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The conundrum of how additive genetic variation is maintained in the face of consistent female preferences in lek mating species is known as the "lek paradox". Female preference for a male sexual trait confers a genetic benefit to their offspring. Under directional sexual selection, this should lead to decreased genetic variance for that trait. This should, in theory, lead to "runaway selection" as described by R. A. Fisher, leading to fixation of the trait within the population and a corresponding dissaption for the benefits of female preference. However, female preference still confers a genetic benefit for offspring fitness within mutliple species. The reason why this paradox is considered in regards to lek mating is that there are no direct benefits received by the female (i.e. nuptial gifts, parental care) which could explain this presence of variation in other mating systems. Multiple theories have been posited over the years to explain preservation of variation within the male population in regards to the sexual trait, and the corresponding benefits of female preference.

Mutation
Mutation alone can significantly impact genetic variation, especially in smaller populations. Results of a 1999 study on the fruit fly Drosophila melanogaster revealed that deleterious mutations could account for about one half of the genetic variation within life history traits.

Condition-dependent hypothesis/genic capture
One potential resolution to the lek paradox is Rowe and Houle's theory of condition-dependent expression of male sexually selected traits. Based on the handicap principle that sexual ornaments allow females to judge male quality, Rowe and Houle argue that sexually selected traits depend on physical condition (condition is a term they used to refer to an organism’s ability to acquire and allocate resources). Condition, in turn, is affected by a large number of genetic loci, including those involved in metabolism, muscular mass, nutrition, etc. As resources are allocated to one of these traits, there are less resources available to allocate to others. Allocation of resources to sexual traits over other life history traits could lead to a decline in condition. Those males that are able to acquire enough resources to allocate to both sexual traits and other life history traits will have the best fitness (handicap principle). Rowe and Houle claim that condition dependence maintains genetic variation in the face of persistent female choice, as the male trait is correlated with abundant genetic variation in condition. This is the genic capture hypothesis, which describes how a significant amount of the genome is involved in shaping the traits that are sexually selected. There are two criteria in the genic capture hypothesis: the first is that sexually selected traits are dependent upon condition and the second is that general condition is attributable to high genetic variance. Genetic variation in condition-dependent traits may be further maintained through mutations and environmental effects. Genotypes may be more effective in developing condition dependent sexual characteristics in different environments, while mutations may be deleterious in one environment and advantageous in another. Thus genetic variance remains in populations through gene flow across environments or generation overlap. In addition, because this theory allows for variation is spread out across multiple loci, there is more retention of mutations within the population.

The condition theory has broad implications. Modern theorists often talk about certain parts of the condition dependence model; either how the environment can impact condition dependent traits (availability of resources) or how antagonistic pleiotropy with life history traits impacts sexually selected traits.

Resource availability
Under this model, in a resource abundant environment, males will be able to allocate more resources to all condition dependent traits, including the sexually selected trait. Therefore, in resource abundant environments, the full range that an individual’s genome can express will be shown through the trait, and because of this, genetic variance in respect to that trait is expected to decline in this type of environment. Conversely, as resources become scarce, genetic variation is expected to contribute more to the phenotypic variation.

In a study conducted in 2000 at the Galton Laboratory, the condition dependence of the sexual trait of stalk length in stalk eyed flies was tested. Stalk eyed flies were raised on four different food sources: corn (nutrient rich), spinach, and cotton (nutrient deficient). After a number of generations, the genotypes, the sexual trait of male eye stalk length (recording eye stalk length as a proportion to body length in order to control for body length), and a number of nonsexual life traits (body size, mass, wing span) were measured. The data showed that there was statistically significant greater genetic and phenotypic variation within eye stalk length (both absolute length and length independent of body size) within the resource poor environment when compared to the control.

Male lesser wax moths, Achoria grisella, use ultrasonic signals to attract mates. In a University of Kansas experiment in 2000, two male sexual traits associated with ultrasonic signals (signal rate and peak amplitude of ultrasonic signals used in mating) were tested for condition dependence. Artificial selection was used to create four separate lines: a population with high peak amplitudes, high signal rates, lower peak amplitudes, and low signal rates. These lines were then placed into six different environments: one control, one with low temperature, one with low temperature and a lower food supply, one with a reduced quality food supply (less honey), and one high temperature environment. Statistical analysis revealed that there was a significant correlation between the environment and the phenotype plasticity of the traits, and that variation was greater in experimental environments when compared to the control for both the high and low lines.

Negative pleiotropy
If an individual male, resources are allocated to a multitude of condition dependent life history traits that are expected to increase fitness alongside sexually selected traits. It is because of this interplay or energetic trade off that is expected to increase genetic variation. Rowe and Houle pointed to the examples of a multitude of bird species, whose energetic investment in mating calls could attract predators and inhibits the amount of time and energy that could be spent foraging for food. It is because of this trade off that there is a certain point where allocation of resources to that trait can be deleterious for the overall condition of the individual.

Poecilia reticulate guppies have several sexual traits (alongside life history traits) that positively correlate with female preference, including carotenoid based-orange color spots, an enlarged caudal fin, and melanin induced black spots Genes coding for orange and black spots are linked to the Y-chromosome. In a 2011 study,  Poecilia reticulate were allowed to inbreed for 8 generations under three different treatments: low inbreeding (10 males and 10 females), intermediate inbreeding (10 families: 5 males and five females), and high inbreeding (where 5 males and 5 females chosen from the previous generation were randomly selected and were allowed to breed). When this was compared to a control population (where inbreeding was prevented), the inbred populations had significantly smaller orange spots, caudal fins, and black spots (all these differences were independent of absolute body size). After allowing the populations to breed in their condition for two more generations, the inbred populations were outbred with unrelated individuals. When the outbred offspring were analyzed however, no significant increase in sexual traits occurred, which indicated that alleles leading to further expression of these traits were successfully purged from the inbred population. Researchers concluded that inbreeding caused an inbreeding depression that eventually lead to the death of unfit individuals. Those individuals that had genetics for high gene expression allocated more resources to sexual traits, and thus could not cope with the deleterious heterozygous alleles imposed on them through inbreeding, thus leading to purging. It should also be noted that orange spots in Poecilia reticulate were found to not be environmentally dependent in other experiments, which may give further credence to this finding.

