Frequency-Dependent Selection

The core idea: fitness that bends with frequency

In the simplest model of natural selection, each variant carries a fixed fitness — a beetle that survives a hungry bird does so whether it is one beetle in a thousand or one in two. Frequency-dependent selection breaks that assumption. Here the fitness of a phenotype is a function of how common it is. Write the frequency of morph A as p and its fitness as w_A(p). If w_A falls as p rises — being abundant is a liability — the selection is negative (the rare-morph advantage). If w_A rises with p — joining the crowd pays — it is positive.

That single twist changes everything about the long-run outcome. Ordinary directional selection grinds variation away: it favors one allele until it fixes and the others vanish. Negative frequency dependence does the opposite. It is self-correcting. Whenever a morph drifts toward dominance, its fitness sags below that of its rivals, and selection pushes it back down. The population is dragged toward an internal equilibrium frequency p* where the two morphs have equal fitness, and it tends to stay there. This is why FDS is classed as balancing selection — it actively preserves polymorphism instead of erasing it.

Negative versus positive frequency dependence

The sign of the dependence determines whether diversity is built or destroyed. The two regimes have opposite stability and opposite ecological logic.

Property	Negative FDS	Positive FDS
Who is favored	The rarer morph	The commoner morph
Fitness vs. frequency	w decreases as p increases	w increases as p increases
Internal equilibrium p*	Stable (attracting)	Unstable (repelling)
Long-run outcome	Stable polymorphism preserved	Fixation of one morph; variation lost
Effect on diversity	Maintains variation	Reduces variation
Typical driver	Predator search image, parasite tracking, mate novelty	Müllerian mimicry, warning-signal conformity, social coordination
Example	Scale-eating cichlid jaws; MHC alleles	Aposematic ring of co-mimics; herd alarm signals

A useful way to read the table: negative FDS rewards being different, positive FDS rewards being the same. The same warning coloration that benefits a Müllerian mimic only once it is common (positive FDS — predators must learn the signal, and rare patterns are tested and eaten) becomes a liability for a palatable Batesian mimic if it outnumbers its toxic model (negative FDS — too many harmless lookalikes and predators stop respecting the signal).

The math: equal fitness at equilibrium

Consider two morphs, A at frequency p and B at frequency 1 − p, with frequency-dependent fitnesses w_A(p) and w_B(p). The change in frequency per generation follows the standard selection recursion:

Δp = p (1 − p) · [w_A(p) − w_B(p)] / w̄

where w̄ = p·w_A + (1 − p)·w_B is the mean fitness. Frequency stops changing (Δp = 0) at the boundaries p = 0 and p = 1, and at any internal point where w_A(p) = w_B(p). That last condition is the heart of the matter: at equilibrium the two morphs have identical fitness.

Take a concrete linear model: w_A(p) = 1 − s·p and w_B(p) = 1 − s·(1 − p), where each morph is penalized in proportion to its own abundance with selection coefficient s. Setting them equal gives 1 − s·p = 1 − s·(1 − p), which solves to p* = 0.5. Whenever A exceeds 50% it pays the larger penalty and shrinks; whenever it dips below 50% it is rewarded and grows. The 50:50 point is a stable attractor. Change the relative slopes or add asymmetric costs and p* shifts away from 0.5, but the qualitative behavior — restoring force toward an interior value — is the signature of negative FDS.

The stability test is the slope of the fitness difference at the equilibrium. If d/dp [w_A − w_B] < 0 at p*, the equilibrium is stable (negative FDS). If the slope is positive, p* is a knife-edge and the population rolls off to fixation (positive FDS). When the fitness function responds with a time lag — for instance because a parasite needs generations to track the host — the restoring force overshoots and the system can settle into sustained oscillations rather than a fixed point. That lagged version is the engine of the Red Queen dynamics in coevolution.

Worked examples in real organisms

The scale-eating cichlid — the cleanest case

The Lake Tanganyika cichlid Perissodus microlepis eats scales torn from the flanks of other fish. Its mouth is asymmetric: a left-handed morph has a jaw twisted to the right and attacks prey from the prey's left side, while a right-handed morph does the reverse. The asymmetry is a single-locus, largely Mendelian trait. Prey fish learn to guard the flank that is attacked most often. So if left-handed predators become common, prey watch their left side, left-handed attacks miss, and right-handed predators — now rare — strike a poorly guarded flank and feed better. Their offspring increase, the prey shift their vigilance, and the advantage flips. Field counts by Hori (1993) and follow-ups show the left:right ratio oscillating around 50:50 with a period of roughly five years — one of the most direct demonstrations of negative FDS holding a polymorphism in place.

