sexual selection

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun The process in nature by which individuals with certain traits, especially secondary sex characteristics such as colorful plumage and large antlers, are chosen more often for mating and thus pass those traits on to their offspring.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A type of natural selection, where members of the sexes acquire distinct forms either because the members of one sex choose mates with particular features or because in the competition for mates among the members of one sex only those with certain traits succeed.