The peacock's tail is perhaps the best-known example of a costly signal or Zahavian "handicap". Let's look at how this signal operates.
Peahens choose mates from a pool of suitors. For simplicity we will assume that these peacock suitors are characteristically unhelpful once mating is completed; they provide sperm but little else by way of resources or parental care. Nonetheless these males vary in quality: some have better genes to offer.
Because the peahens cannot judge a male's genetic quality directly, they instead attend to signals that the males provide: peacocks advertise their quality via bright plumage and a long flamboyant tail. This advertisement is a handicap in the sense that it is energetically costly to produce and maintain, and it is possibly dangerously conspicuous as well.
The cost of producing a long tail varies among males. A weak and sickly
male can scarely afford to divert energetic resources from basic upkeep to the production
of ornaments, and moreover he would have a hard time escaping from a predator if
his flight was hindered by a long tail. A strong and healthy male, by contrast,
can readily afford the additional costs of producing bright colors and a
long tail, and moreover can usually escape a predator even when his flight
is somewhat restricted by the length of his tail.
Because only the high-quality males can afford bright colors and long tails, peahens prefer mates with these characteristics. High quality males, for their part, produce
these bright colors and extravegent plumes to ensure that they are
chosen as mates by females. Low quality males cannot afford to do so, and so they
will produce duller colors and shorter tails. (Perhaps next year they
will be stronger and thus will be able to be more ambitious in their plumage.)
And thus among peafowl, the bright colors and long tails
are honest signals of male quality, used by females to choose their mates. This is
the basic idea behind the use of the costly signals in a sexual selection context.
Of course, the costly signal need not involve bright coloration and extended
tail feathers; a big
rack of antlers, an elaborate song, a captured prey offered as a gift, or any
number of other expensive ornaments or gestures could serve equally well. Nor, for
that matter, must the male sex be the signalling sex. In some cases, females may use
costly signals to advertise their own qualities to male suitors.
Nur and Hassen (1984) lay out this basic argument with an
elegant graphical approach. Grafen (1990a,b)
provides a mathematical demonstration that such a system is evolutionarily
stable. Johnstone (1995) reviews the empirical evidence for this type of
sexual selection signalling. In addition, numerous other papers consider
the various subtleties of costly signalling in a sexual selection context.