Runaway sexual selection refers to one of the indirect benefits of sexual selection for females. When a preference for a certain trait exists within a species, it is beneficial for a female to mate with a male, or multiple males, with that trait. The idea behind this is, that while the female may not benefit at all from being choosy about the male she mates with, she increases the liklihood that her sons will share this trait, and be "sexy" or preferred by other females. When females prefer her sons, he stands a greater chance of producing more offspring. Because these offspring are related to the female and share some of her genetics, she is indirectly benefitting and increasing her own fitness. (Futuyma, 2005).
Often Irish Elk are used as a prime example of runaway sexual selection and how it can lead to extinction. It is said that female preference for large antlers lead the male Irish Elks to grow antlers so large that they were no longer able to fulfil the nutritional needs necessary for such large antlers, and thus went extinct. However, a study by Worman and Kimbrell (2008) showed that it was in fact the effect of lack of nutrients available to the females that most likely lead to the extinction of the species. Even if a certain trait is sexually selected for, that does not mean that natural selection cannot act on it as well. In the case of antler mass, size could be be changed due to natural selection, and these genetically variable secondary characteristics would simply be selected for in a different way in order to allow for the perpetuation of the species.
Futuyma, D. (2005). Evolution. Sunderland, MA: Sinauer Associates, Inc.
Worman, C., Kimbrell, T. (2008) Getting to the hart of the matter: Did antlers truly cause the extinction of the Irish elk?. Oikos, 117(9), 1397-1405