Frequency-dependent selection occurs when the fitness of a phenotype, genotype, or allele varies with its relative abundance in the population.
Frequency-dependent selection occurs when the differential survival and reproduction of organisms in a population depends on the trait (allelic, genotypic, or phenotypic) frequencies of other conspecifics in the same population. It is common in nature and perhaps even the norm for most biological systems (Dieckmann and Ferriere 2004). Traits that affect mating success, resource competition, and predation, for example, often generate situations where the relative fitness of a trait variant depends on its frequency in the population. Despite its ubiquity, frequency-dependent selection is too often neglected when reasoning about selective processes.
Types of Frequency-Dependent Selection
There are two basic varieties of frequency-dependent selection: negative frequency-dependent selection and positive frequency-dependent selection.
Negative frequency-dependent selection has clearly garnered the lion’s share of attention in evolutionary population biology. It occurs whenever the fitness of a trait decreases as its frequency relative to competing trait variants in a population becomes greater. Put simply, becoming more common makes a trait, along with the organisms that bear it, less fit.
Undoubtedly, the most celebrated example of negative frequency-dependent selection comes from the work of Carl Düsing and subsequent articulation by Ronald A. Fisher, after whom it has come to be called “Fisher’s Principle” (Fisher 1930; Edwards 1998). It has been shown that, for any out-breeding sexual species, the probability of an individual being able to breed depends on the frequency of its own sex in relation to the opposite sex. The explanation of equal sex ratio begins by assuming that the reproductive cost of producing a female is equal to that of producing a male and, then, stipulating a biologically realistic scenario in which excess females are born to the parents (P) of first-generation offspring. In such circumstances, any first-generation offspring (F1) of the male sex would have better mating prospects on average than any first-generation offspring of the female sex. Consequently, a first-generation (F1) male tends to contribute more offspring on average to the subsequent second-generation (F2) than its female counterpart. Now, from the perspective of the original parental generation (P), any genetic disposition to produce more male offspring will have been favored by natural selection as it yields more average grandoffspring (F2). Genes for producing male offspring are accordingly expected to spread in the population until the sex ratio reaches 1:1 (50% male, 50% female). At that point, however, the selective advantage which accrued to genes for producing male offspring ceases since males no longer have better mating prospects than females of the same generation. The sexes then have equal relative fitness. Furthermore, capacities that produce females will be at a selective advantage whenever there are excess numbers of male offspring. Whereas the male phenotype and any genetic mechanisms which bias gamete formation in its direction were favored in circumstances of excess female production, exactly the opposite holds true when there are excess numbers of male offspring. There is thus a pendulum-like frequency change in evolutionary dynamics which stabilizes around the equilibrium sex ratio of 1:1 and ultimately explains why a sex-determination mechanism yields equal proportions.
Examples of negative frequency-dependent selection abound. Within biological game theory, which focuses exclusively on phenotypic traits (or strategies) and the optimal outcomes (or payoff states) of episodic natural selection, an organism playing an aggressive or confrontational strategy known as “hawk” will flourish in a population comprised primarily of passive players known as “doves.” However, a dove will tend to do better in a population composed mainly of hawks (Maynard Smith 1982). It has recently been shown (Kokko et al. 2014) that the head-color polymorphism of red and black Gouldian finches (Erythrura gouldiae) strongly supports the game-theoretical model for limited aggression in an animal population. The aggressive red morph is behaviorally dominant and successfully invades black populations, but when red “hawks” become too common, their fitness is severely compromised via decreased parental ability. Other studies indicate negative frequency-dependent selection for self-sterility alleles in plants, handedness in the feeding morphology for scale-eating cichlid fish, and male reproductive strategies in a marine isopod (Stevens 2011).
For a human example, we need to look no farther than studies of host-pathogen coevolution. The African sleeping sickness parasite (Trypanosoma brucei) sequentially changes surface antigens as hosts develop antibodies. Host antibodies tend to target the most common antigens, and negative frequency-dependent selection preserves genetic diversity of parasite antigens as well as genetic diversity of the antibodies in their hosts (Stevens 2011). Overdominance or heterozygote advantage presents yet another interesting example in this area. Overdominance occurs when the heterozygous genotype is selected over either of the homozygous genotypes. The classic case involves sickle-cell disorder in malaria-ridden regions. There is a frequency-dependent component in this case because rare (deleterious recessive) alleles are disproportionately found in heterozygous genotypes, whereas common alleles are disproportionately found in homozygous genotypes. So rare alleles always appear to have an advantage.
