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The Graded-Signals Hypothesis
The graded-signals hypothesis was first suggested by Nunn in 1999, and suggests that exaggerated sexual swellings exist in female primates to indicate their fertile period to the males of the species; a larger swelling suggests that ovulation is more likely to occur, thus increasing the female's fertility.

Inter-sexual conflict is considered, within this hypothesis, to be a key factor in the development of exaggerated sexual swellings. As male reproductive strategies of coercion (including infanticide and prolonged mate-guarding) may be costly to females, it has been necessary for females to resist these, through developing features or counter-strategies that will protect them whilst still allowing for successful reproduction. This can be explained through the combination of a number of previous hypotheses; most notably obvious-ovulation, best-male, and many-males.

In terms of obvious-ovulation, the swelling of the perineal skin has been likened to a distribution curve that would represent that probability that the female would ovulate, with larger swellings suggesting that ovulation is more likely to occur. As such, females are more likely to attract the attention of dominant, or "better", males when their swelling size peaks, and it has been shown that dominant males tend to only mate-guard at this peak swelling point, thus including the best-males hypothesis. This mate-guarding is costly to the male, and so they tend only to monopolise any single female for the most likely period of ovulation; once her swellings start to shrink, the male will move onto a female whose swellings are still growing to reach their peak. In these periods before and after the peak, females still continue to mate with lower-ranking males, as their probability of ovulation is not so high, but conception is still possible. This then serves to confuse the paternity of the offspring amongst the males, linking to the many-males hypothesis, and also resulting in reduced infanticide by the males within the species. Therefore, the protective role of the swellings against male coercion serve, in some ways, to manipulate male behaviour into benefiting the female, and enhancing the female's chances at successful reproduction.

As one of the more recent hypotheses, the graded-signals hypothesis still has limited research supporting it as the evolutionary function of sexual swellings. However, the growing literature base is supportive of the hypothesis; if not as the sole reason behind the evolution of the swellings, then perhaps in conjunction with the reliable indicator hypothesis.

The Reliable Indicator Hypothesis
Having reasoned that the best-male and many-males hypotheses did not fully explain why estrus must be advertised so prominently, Pagel proposed the reliable indicator hypothesis, suggesting that exaggerated swellings evolved through sexual selection due to the need for an honest signal of female quality (both their likelihood of conception and their genetic quality)  as a result of female-female competition to attract males. The hypothesis makes several assumptions: that females compete for access to male mates; that females differ in quality; that the characteristics of their sexual swellings honestly reflect these differences; and that males use certain swelling characteristics to allocate their mating efforts to the highest quality females. Should this be the case, swellings should occur in communities consisting of multiple adults of both sexes, in which males are the choosier sex due to the high mating costs of such groups, and when female competition is at its greatest. Such conditions have been described as "reversed sexual selection", as it is the females that ultimately make the mate choice in most species, and seemingly only this hypothesis that suggests the opposite.

For such a signalling system to be a reliable indicator of quality, it must fulfil two criteria: that the trait is costly to produce, and that mating effort is costly for the males in the group. In regards to sexual swellings, both of these ring true. In terms of costliness, swellings affect a female's weight and centre of gravity, affecting their ease when travelling. The skin itself increases vulnerability to predators due to its conspicuousness, as well as to infection. Additionally, the increased attention from males also puts females at a risk of injury through male aggression. In terms of the cost to males, mate guarding has been found to significantly reduce foraging in male baboons, therefore reducing their available food. Additionally, males expend effort in both grooming and consorting the female with whom they are mating, as well as warding off other males; the more attractive the female is, the greater the male-male competition, therefore increasing the risk to the male, as fights between baboons are potentially lethal.

Although Pagel performed a field experiment which found support for all predictions of the hypothesis through the observation of olive baboons (Papio anubis), its methodology has since been criticised, and subsequent research has failed to find empirical evidence that sexual swellings reliably indicate female quality in this, and other, species (e.g. chimpanzees, mandrills, and barbary macaques). For example, one of the main predictions is that higher quality, and therefore most fertile, females should consistently display the largest swellings. However, the largest swellings often occur in the least fertile females, or those least likely to raise surviving offspring; adolescents, those that have never borne offspring, and those that have had several ovulation cycles without conceiving.

Despite the lack of empirical evidence for this hypothesis being the sole evolutionary function for exaggerated sexual swelling, it has been suggested that the reliable indicator hypothesis may work together with the graded-signals hypothesis. This suggestion is based on evidence that swelling size advertises the level of fertility, and therefore reproductive quality, between one female's ovulation cycles, rather than between the overall quality of each female. Therefore, males may initially use swelling size as a cue to identify which females are close to ovulation (as predicted by graded-signals), before considering each females' swelling size as an indicator of their quality, and then choosing the female with the larger swelling (as predicted by reliable indicator). This would also account for the variable patterns in swelling size fluctuation across species and populations.

The Cost-of-Sexual-Attraction Hypothesis
Wrangham proposed the cost-of-sexual-attraction hypothesis as a result of comparing the number of sexual cycles between conceptions that are experienced by both parous and nulliparous female chimpanzees, as well as parous Western and Eastern chimpanzees (Pan troglodytes verus and Pan troglodytes schweinfurthii), and the size of the sexual swellings that came with these differences. Through observing these groups in both species, he suggested that the most important factors in determining how obviously a female displays the ovulatory stage in her cycle are the level of scramble competition that exists between the females of the group for resources such as food, and also the difference in travelling costs for parous and nulliparous females.

With the assumption that females require a certain number of copulations before they can conceive, this would suggest that they would achieve this number faster either by having a high number of ovulatory cycles between conceptions, or by appearing more attractive to males around the time of ovulation by having larger swellings. However, more obvious ovulation leads to more male coercion, which may have negative consequences, such as undesired consortship from a low-ranking male, or injury from forcible mating. Therefore, females will only accept this high level of coercion if the scramble competition in their community is high, and if the coercion will allow them to reach their required number of copulations in a short time. For example, Eastern chimpanzees who have previously produced offspring tend to experience high within-group scramble, and so are driven towards having fewer ovulatory cycles between conception. As a result, they need to mate with a high number of males during each ovulatory period. They therefore need to appear more attractive during these periods, and so they develop larger sexual swellings.

Although Wrangham's model was justified by his observations, there has not been much other support for the hypothesis. Deschner and Boesch investigated the hypothesis directly by observing the same species and found that it was unable to support their results, and so proposed the social passport hypothesis as an alternative.