In the grey treefrog, Hyla Versicolor, both male call duration and male call rate are selected for by females. However, there is a tradeoff between call rate and call period, meaning that those males that have calls for a long duration cannot call as often, and those that have a fast call rate cannot sustain as a long a call. A study at the College of Charleston, South Carolina in 2011 analyzed call rate and duration within a population of frogs which were placed in simulated wild environments. The researchers concluded that there was a genetic basis this antagonistic relationship.

Selection for Outbreeding/Heterozygosity
Fitness frequently decreases with inbreeding by affecting a multitude of traits. This can convey advantages such as disease resistance and the deletion of deleterious alleles The model put, forward by Jane M. Reid, relies on four assumptions: 1) that variation within the inbreeding coefficient (f) 2) the presence of an inbreeding depression of the sexually selected trait 3) a fitness benefit for outbreeding must be generated due to a decrease in fitness with increased inbreeding 4) the population must be structured in such a way that inbred individuals are more closely related to the set of mates. Under this model, genetic variance is maintained because females select for it.

In song sparrows, females are known to prefer males with larger song repertoire sizes. Males who had larger song repertoires bred earlier and are more likely to mate .. In an isolated population of song sparrows on Mandarte Island (which are all marked, and whose social pedigree had been documented since 1981), a 2007 study conducted by James M. Reid found that song repertoire size in male song sparrows was negatively correlated with the male’s mean kinship with the female population (calculated by taking the average of an individual male’s kinship with each possible female mate pair).

Antarctic fur seals, Arctocephalus gazelle, migrate during mating season to colonies of largely static lekking males. A 2007 study in Bird Beach, South Georgia, 76.5% of females did not mate with the closest male upon arrival, travelling up to 35 meters. DNA analysis indicated that there was a negative correlation between distance travelled by the female and interrelatedness between the mating pair. However, interactions between male-female IR and heterozygosity suggested that heterozygous males are less attractive if they have a high IR with the female. A graph that plotted observed heterozygosity or homozygosity at each loci with distance travelled by the female yielded statistically insignificant, yet positively sloped, results indicating that the effect of fitness is genome-wide

Frequency-Dependent Selection
The Hamilton and Zuk model addresses the lek paradox, arguing that the cycles of co-adaptation between host and parasite resist a stable equilibrium point. Hosts continue to evolve resistance to parasites and parasites continue to bypass resistant mechanisms, continuously generating genetic variation. They applied this theory specifically to MHC genes in vertebrates which are involved with the delivery of antigens to the immune system. Under this model MHC allele frequencies should undergo cycles within a population, and MHC alleles should predict the expression of sexual ornaments.

A long term study of MHC1 allele frequencies within a population of reed warblers indicated that the frequency of the MHC1 B4b allele had fluctuated over the years. In a study of human populations, HLA-11 alleles confer resistance to the Epstein-Barr virus, but only in populations where the HLA-11 allele is rare (suggesting an evolutionary “arms race” between the virus and resistance.

In 1997 a study conducted by Torbjörn Von Schantz and his colleagues revealed that in pheasants spur length (which was found to be positively correlated with age, viability, and body size) was increased in pheasants that possessed specific alleles in the MHC gene. In a 2005 study in Australia, adult male sand lizards were collected during mating season. RFLP analysis indicated that some of the males had an allele not found in others. Males that had this allele were more aggressive, more resistant to parasitism by ticks, and had increased mating success

Weakness of Sexual Selection
Another theory is that sexual selection on its own is not strong enough to deplete genetic variance, and as such, there is no lek paradox. This will occur if the sexual ornament or selected trait is not a reliable indicator of fitness increasing genes, or if males can utilize alternative mating tactics to hinder directional sexual selection.

In several species of ungulates, there is a preference for females to mate with males that are located toward the center of a lek rather than a male on the periphery. In 2011, Jakob Bro-Jørgensen studied this phenomena in the topi antelope in the Olare Orok Conservancy in Kenya. His study found that, while on average the antelopes located at the center of the lek were larger and stronger than those on the periphery, there was a tendency for smaller males on the periphery to shift into the center. He also found that those males that moved from the periphery (in the first year of observation) to the center (in the second year) had a significant increase in mating success. In addition, peripheral males that did not show signs of territorial However, it was also noted that these shifting males had lower competitive ability then those established in the center, as they had a short tenure in these areas when challenged by other males.

Buff-breasted sandpipers are lek mating shorebirds. Males wattract females by elaborate flights and ground displays, leading to the male leading the female to a small depression where copulation takes place. Observational data collected from a population of lek mating buff-banded sandpipers in 1996 indicated that there were certain males that had higher mating success and had much higher solicitations of females by males than others. However, the researchers ran a paternity test that conflicted with the conclusions of this data. In a paternity test, it was found that only 6.8% of males sired more than four young (the modal number of offspring) within the year, and that overall variation was lower than reported in the observational analysis. They also concluded that each clutch was only sired by one male, indicating more of a monogamous relationship. Researchers theorized that the males may have used alternative mating methods (such as mimicking female behavior to steal a mating attempt), which increased the mating success of birds that did not necessarily have the most exaggerated sexual trait.