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Frequency-dependent selection

Frequency-dependent selection is a mode of in in which the of a , , or varies as a function of its relative frequency in the , rather than being constant across all conditions. This dependence arises because interactions among individuals, such as , predation, or , create selective pressures that change with the composition of the . The concept gained prominence in the 1970s through reviews in and . There are two primary forms of frequency-dependent selection: negative and positive. In negative frequency-dependent selection, the fitness of a type increases when it is rare and decreases when it is common, often stabilizing polymorphisms by favoring rarity and preventing any single variant from dominating the population. Conversely, positive frequency-dependent selection occurs when the fitness of a type increases with its frequency, reinforcing the spread of common variants and potentially leading to fixation or loss of diversity, as seen in processes like positive . These dynamics are frequently modeled using , where strategies' payoffs depend on their prevalence, as pioneered by . Frequency-dependent selection plays a crucial role in maintaining , influencing , and mediating to changing environments, including scenarios of evolutionary rescue from . Recent studies, including meta-analyses as of 2024 and experiments in 2025, underscore its ubiquity in maintaining variation across taxa. Notable examples include color polymorphisms in damselflies, where preferences drive negative frequency-dependent selection on female morphs, and predator-prey systems like the scale-eating Perissodus microlepis, where left- and right-mouthed individuals balance via negative frequency dependence. In human-related contexts, it has been invoked in models of infectious dynamics, where pathogen evolves based on frequencies. Overall, this selective mode underscores how population-level interactions shape evolutionary trajectories beyond simple directional pressures.

Fundamentals

Definition

Frequency-dependent selection is a mechanism of natural selection in evolutionary biology wherein the fitness of a genotype or phenotype is not fixed but varies as a function of its relative frequency within the population. This contrasts with frequency-independent selection, in which the fitness of a genotype or phenotype remains constant irrespective of its prevalence in the population. In frequency-dependent selection, interactions such as competition, predation, or mating success among individuals cause the adaptive value of a trait to change depending on how common or rare it is relative to alternatives. This form of selection differs from other types, such as directional or , which generally operate under the assumption of constant values across varying distributions; frequency-dependent selection uniquely incorporates the population's composition as a dynamic that directly influences relative . To understand this , key concepts from are essential: the p represents the proportion of a specific in the ; w denotes the relative or survival rate of individuals carrying that ; and mean \bar{w} is the average across all in the population, serving as a normalizing factor. These terms build on the foundational principles of , where heritable variation in leads to changes in frequencies over generations. In mathematical terms, the change in \Delta p under selection can be expressed in a general form for a two-allele as \Delta p = \frac{p(1-p)(w_1 - w_2)}{\bar{w}}, where w_1 and w_2 are the marginal es of the two alleles, and \bar{w} is the population . Under frequency dependence, w_1 and w_2 are themselves functions of p, reflecting how allele interactions alter based on abundance. This formulation highlights how frequency-dependent selection can stabilize polymorphisms by adjusting dynamically.

Historical Context

The concept of frequency-dependent selection has roots in the early experimental observations of the modern synthesis era, where and noted that genotypic in populations of pseudoobscura varied with frequencies during laboratory studies of chromosomal inversions. This work, published in 1946, provided initial that selection pressures could shift based on relative abundances, building on Wright's earlier shifting from , which emphasized how drift and selection in subdivided populations could lead to dynamic frequency changes across adaptive peaks. and , key architects of the modern synthesis, had primarily modeled selection with constant coefficients, but these early findings highlighted gaps in explaining persistent genetic polymorphisms beyond simple . The concept was first formalized in the 1960s through theoretical and experimental advances in , particularly by , who demonstrated frequency-dependent effects in and mating success in species. Ayala's 1971 paper explicitly described how competitive fitness between species declines as their relative frequencies increase, providing a mechanistic basis for coexistence. This was followed by the seminal 1974 review by Ayala and Cathryn A. Campbell, which synthesized experimental evidence and theoretical models, establishing frequency-dependent selection as a key form of balancing selection that addresses limitations in the modern synthesis by maintaining polymorphisms through dynamic fitness interactions rather than solely . A major milestone came in 1969 with Bryan Clarke's analysis of negative frequency dependence in Batesian mimicry systems, where rare morphs gain protection from predators, promoting balanced polymorphisms in sympatric species. Clarke's subsequent 1979 review further solidified the empirical support for apostatic selection in mimicry and molecular polymorphisms, emphasizing its role in diversity maintenance. In the 1980s, John Maynard Smith integrated the concept into , using evolutionarily stable strategies to model frequency-dependent outcomes in behavioral interactions, as detailed in his 1982 book. Later evolutionary ecologists, such as , expanded the idea beyond to ecological contexts, incorporating frequency and in models of resource competition and social systems during the late 1970s and 1980s. This progression highlighted how frequency-dependent selection complemented the modern synthesis by providing a versatile framework for understanding evolutionary stability in complex, interactive populations.

