

A fully recessive deleterious allele, fitnesses 1, 1, and 1 − s, changes in frequency by an amount on the order of −s q² when rare. Halve q and the response falls by about four. Selecting only against affected homozygotes therefore removes a rare recessive very slowly. Most copies are in heterozygotes.

Drift still eliminates alleles while selection acts. For a new, weakly beneficial, additive allele, in a population large enough that selection is not swamped, the fixation probability is about 2s, not about 1. An allele with s = 0.01 is lost about 98 times in 100. Below the size where 4Ne s is no longer large, even a beneficial allele is nearly neutral and fixes with probability near 1/(2N). Beneficial means “spreads if it survives sampling”, not “will spread”.

6.1.2 Mutation–selection balance #

Mutation reintroduces deleterious alleles as fast as selection removes them. For a fully recessive deleterious allele the equilibrium frequency is about √(μ/s), where μ is the mutation rate to that allele per generation. For an allele with heterozygous effect hs (fitnesses 1, 1 − hs, 1 − s), if heterozygotes carry most of the selectable harm, the equilibrium is about μ / (hs). The second frequency is much lower.

An illustration of the formulae, not a count from a named disease: μ = 10⁻⁶ and s = 0.1 give a recessive equilibrium near √(10⁻⁵), about 0.003, and an additive equilibrium (h = 0.5) near 10⁻⁶ / 0.05 = 2 × 10⁻⁵. At q = 0.003, only about one deleterious copy in three hundred sits in a homozygote. That is why selection is poor at removing rare recessives. Many real deleterious alleles are partly dominant; mutation experiments in Drosophila find a modest average heterozygous effect rather than zero. Those alleles equilibrate rarer than the recessive formula suggests. Alleles that nevertheless reach appreciable frequencies are enriched for near-complete recessives, or for alleles with a heterozygote advantage, such as S.

Human mutation rates are about 10⁻⁸ per base pair per generation. The μ in these formulae is per locus and counts only mutations of the relevant class. Substituting a per-base rate as if it were a per-locus rate produces a nonsense frequency.

This equilibrium is not balancing selection. The deleterious allele is not favoured when rare. It is reintroduced when rare. Stop mutation, and selection would eventually remove it. Stop selection, and mutation would make it common.

6.2 Sweeps and frequency dependence #

6.2.1 Hitchhiking and selective sweeps #

A beneficial allele spreads as a piece of chromosome. Neutral variants on the same haplotype increase with it. That is genetic hitchhiking (Maynard Smith and Haigh). The tighter the linkage, the longer the association survives recombination.

A selective sweep is the case in which one beneficial copy rises from rarity to fixation and replaces neighbouring variation with its own haplotype. The scar is local along the chromosome, wide if selection was strong or recombination rare, and long in haplotype length if the sweep was recent. Not every valley of low variation is a sweep. Background selection removes deleterious mutations and the neutral variants linked to them, and it lowers nearby diversity without anyone fixing a beneficial allele. A demographic crash lowers diversity across the genome at once. Telling these patterns apart is a statistical problem and is not a protocol given here. The idea is the one required: linkage exports selection from the sites that feel it to the sites that do not, so the neutral theory’s picture of independent sites fails where recombination is low.

A sweep from standing variation, or the same beneficial change arising more than once, starts on more than one haplotype. The scar is weaker. Absence of a classical sweep is not absence of selection.

6.2.2 Frequency-dependent selection #

Frequency-dependent selection means the fitness of a phenotype depends on how common it is.

Negative frequency dependence favours a type when it is rare. The equilibrium is stable. Self-incompatibility in flowering plants is the clean case. Pollen carrying an allele that matches the stigma is rejected, so a rare allele is rejected by fewer partners and succeeds more often. Dozens of alleles can be maintained. No heterozygote superiority is required. The physiology of the pollen tube belongs with plant reproduction; the frequency dependence is the evolutionary fact.

Scale-eating cichlids, Perissodus microlepis, are the behavioural illustration: left- and right-facing mouths, with the rarer attack side favoured once prey attend to the common one. The handedness polymorphism is real. How regularly the frequencies oscillate is more disputed than the original account. Self-incompatibility does not need that caveat.

Positive frequency dependence favours a type because it is common. A warning colour predators have learned, or a preference for the majority mate, can work this way. The common type goes to fixation, and a rare type can be eliminated even if it would be better under another regime. Mean fitness need not rise. The favoured type is favoured by the mix, not by a fixed rank order of genotypes.

6.3 Key terms, summary, and self-check #

Key terms. Dominance; additive allele; mutation–selection balance; hitchhiking; selective sweep; background selection; negative frequency dependence; self-incompatibility; positive frequency dependence.

Summary. A rare dominant is exposed and a rare recessive is hidden, so advantageous dominants spread at once and advantageous recessives wait for homozygotes. The same hiding puts a deleterious recessive at about √(μ/s), against about μ/(hs) when heterozygotes are also harmful. A new beneficial additive allele in a large population still fixes only with probability about 2s. Sweeps drag linked neutral variants and cut local diversity; background selection cuts diversity without a beneficial fixation. Negative frequency dependence, as in self-incompatibility, protects rare alleles. Positive frequency dependence removes them.

Self-check.

1. Why does a rare advantageous recessive spread more slowly than a rare advantageous dominant?

2. Why is selection against affected homozygotes slow to remove a rare recessive, even if those homozygotes leave no offspring?

3. With μ = 10⁻⁶, s = 0.1, and h = 0.5, contrast the recessive and additive equilibria. Which part of the exercise is not a measurement?

4. How does a sweep reduce nearby neutral variation, and how does background selection do something similar without one?

5. Why does a rare self-incompatibility allele have higher fitness than a common one? Is that heterozygote advantage?

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