Batesian mimicry — protection that erodes with abundance

A harmless Batesian mimic copies the warning coloration of a toxic model. Predators that have been stung learn to avoid the pattern. But the protection is frequency-dependent: each encounter with a palatable mimic teaches the predator that the signal sometimes lies. While mimics are rare relative to the toxic model, almost every test bite is genuinely noxious and the signal stays honest. As mimics grow common, predators encounter more harmless "impostors," the deterrent weakens, and mimic fitness falls. This caps mimic abundance and can maintain multiple mimetic forms in the same species — the polymorphic females of the swallowtail Papilio dardanus are the classic illustration.

Plant self-incompatibility — the rare pollen wins

Most flowering plants reject their own pollen and the pollen of close relatives through self-incompatibility (S) loci. A pollen grain is rejected if it shares an S-allele with the stigma. Pollen carrying a rare S-allele matches few potential mates and is therefore compatible with almost every flower it lands on, while common-allele pollen is rejected often. The rarer the allele, the higher its reproductive success — textbook negative FDS. The result is spectacular allelic diversity: a single S-locus can carry dozens to over a hundred alleles in a population, far more than neutral processes could sustain.

MHC and the immune arms race

The major histocompatibility complex presents pathogen peptides to the immune system. Pathogens evolve to evade the most common MHC alleles in their host population, so individuals carrying rare MHC alleles resist infections that the majority cannot. This rare-allele advantage — reinforced by disassortative mate choice for novel MHC — keeps the locus extraordinarily polymorphic. The human HLA system now has more than 19,000 catalogued alleles, the most variable coding region in the genome, a diversity widely attributed to negative FDS layered on top of any heterozygote advantage.

Frequency-dependent selection versus heterozygote advantage

FDS is often confused with overdominance (heterozygote advantage), because both are forms of balancing selection that keep two alleles in a population. The distinction is mechanistic and matters.

Feature	Negative FDS	Heterozygote advantage
Source of balance	Fitness depends on morph frequency	Heterozygote has highest fixed fitness
Is fitness constant?	No — changes as frequencies change	Yes — each genotype's fitness is fixed
Best genotype	Whichever is currently rare	Always the heterozygote
Equilibrium set by	Where morph fitnesses cross, wA=wB	Ratio of homozygote selection coefficients
Maintains >2 alleles easily?	Yes (e.g. dozens of S-alleles, MHC)	Hard — classically two-allele
Canonical example	Scale-eating cichlid; MHC; S-alleles	Sickle-cell trait vs. malaria

A quick diagnostic: if you can change a genotype's fitness simply by changing how many copies of it exist around it, you are looking at frequency dependence. If its fitness stays put no matter the surrounding mix, you are looking at overdominance or plain directional selection.

Why it matters across biology

• Maintaining variation. Negative FDS is one of the few forces, alongside overdominance and spatially varying selection, that can hold a polymorphism stable over long timescales rather than letting one allele fix.
• Host–parasite coevolution. Rare-genotype advantage drives the Red Queen and is a leading explanation for the maintenance of sexual reproduction over clonal reproduction.
• Speciation and behavior. Disruptive negative FDS can favor extreme morphs, feeding character displacement and contributing to divergence.
• Public health. Antigenic and drug-target diversity in pathogens is shaped by FDS; rare strains escape herd immunity, which is why dominant influenza or SARS-CoV-2 lineages are periodically displaced by rarer variants.
• Conservation genetics. Small populations lose the rare alleles FDS would otherwise protect, collapsing MHC and S-locus diversity and raising disease and inbreeding risk.
• Game theory. Evolutionarily stable strategies — hawk-dove, alternative male mating tactics — are FDS recast as payoffs that depend on what everyone else is doing.

Common misconceptions

• "FDS means the rare type always wins." Only under negative FDS. Positive FDS favors the common type and erases the rare one.
• "It's the same as heterozygote advantage." Both balance, but FDS fitness is frequency-dependent; overdominance fitness is fixed.
• "FDS always settles to a steady ratio." Time-lagged negative FDS can oscillate indefinitely instead of settling — the Red Queen never stops running.
• "Rare is better because of low competition." Plain density dependence isn't FDS. FDS is specifically about the fitness of a phenotype relative to the frequency of that phenotype, not total population size.
• "It maintains only two morphs." Negative FDS readily sustains many — dozens of S-alleles, thousands of MHC alleles.