Types

Positive Frequency-Dependent Selection

Positive frequency-dependent selection is a form of in which the fitness of a particular or increases as its frequency rises within a , thereby conferring a relative advantage to more common variants. This dynamic arises because rare phenotypes often experience reduced fitness due to mismatches with prevailing ecological or social conditions, while common ones benefit from alignment with those conditions. Key mechanisms driving this process include social conformity, where individuals gain advantages by matching dominant behaviors in group interactions, such as in the of traits among group-living ; predator avoidance through majority signaling, as predators more readily learn to avoid widespread warning patterns; and resource specialization, where frequent phenotypes optimize exploitation of specific niches, enhancing efficiency as they become prevalent. The fitness landscape under positive frequency-dependent selection can be modeled with functions where relative fitness rises linearly with frequency, such as w(p) = 1 + s p, with s > 0 representing the positive selection coefficient and p the frequency of the phenotype. Here, the fitness of the common type exceeds that of rarer alternatives, creating a snowball effect that accelerates the spread of the dominant variant. Equilibria where frequencies are low for the advantageous type are unstable, as any slight increase in frequency tips the balance toward further proliferation, while deviations decrease it toward elimination. Evolutionarily, this form of selection typically results in the loss of , as it drives the fixation of a single or , reducing polymorphism within the . Unlike negative -dependent selection, which favors rarity and sustains diversity, positive -dependent selection promotes uniformity by rewarding commonality. A conceptual diagram of this process illustrates a payoff matrix where the common strategy yields higher against itself and especially against rare alternatives, depicted as an upward-sloping curve with on the x-axis and relative on the y-axis, showing divergence from the unstable low- toward fixation at p = 1.

Negative Frequency-Dependent Selection

Negative frequency-dependent selection is a form of balancing selection in which the fitness of a phenotype or genotype declines as its frequency within the population increases, thereby providing a relative fitness advantage to rarer variants and promoting genetic diversity. This process favors the persistence of multiple alleles or morphs by ensuring that uncommon types experience higher per capita reproductive success compared to abundant ones. The mechanism underlying this selection often involves negative biotic interactions that disproportionately affect common types while allowing rare types to evade disadvantages. In predation scenarios, rare prey phenotypes are less likely to be detected or preferentially targeted by predators, which develop search images or biases toward prevalent morphs, leading to elevated survival for the uncommon variants. Similarly, in -parasite systems, rare genotypes incur lower rates because parasites or pathogens are adapted to exploit the most frequent types, resulting in reduced parasite load for rarer hosts. For , common phenotypes face intensified rivalry for limited resources, such as niche overlap in or use, which saturates their fitness gains and diminishes their competitive edge relative to rarer competitors with access to underutilized opportunities. These interactions create a feedback loop where the rarity itself confers , amplifying the selective against dominance by any single type. Mathematically, the of a under negative -dependent decreases as a of its p; a simple linear example is given by w(p) = 1 - s p, where s > 0 is the , ensuring that relative is highest when p is low and declines as p approaches 1, thus benefiting . More generally, curves exhibit a negative with respect to , often crossing to allow mutual invasibility between types. The evolutionary outcomes of this selection include stable polymorphism, where multiple phenotypes or alleles coexist at equilibrium frequencies determined by the balance of their frequency-dependent fitnesses, preventing fixation or loss of variants. It can also generate cycles in allele frequencies, with rare types rising in abundance until they become common and subsequently decline, or establish protected polymorphisms that safeguard rare alleles from elimination even under genetic drift. Equilibria arise when the average fitnesses equalize, typically around intermediate frequencies where no single type holds a net advantage. A conceptual diagram illustrating this process typically shows a balancing selection curve plotting relative against : the line for a given starts high at low frequencies (enabling invasion by rares), slopes downward as frequency rises (reflecting declining fitness for commons), and intersects the line (often at y = 1 for relative ), demonstrating how rare alleles spread while common ones recede until coexistence is achieved.

