Over the weekend I attended a conference at the University of Chicago on The Biological Basis of Preferences and Behavior, and Balazs Szentes stole the show with a new theory of the peacock’s tail. In Balazs’ theory a world without large and colorful peacock plumage is simply not stable.
A large tail is an evolutionary disadvantage: it serves no useful purpose and it slows down the male and makes him conspicuous to predators. So why do genes for large tails appear and take over the population of male peacocks? Balazs’ answer is based on matching frictions in the peacock mating market. Suppose female peacocks choose which type of male peacock to mate with: small or large tails. Once the females sort themselves across these two separate markets, the peacocks are matched and they mate.
The female peacocks are differentiated by health, and within a peacock couple health partially compensates for the disadvantageous tail. In the model this means that healthy females who mate with big-tailed peacocks will produce almost as many surviving offspring as they would if they mated with peacocks without the disadvantage of the tail.
This substitution between the characteristics of female and male peacocks creates a selection effect in the mating market. Consider what happens when a small-tailed peacock population is invaded by a mutation which gives some male peacocks large tails. Since female peacocks make up half the population of peacocks there is now an imbalance in the market for small-tailed peacocks. In particular the males are in excess demand and some females will have trouble finding a mate.
On the other hand the big-tailed male peacocks are there for the taking and its going to be the healthy female peacocks who will have the greatest incentive to switch to the market for big tail. The small cost they pay in terms of reduced quantity of offspring will be offset by their increased chance of mating. The big tails have successfully invaded.
Once they have taken over the population (Balasz shows that under his conditions there is no equilibrium with two kinds of male peacocks) he same selection effect prevents small tails from invading. When a small-tail mutation appears all the females will want to mate with them. The market for small tail gets flooded with eager females up to the point where some of them are going to have a hard time finding a mate. Given this, each female must decide whether to take a gamble and try to mate with the small-tail male or have a sure chance of mating with a large tail.
The unhealthy females are going to be the ones who are most willing to take the risk because they are the least compatible with the large-tail males. This means that the small-tail mutants can only mate with unhealthy females and (under the conditions Balazs identifies) this more than offsets their advantage, they produce fewer offspring than the large-tails and they are driven out of the population.