Positive frequency-dependent selection often goes unmentioned alongside its more oft-cited counterpart. It is, nevertheless, no less important to evolutionary dynamics. Positive frequency dependence occurs when the fitness of a trait variant increases as its frequency relative to competing trait variants in a population becomes greater. In other words, becoming more common makes a trait type, along with the organisms that bear it, more fit.
Perhaps, the most uncontentious example of positive frequency dependence is that of Müllerian mimicry (Müller 1879). Consider, for example, viceroy and monarch butterflies. Both species share an honest color indication of their unprofitability (noxious taste) to predators in the form of bright orange wing coloration and pattern. It is likely the case that predators (e.g., birds) must kill a certain number of individual butterflies with a certain signal before they learn to avoid it. When predators must learn to avoid only one signal instead of two or more distinct signals, it decreases any individual butterfly’s risk of being killed. By sharing an honest warning signal, then co-mimic species can benefit from the shared mortality costs of educating the predators to avoid that signal. An increase in the number of any of the co-mimics should benefit all, as the more individuals there are that share the honest signal, the lower the per capita predation risk. Consequently, rare signal variants that are not genuinely distasteful or simply much less distasteful to predators should be at a disadvantage (Ihalainen et al. 2008).
The Importance of Positive and Negative Frequency-Dependent Selection
Frequency-dependent selection is apparently widespread in many natural populations. While the extent of its scope is a somewhat recent discovery, the phenomenon of frequency-dependent selection has been entertained since the work of Charles Darwin. Why, then, is so much current research focused on elucidating frequency-dependent selection?
Answering this question requires briefly revisiting the general features of natural selection. As resources are limited, there will be heightened intraspecific competition among individuals within a population who bear distinctive heritable trait variants. Insofar as these trait variants differentially affect the average probability of survival and reproduction for the individuals that bear them, the frequency of such traits will systematically change across generations. Trait variants that increase relative fitness tend to become more common or even go to fixation, while less fit variants correspondingly decrease or possibly disappear. This is the (oversimplified) microevolutionary basis for adaptation and ultimately the macroevolutionary phenomenon of speciation. Note that the role of natural selection is primarily one of culling existing variation and, thereby, continually adapting populations to deal with local environmental challenges to survival. The explanatory problem is that most populations exhibit abundant genotypic and phenotypic variation which cannot alone be explained by observed rates of mutation or migration.
It is precisely at this point where the appeal of negative frequency-dependent selection becomes clear. Because becoming more common reduces the fitness of a trait variant, rare trait variants can be maintained. Here is an explicit way to maintain genetic and phenotypic variation in a population that does not rely on reference to a spatially or temporally variable environmental. Negative frequency-dependent selection is thus typically considered a form of “balancing selection” in that it explains the preservation of variation and extends the possibility of evolutionary rescue.
Positive frequency-dependent selection, in contrast, amplifies the effects of directional selection. Other things being equal, directional selection in finite populations will increase the relative frequency of the fittest trait variants and eventually drive them to fixation if unencumbered. Positive frequency dependence simply accelerates this process since it increases the relative fitness of a common trait variant as its relative frequency increases. There will correspondingly be ever stronger selection against rare variants as they become scarcer. This can obviously have dramatic consequences regarding the rates of adaptive evolutionary change.
Conclusion: The Conceptual Challenge of Frequency-Dependent Selection
Frequency-dependent selection makes fitness values depend on a constantly evolving trait distribution in a population. As such, an individual cannot reliably transmit its fitness to its offspring even when it has the capacity to transmit its traits with perfect fidelity. But if fitness is not stable across generations because of frequency dependence, then mean fitness in a population will not necessarily increase. Gene frequencies might just cycle indefinitely without ever attaining equilibrium (Rice 2004, p. 14). This is a bleak outcome, for it threatens to sever the intuitive explanatory link between natural selection and adaptation.
Responses to this rather dire possibility have fallen largely into two camps. In order to preserve the causal and explanatory connections between natural selection and adaptation, some contend that individual fitness can be maximized despite the apparent problem posed by frequency dependence. Notable among those who are so inclined is the theoretician Alan Grafen, who has dubbed his approach the “Formal Darwinism Project” (Grafen 2009). An altogether different response can be found in a research program that is based on the mathematical framework known as “adaptive dynamics” or “evolutionary invasion analysis” (Geritz et al. 1998). This approach arose in the early 1990s largely in response to the conceptual difficulties posed by frequency-dependent selection. It extends evolutionary game theory to account for more realistic ecological dynamics, and it can incorporate both frequency- and density-dependent selection. Only time will tell whether either of these responses suffices to meet the challenges posed by frequency-dependent selection.
I would like to acknowledge the grant that currently funds my research: ARC Australian Laureate Fellowship project A Philosophy of Medicine for the 21st Century (Ref: FL170100160).
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