Mathematical Models

Population Genetic Frameworks

In , the foundational framework for modeling frequency-dependent selection begins with the discrete-generation model for a diallelic locus in an infinite, randomly . The change in from one generation to the next is given by \Delta p = \frac{p q (w_A(p) - w_a(p))}{\bar{w}(p)}, where p is the frequency of A, q = 1 - p is the frequency of a, w_A(p) and w_a(p) are the frequency-dependent marginal fitnesses of the alleles, and \bar{w}(p) = p w_A(p) + q w_a(p) is the mean fitness. This generalizes the standard selection model by allowing fitnesses to vary as functions of p, capturing how interactions among genotypes influence evolutionary change. A continuous-time approximation facilitates analytical tractability for gradual changes, particularly when generations overlap or selection is weak. The dynamics are approximated as \frac{dp}{dt} = p(1-p) s(p), where s(p) represents the frequency-dependent selection gradient, often defined as s(p) = (w_A(p) - w_a(p)) / \bar{w}(p) or a similar normalized difference in relative fitnesses. This describes the rate of evolution as a product of genetic variance p(1-p) and the selective advantage, enabling predictions of trajectories toward fixation or polymorphism under varying dependencies. Equilibria occur where \Delta p = 0 or dp/dt = 0, which holds when w_A(\hat{p}) = w_a(\hat{p}) = \bar{w}(\hat{p}) at some interior frequency \hat{p}. For stable polymorphism, local stability requires that the selection gradient diminishes as the becomes more common, specifically when \partial (w_A - \bar{w}) / \partial p < 0 evaluated at \hat{p}. This condition ensures that deviations from \hat{p} induce restorative selection, maintaining genetic variation; conversely, the opposite inequality leads to unstable equilibria and potential loss of polymorphism. These models assume an infinite population size to neglect stochastic drift, random mating with no linkage disequilibrium beyond the locus of interest, discrete non-overlapping generations (or continuous approximation thereof), and absence of mutation, migration, or other evolutionary forces. Extensions to finite populations incorporate drift via diffusion approximations but retain the core deterministic dynamics for large N. Such frameworks apply to both positive and negative frequency-dependent selection by specifying appropriate forms of w_A(p) and w_a(p).

Game Theory Applications

Evolutionary game theory provides a framework for modeling frequency-dependent selection by incorporating strategic interactions among individuals, where the fitness of a strategy depends on its frequency in the population. In the 1970s, John Maynard Smith integrated classical into evolutionary biology, adapting concepts from economics to analyze animal behavior and selection pressures that vary with strategy prevalence. This approach emphasizes payoffs from interactions rather than fixed traits, allowing for the prediction of stable outcomes under frequency dependence. A central concept is the evolutionarily stable strategy (ESS), which is a strategy that, if adopted by most individuals in a population, resists invasion by alternative strategies. Formally, a strategy I is an ESS if, for any mutant strategy J \neq I, either the expected fitness of I against a population of I exceeds that of J against I, denoted w(I, I) > w(J, I), or if w(I, I) = w(J, I), then w(I, J) > w(J, J). Here, fitnesses w are frequency-dependent, calculated as weighted averages of payoffs based on the proportions of strategies encountered. This criterion captures how selection favors strategies that perform well against themselves while exploiting or resisting rarer alternatives. The Hawk-Dove game illustrates these principles in conflicts over resources, such as territory or mates, with two pure strategies: (escalate to fight) and Dove (display and retreat). The payoff assigns values based on outcomes: Hawk versus Hawk yields (V - C)/2 for each (where V is resource value and C > V is fight cost), Hawk versus Dove yields V for Hawk and 0 for Dove, and Dove versus Dove yields V/2 each. Let p be the frequency of Hawk; the of Hawk is then w_H(p) = p \cdot \frac{V - C}{2} + (1 - p) \cdot V, and for Dove, w_D(p) = p \cdot 0 + (1 - p) \cdot \frac{V}{2}. When C > V, no pure strategy is an ; instead, a mixed ESS emerges at p^* = V/C, where rare strategies have higher , exemplifying negative frequency-dependent selection that maintains polymorphism. Invasion analysis shows that deviations from p^* favor the underrepresented strategy, stabilizing the equilibrium. These models link directly to types of frequency-dependent selection: negative dependence often produces cycles or stable mixtures, as in Hawk-Dove where increasing frequency reduces a strategy's relative payoff, promoting diversity; positive dependence can yield , with two pure ESSs where the invading strategy fails if the resident is common, leading to alternative stable states based on initial conditions. Such dynamics highlight how strategic interactions drive evolutionary outcomes beyond simple frequencies.

