A lek is an area where many males of a species come together and display. These displays can include very elaborate vocalizations, plumage, and behaviors such as the complex dances of some birds of paradise. The displays play a very important role in mate selection in these species because they are the only trait that the females who visit the lek have to judge which male to mate with. Males of lekking species do not hold territories where the female can raise her young and find food or provide parental aid in any other form. The females provide all the care for their young, so what are the females choosing in a mate? They are choosing genes. Males that have traits that make them attractive have the genes that code for those traits, and so the offspring of these males should also have those traits and be attractive. So, by choosing attractive mates, the females are maximizing the odds that their own genes will also be passed on to the next generation. This setting results in some theoretical complications in terms of sexual selection. One important one is that if females pick traits over and over again for generation after generation all the males will end up having the same traits. If all the males are the same, there will be no way for the females to tell which males are the fittest and therefore who to pick to mate with and the whole system will collapse. Yet this does not happen. So how is variation being maintained in the face of strong selection? This is the lek paradox.
Several solutions to the lek paradox have been proposed. One is that females may not choose the same trait every breeding season. This is often referred to as the fluctuating selection hypothesis (Jia et al. 2000), and it states that during one breeding season large males are favored, but then next breeding season it is males with the longest tails that are preferred, and the breeding season after that it is the loudest males that do the best. This basically describes fads in fashion. Also, preferences may not change breeding season to breeding season, but instead the large males may be favored for several seasons and then the shift to a different trait may be more gradual. Either way, these changing preferences would result in the maintenance of genetic diversity.
Another possible resolution is that females may disagree with one another as to the most important traits. This has been shown in Guppies by Brooks and Endler (2001) where females were allowed to chose between different males. Most females seemed to agree that large males were the most fit, but when females were presented with males of equal size, some preferred males with large amounts of orange on their tails, while others preferred males that more black spots on their sides. This disagreement would also maintain genetic variability.
A third proposed solution is that females are making an overall assessment of male fitness taking into account many traits. This idea is called the genetic capture hypothesis (Rowe and Houle 1996), and it states that overall fitness is dependent on many morphological and physiological features. In other words, for a male to be fit he must be able to find lots of food and escape predators and resist parasites etc. All these abilities are coded for by many many genes, and it is the sum total of these genes that the females are choosing.
These hypotheses are not mutually exclusive, so in all likelihood there is a combination of factors at work. But determining which is the dominant force is still an interesting goal, and still very much in dispute.