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How Alan Grafen proves Zahavi's Handicap principle in sexual selection


Struggling with Amotz Zahavi's verbal model of 'stotting'
John Maynard Smith Scientist
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The notion is that if you see an antelope stotting - that's when they do these great leaps into the air - and I think this may well be right, I'm not contradicting it - they... when a predator is around, instead of running away as fast as they can, they run along and then they leap in the air, it's a very dramatic sight, and leap up like this. Zahavi's interpretation of that would be that it's a real handicap, if you're trying to get away from a predator, to leap in the air and then run, I mean, it slows you down. So the fact that the antelope is, so to speak, able to do this, is saying to the predator, 'Look, I'm so good, I can actually handicap myself by leaping up in the air like this and slowing myself down, and still get away, so forget it and don't bother to chase me.' Whereas, if it's rather a feeble antelope, it's running like hell to get away because it daren't stott. That's the sort of verbal formulation of it. The question to me was always: Can you formalise it? It's very much as it was with George Price's notion of retaliation, can you make a formal model of this which will show that the thing will work, because, for me, I can't operate with verbal models. I have to have a... a formal mathematical model, essentially because if you make a mathematical model, you have to say what you mean. You have to define your terms. And even if you don't, anybody else looking at the model can see what you must have assumed in order for the thing to go the way you say it does. And then the point of a mathematical model is really to make it absolutely clear what is being said. And after Amotz had published his original handicap model, I tried to formalise it. And I... in the context of sexual selection, which is the context in which he'd first talked about it, and I made a formal model of it, which didn't work, did not lead to the conclusions that he claimed it did. And I sent it to him and said, 'Look, Amotz, I'm in real trouble here, I'm obviously not modelling what you say I ought to be modelling because I'm not getting the answer you get. You know, where am I going wrong, where are the assumptions that I put into this model not what you think they ought to be?' And actually, it's... it was one of the worse weekends of my life. Amotz and I sat in the chairs that you and I are sitting in now, for a whole weekend, really, trying to come to terms with this. And when he left, Sheila said to me, 'He is not to come again.' And this is not because he misbehaved, but because I was in such an impossible mood at the end of it. I had... I felt, at the end of two days conversation, he hadn't understood a single word I'd said. And I found this very frustrating, arrgggh, you know, I was really... but I'm sure he felt the same. I think at the end of two days conversation he felt I hadn't understood a word he'd said, and I think we were both right. You know, information had not flowed between us. And it wasn't personal dislike, it was just a complete inability to understand somebody who thinks totally intuitively and verbally, and somebody who has to have it all made easy with... with maths. And I was left persuaded that there probably wasn't much in this, you know. I mean, that I could forget the handicap thing, if it couldn't be made clear, I wasn't going to bother with it.

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.

Listeners: Richard Dawkins

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".

Tags: George Price, Sheila Maynard Smith, Amotz Zahavi

Duration: 3 minutes, 23 seconds

Date story recorded: April 1997

Date story went live: 24 January 2008