Examples

Predation and Mimicry

In , multiple species of unpalatable or toxic organisms evolve similar warning signals, such as bright coloration patterns, to deter predators collectively. This system exemplifies positive frequency-dependent selection (FDS), where the fitness of a mimetic morph increases as its frequency rises in the population. Rare morphs experience higher predation rates because predators are less likely to have learned to avoid them, whereas common morphs benefit from shared defensive education of predators across the mimicry ring. For instance, field experiments using artificial models matching local wing patterns demonstrated that predation by birds was significantly higher on rare morphs compared to common ones, supporting positive FDS in maintaining convergence. Apostatic selection represents a form of negative FDS in predator-prey interactions, where predators develop search images for abundant prey morphs, resulting in disproportionately higher predation on common phenotypes and relative safety for rare ones. This mechanism helps maintain color polymorphisms in prey populations by favoring rarity. In guppies ( reticulata), natural populations exhibit extreme male color pattern diversity, which is sustained by such predation-driven selection. Mark-recapture studies in wild Trinidadian streams showed that male guppies with rare color patterns had higher survival rates than those with common patterns, providing direct evidence of negative FDS acting on visual polymorphisms. Host-parasite often involves negative FDS, where rare host genotypes confer resistance to prevalent parasite strains, thereby preserving at loci like the (). molecules present parasite antigens to the , and heterozygosity or rare alleles enhance resistance to common pathogens, preventing any single genotype from dominating. In (Ovis aries), variation correlates with juvenile survival and resistance to intestinal nematodes (strongyles), with rare alleles showing superior protection against circulating strains. This dynamic maintains high MHC polymorphism through antagonistic . Laboratory experiments with and its bacterial parasite Pasteuria ramosa illustrate negative FDS in host-parasite systems, where infection success depends on matching host and parasite genotypes, akin to predation rates varying with genotypic . In coevolution assays, rare host clones resisted common parasite isolates more effectively, leading to fluctuating selection that sustains clonal diversity. These controlled infections revealed that parasite transmission rates declined for common host-parasite combinations, mirroring frequency-dependent predation dynamics and supporting the role of such interactions in polymorphism maintenance.

Social and Mating Systems

In systems, positive frequency-dependent selection can arise when females preferentially select males exhibiting the most common traits, thereby accelerating the fixation of those traits within the population. This dynamic is exemplified in models of in , where preferences for prevalent male phenotypes create a that reinforces the dominance of common types. For instance, O'Donald's encounter models demonstrate that partial choosiness by females leads to frequency-dependent success, favoring common male traits and hastening their spread under positive selection pressures. Such mechanisms contrast with rare-male advantages but highlight how conformity in mate preferences can drive rapid evolutionary fixation in insect populations. Social foraging behaviors in birds often exhibit positive frequency-dependent selection through , where individuals adopting the majority strategy gain advantages in group dynamics. In experimental studies with house sparrows, rare joining strategies are exploited by conformist groups, reducing the of nonconformists and favoring the spread of common tactics. This promotes efficient resource exploitation in flocks, as individuals copying the prevalent experience higher success rates when personal information conflicts with . Similar patterns occur in wild populations, where positive frequency dependence stabilizes group-level foraging norms, enhancing overall in variable environments. Negative frequency-dependent selection plays a key role in maintaining in microbial biofilms via mechanisms that punish rare cheaters. In bacterial communities, such as those formed by species, rare cheater mutants exploiting public goods like extracellular polymers face targeted suppression through mechanisms like quorum-sensing-mediated policing, which reduces their relative fitness when infrequent. This dynamic ensures that cooperation persists, as the advantage to cheaters diminishes with their commonality, stabilizing polymorphic populations. Empirical tests with confirm that cheaters undergo negative frequency-dependent selection, with their invasion success limited by group-level sanctions that favor cooperators in biofilms. Such processes underscore how enforces in microbial social systems. Field studies on in the elderflower (Dactylorhiza sambucina) reveal negative frequency-dependent selection favoring rare flower morphs through enhanced . In this rewardless species, purple and yellow morphs exhibit a polymorphism maintained by preferences, where rarer colors receive disproportionately higher visitation and rates due to generalization and search . Manipulative experiments altering morph frequencies demonstrated that rare morphs achieve up to twofold greater male and female , directly attributing this to negative selection dynamics. This mechanism parallels ecological processes like predation but operates via behavior in reproductive systems, sustaining floral without rewards.

