Game theory and the peacock's tail

Over at Cheap Talk, Jeff Ely has posted on a presentation by Balazs Szentes at The Biological Basis of Preferences and Behavior conference. Ely writes:

Balazs Szentes stole the show with a new theory of the peacock’s tail. …

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. …

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.

Szentes’s theory illustrates the mixed feelings I expressed in my recent post about some of the presentations at the conference. The model underlying the theory is clever and interesting, but Szentes’s focus is more on the game theory than the evolutionary problem that the model is proposed to address. The model offers limited insight into the evolution of the peacock’s tail as the assumptions underpinning the model do not hold.

First, the model requires an assumption of monogamy, which peacocks are not. As for most males with ornaments, the peacock’s tail is used to attract multiple partners to make up for the handicap that the ornament imposes (as the more established theory suggests). The model also assumes that the males are indifferent as to who they mate with (despite being monogamous), with high quality females unable to attract male interest above that of females of low quality.

Without those assumptions, the findings derived from the model no longer hold. In some respects, the sexes in the model appear backward, as a lack of males willing to give sperm is not an issue in most species. The low investment by males makes females the scarce resource.

I expect that these issues are of less concern to Szentes (or, based on his post, Ely) than they are for me, as his interest lies more in the model than its particular application. Szentes appeared to be aware of these critiques when they were raised at the conference.

If the model is not useful in explaining the peacock’s tail, what situation might the model describe? Instead of talking of disadvantaged males with tails, could we talk of low quality males and use the model to explain the persistence of low quality males in a population? This is an interesting model looking for a use.

*The videos are many of the presentations are now up.

One thought on “Game theory and the peacock's tail

  1. Do they even understand the concepts of predation, pattern-recognition, and camouflage? Those are all elements critical to understanding this model that they are challenging, of which they, or you–it’s not immediately apparent to me–seem to be entirely overlooking–the old model’s not concerning itself simply with a matter of assuming the ‘scarcity’ or ‘abundance’ or ‘quality’ of mate availability, it’s about the apparent fact that the trait itself is ‘not’ scarce within the male peacock population, despite it presenting no clear survival advantage, and a distinct disadvantage to the males in question–and yet they are able to survive to pass the trait on, and for it to be exhibited in prevalence within the species. The big fancy tail is not apparently advantageous to an actual peacock, when compared with the relatively dull-colored, small-tailed peahen’s camoflauge, yet the big fancy tail seems to persist expressly in the male half of the population–why? That is still a completely reasonable question to ask.

    Also, on a side note: Beginning any behavioral theory with the line ‘suppose x chooses’, rather than with evidence of an observed behavior, is quite the motivated leap in logic. ‘Suppose’ we are living in a world where peacocks do not actually exist, and are actually a means toward making human social commentary? But then, ‘Suppose’ there is no correct way to feel about human society, and we would all be better off ruled by aliens from outer space? Suppose that pickaxes in human faces are homeopathic. We can ‘suppose’ endlessly in any which direction we please. It’s called ‘fantasy’. But suppose that we fantasize in front of a speeding train? Was that train simply fantasized? We can go on and on like this forever, never really getting anywhere, masturbating philosophically until we are run over. Suppose that a different tactic is called for, please?
    There is no necessity for a supposition of ‘choice’ in this model, dead, eaten peacocks, are simply not viable mates for peahens to ‘choose’ from–so for what reasons does the trait not seem to self-eliminate and get the damn things killed before being able to pass on the trait? That is the question that the model your friend is assaulting, proposed to try and answer.
    The classical assumption is that the mutation is needless, but has nevertheless come to be visually associated by the female of the species as a clear and easy visual signifier of a male that can survive attempts at predation, despite the apparent handicap. It’s presumed to be a phenotype loosely associated with the health of the bird in question, or some other under-observed aspect of its physiology that lends to its survival that is not as readily visible. To go anywhere further with such a model, we’d first have to do more than suppose that some kind of ‘choice’ is taking place, and actually search for the existence of such a selection mechanism, otherwise all we are left with is philosophical fantasy masturbation. The fact of the matter is: the ornate-tailed male peacock does survive, it does continue to impregnate the filthy slut–err, peahen–and this ‘continues’, through time, and is thereby ‘sufficient in quality’, or at least, sufficient enough from the perspective of scientists observing peacock populations, to be able to continue observing that characteristic for as long as such studies have been conducted. Why? Are we just looking at too small a sample size of peacocks? Is this trait, in actuality, gradually on the verge of disappearance from the population? Is there any evidence of the comparable success of the muted color patterns and short tails, in the population, that are being overlooked, missing in the data? Is the entire base premise of the original theory faulty somehow? These are the sorts of questions that need asked.
    The idea that you would step around these questions and look for ‘something else’ to apply the model to anyway, rather than discarding the aspects of the model that don’t work, and re-examining your base assumptions, is not what I would consider good science. If you have a map, and it suggests you walk off a cliff, you don’t go looking for alternative uses for that map in helping you navigate a different aspect of another fantasy city, you rework the parts of the map that are lacking in detail, or which offer demonstrably false details–up to and including discarding the whole map and starting fresh, if it is not representative of the phenomena you are taking into account.
    That is how you do a Science. It’s not whatever you and your friend are doing–apparently looking for alternative uses for some rusty old discarded hedge trimmers you found while standing on a railroad track together. Keep them away from me, please.

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