The late British biologist John Maynard Smith (1920-2004) is famous for applying game theory to the study of natural selection. At Eton College, inspired by the work of old Etonian JBS Haldane, Maynard Smith developed an interest in Darwinian evolutionary theory and mathematics. Then he entered University College London (UCL) to study fruit fly genetics under Haldane. In 1973 Maynard Smith formalised a central concept in game theory called the evolutionarily stable strategy (ESS). His ideas, presented in books such as 'Evolution and the Theory of Games', were enormously influential and led to a more rigorous scientific analysis and understanding of interactions between living things.
In the context of sexual selection, the male or the males want to persuade the females to mate, the females want to choose a good male. The males vary in what Alan calls quality, and that's what the female wants, she wants a male of high quality, for some reason, perhaps he'll look after the kids well, or something. But she can't detect quality, all she can detect is the signal the male makes. In the model, the male has to decide, in terms of his quality, how expensive a signal he'll make. It's like, you know, how much money will you spend buying the girl a big meal or a ring or something, it's really how much will I spend to try and persuade this female that I'm the chap. But the higher their quality, the more expensive a ring they can afford to buy without ruining themselves. So, by looking at the signal, which is costly, the female can actually deduce what the male's quality must be. And by choosing males with a more expensive signal, they get males with a higher quality. And what Alan showed, by some pretty filthy mathematics, if I may so, it's well above my head, much of it, but it's OK, is that it could be evolutionary stable for the higher quality males to make more expensive signals, and for females to choose the males which made the more expensive signals. It is, in other words, and I think Alan intended it to be, in fact he says he intended it to be, a model of the intuitive ideas that Amotz Zahavi was expressing, and it works. And I think it's an important paper. And it made me, and I think others, take it... take the original idea seriously, because now we have, you know, we can see what is actually being said, or the context in which it is being said.
Can you put your finger on where we went wrong before?
Yes, yes I can, though it's a little difficult to explain verbally. It's... it's... well I think there are two things, one which is quite explicit in Alan's paper and the other one of which is not. The thing that is explicit in Alan's paper is this, that he assumes that... supposing I hold... the signal consists of holding up a flag or something, and it's expensive to hold up this flag for some reason or other, the idea... what has to be true is that if I'm a high quality male, it doesn't cost me very much to hold up the flag, because I'm so strong I can hold it up without it costing me very much. If I'm a low quality male, it costs me more. It's as if when the young man goes in to buy the ring for the girl, if he's not very well off, they charge him more. It seems a bit unfair, but it's perfectly plausible, in a biological context, that a high quality male might be able to do something without it costing very much, whereas a low quality male, it costs him a lot more. And it's that cost... making cost dependent upon your quality which makes the model work. And in my model, I didn't attempt to model Amotz's thing, I didn't put that in because I don't think Amotz said it, and I was trying to model what he said. And unfortunately, Amotz was not able to put his finger on it and say 'But look, John, you've assumed that, and I don't... I want you to assume something different'.
So the essence is that in Alan Grafen's model, the low quality male has to pay the cost, whereas in your interpretation of Zahavi's original model, the low quality male would have elected not to even try... to pay.
But also, I think a more important thing was that in my version, the cost would be the same for the low quality and the high quality male, whereas in Alan's version, the high quality male pays less, because he's so strong it doesn't cost him much. Yes. And it turns out to make the crucial difference as to whether the things works or not.
Title: How Alan Grafen proves Zahavi's Handicap principle in sexual selection
Richard Dawkins was educated at Oxford University and has taught zoology at the universities of California and Oxford. He is a fellow of New College, Oxford and the Charles Simonyi Professor of the Public Understanding of Science at Oxford University. Dawkins is one of the leading thinkers in modern evolutionary biology. He is also one of the best read and most popular writers on the subject: his books about evolution and science include "The Selfish Gene", "The Extended Phenotype", "The Blind Watchmaker", "River Out of Eden", "Climbing Mount Improbable", and most recently, "Unweaving the Rainbow".