Implications

Polymorphism Maintenance

Negative frequency-dependent selection serves as a primary mechanism of balancing selection, counteracting the tendency for to drive alleles toward fixation by favoring rarer variants within a . This dynamic process ensures that no single dominates, thereby preserving genetic and phenotypic over time. A classic example involves the (HLA) system, where extensive allelic is sustained by pathogen-driven negative frequency-dependent selection. Pathogens adapt to exploit common HLA alleles for immune evasion, conferring a selective advantage to rarer alleles that better resist and thereby perpetuate high polymorphism levels across human populations. Different ABO blood types confer varying resistance to infectious diseases, including caused by , contributing to balancing selection that maintains polymorphism. The genetic outcome of this selection regime is the establishment of protected polymorphisms, in which multiple coexist at stable equilibrium frequencies greater than zero. Under negative frequency-dependent selection, the relative of an allele rises as its frequency falls, creating a feedback loop that stabilizes diversity and resists erosion by other evolutionary forces. This results in populations harboring a broader array of genotypes than would occur under constant or positive frequency-dependent selection. Strong empirical support for polymorphism maintenance comes from the (HLA) system, where extensive allelic diversity is sustained by pathogen-driven negative frequency-dependent selection. Pathogens adapt to exploit common HLA alleles for immune evasion, conferring a selective advantage to rarer alleles that better resist and thereby perpetuate high polymorphism levels across human populations. Despite its efficacy, negative frequency-dependent selection's ability to maintain polymorphisms is conditional and can fail under certain demographic and ecological pressures. In small populations, dominates, randomly fixing or eliminating and overriding the stabilizing effects of selection. High rates similarly undermine persistence by homogenizing frequencies across subpopulations, disrupting the local rarity advantages essential for balance; effective maintenance requires selection strengths that surpass both (inversely proportional to ) and intensities.

Evolutionary Dynamics

Frequency-dependent selection (FDS) profoundly influences long-term evolutionary processes by shaping rates, promoting , and driving coevolutionary dynamics. In particular, positive FDS accelerates the fixation of beneficial traits in fluctuating environments, as the increasing of an advantageous variant enhances its relative , creating a loop that hastens its spread to fixation once it surpasses an initial threshold. This mechanism contrasts with constant selection, where fixation proceeds at a more linear pace, and is especially relevant when environmental shifts favor initially rare innovations, allowing populations to track changes more rapidly. Mathematical models of FDS have demonstrated that such dynamics can enhance overall adaptive potential under variable conditions. FDS also contributes to speciation by fostering reproductive isolation through frequency-dependent mate preferences. In cichlid fishes of African lakes, such as species in the genus Pundamilia, females exhibit preferences for conspecific male coloration that intensify when rare phenotypes are involved, selecting against hybrids and promoting genetic divergence. This negative FDS in mating systems generates disruptive selection, accelerating the evolution of prezygotic barriers and explaining rapid radiations, as seen in Lake Victoria where declining speciation rates align with predictions from frequency-dependent models of mate choice. Such processes highlight FDS's role in macroevolutionary diversification without requiring ecological niche partitioning. In coevolutionary contexts, negative FDS sustains oscillatory dynamics in host-parasite interactions, embodying the where hosts must continually evolve to counter evolving parasites. Experimental coevolution between the Potamopyrgus antipodarum and the trematode Microphallus sp. revealed that common host genotypes decline in frequency under parasite pressure, while rare genotypes increase, leading to cyclic shifts in genotypic dominance over generations. This rare-type advantage drives perpetual arms races, maintaining and preventing fixation of any single resistance strategy, as parasites adapt to prevalent hosts, thereby fueling ongoing . Contemporary applications of FDS underscore its relevance to human-induced evolutionary challenges, notably in the spread of antibiotic resistance. In clinical populations of carrying extended-spectrum β-lactamase plasmids, rare resistant strains exhibit higher relative fitness at low frequencies due to negative FDS, facilitating their rapid proliferation even without antibiotics and stabilizing resistance at intermediate levels post-exposure. This dynamic explains the persistence of resistance genes in bacterial communities, complicating control efforts and illustrating how FDS can amplify adaptive responses to selective pressures like use.

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