Handicaps and Signalling

1. Handicaps and Signalling How models can help

2. Lecture Plan • Handicaps suggested by Zahavi (1975) • Handicaps contested • A model of the handicap principle • Lessons from the model

3. Lecture Plan • Handicaps suggested by Zahavi (1975) • Handicaps contested • A model of the handicap principle • Lessons from the model

4. 1. Context of new ideas and contest of principles 2. Anecdotal biology 3. Modellers as judges

5. “The utility of articles valued for their beauty depends closely on the expensiveness of the articles. A homely illustration will bring out this dependence. A hand-wrought silver spoon, of a commercial value of some ten to twenty dollars, is not ordinarily more serviceable... than a machine-made spoon of some “base” metal such as aluminium, the value of which may be no more than some ten or twenty cents.” Then he argues that the silver spoon is often a less effective contrivance as a spoon, and considers the point that it is a more beautiful object. What is the nature of this concept of beauty? He points out that 1. Silver is 100 times more valuable but not in itself intrinsically more beautiful or mechanically serviceable 2. If a spoon were to appear to be hand-wrought but in fact was only a very good imitation, then it would not be valued very highly 3. If only the lighter weight betrayed the nature of an imitation spoon, it would not be more valued than an ordinary aluminium spoon. Thus we have a ‘pecuniary canon of taste’. That is, beauty is what displays wealth. Thorstein Veblen (1899) The Theory of the Leisure Class: an economic study of institutions. Page 94.

6. In the view of economic theory the expenditure in question is no more and no less legitimate than any other expenditure. It is here called "waste" because this expenditure does not serve human life or human well-being on the whole, not because it is waste or misdirection of effort or expenditure as viewed from the standpoint of the individual consumer who chooses it. ... But it is, on other grounds, worth noting that the term "waste" in the language of everyday life implies deprecation of what is characterized as wasteful.... Relative or competitive advantage of one individual in comparison with another does not satisfy the economic conscience, and therefore competitive expenditure has not the approval of this conscience. Thorstein Veblen (1899) The Theory of the Leisure Class: an economic study of institutions. Page 78.

7. Lecture Plan • Handicaps suggested by Zahavi (1975) • Handicaps contested • A model of the handicap principle • Lessons from the model

8. 1. Maynard Smith 1976 was first off the block 2. Became a favourite subject, with three locus population genetic models Maynard Smith 1976 Kirkpatrick 1986 (“The handicap mechanism of sexual selection does not work”) Pomiankowski 1987 (“Sexual selection: The handicap principle does work -- sometimes”) 3. Theoreticians argued, but also theoreticians intimidated other biologists.

9. Lecture Plan • Handicaps suggested by Zahavi (1975) • Handicaps contested • A model of the handicap principle • Lessons from the model

10. 1. Males must vary in a way that matters to females (call it ‘quality’), but is invisible to them 2. Males must express an observable trait, which can depend on ‘quality’. The male strategy is a function that says how the observable trait depends on quality 3. Females can draw an inference about the invisible trait from the observed trait. The female strategy is a function that says how the inferred quality depends on the observed trait.

11. Basic assumptions 1. The tail is costly i.e. a longer tail leads to lower fitness (all other things held equal) 2. A female’s fitness is higher, the more accurately she assesses the quality of males 3. A male is fitter the more highly his quality is assessed by females. Differential cost assumption 4. The ratio of the marginal cost of advertising to the marginal advantage of improved assessment must be an increasing function of quality

12. tail quality quality tail A male who has a short tail whatever his quality A female who views all males as average quality A male who has a longer tail if he turns out of higher quality A female who interprets a longer tail to mean higher quality A male who has a shorter tail if he turns out of higher quality A female who interprets a shorter tail to mean higher quality A male who has a long tail whatever his quality A female who views all males as high quality Can we find a male strategy and a female strategy such that, if the population is all playing those strategies, an individual couldn’t increase his or her fitness by choosing a different strategy?

13. tail quality quality tail A high quality male could gain by breaking the rule and having a shorter tail -- the tail would cost less and females would rate him just the same. Therefore this is no equilibrium. Can we find a male strategy and a female strategy such that, if the population is all playing those strategies, an individual couldn’t increase his or her fitness by choosing a different strategy?

14. tail quality quality tail A low quality male could gain by breaking the rule and having a shorter tail -- the tail would cost less and females would rate him of higher quality, so he gains all round. Therefore this is no equilibrium. Can we find a male strategy and a female strategy such that, if the population is all playing those strategies, an individual couldn’t increase his or her fitness by choosing a different strategy?

15. tail quality quality tail A female would gain by deviating from the population strategy and estimating the quality of a male to decrease with tail length, as this is how the males are behaving. Therefore this is no equilibrium. Can we find a male strategy and a female strategy such that, if the population is all playing those strategies, an individual couldn’t increase his or her fitness by choosing a different strategy?

16. tail quality quality tail Males can’t gain because they have minimum cost tail length and females aren’t attending to tail length Females can’t gain because males are providing no information about quality. Therefore this is an equilibrium -- the ‘non-signalling equilibrium’. Can we find a male strategy and a female strategy such that, if the population is all playing those strategies, an individual couldn’t increase his or her fitness by choosing a different strategy?

17. tail quality quality tail Females are correctly inferring quality from tail length -- so they are optimal. Provided longer tails are costlier for lower quality males, then neither low nor high quality males can gain by changing. Therefore this is an equilibrium -- the ‘signalling equilibrium’. Can we find a male strategy and a female strategy such that, if the population is all playing those strategies, an individual couldn’t increase his or her fitness by choosing a different strategy?

18. Lecture Plan • Handicaps suggested by Zahavi (1975) • Handicaps contested • A model of the handicap principle • Lessons from the model

19. What does the model do ‘locally’? • Shows Zahavi’s idea works • Makes assumptions explicit • Constructs a useful logical framework (strategy is a function) • Identifies the handicap model as about signalling, and shows how to make progress with signalling ideas

20. What does the model do more broadly? • Shows sexual selection can work without linkage disequilibrium • Focusses attention on ‘real’ benefits to mate choice • Moves towards a more complex view of animal’s decision-taking • Gives hope to non-modellers and tasks for modellers

21. How is the model inadequate? • Single, one-way signal; fixed roles • Quality is non-genetic (genetic is too hard to model) • One-dimensional signal • No uncertainty in perception • No ‘costs of receiving’ • Variation in ‘need’ not emphasised • Only two interactants • Cheating Johnstone (1998), Maynard Smith and Harper (2003)

22. Lecture Plan • Handicaps suggested by Zahavi (1975) • Handicaps contested • A model of the handicap principle • Lessons from the model

23. References Zahavi, A. 1975. Mate selection -- a selection for a handicap. J. theor. Biol. 53, 205-214. Zahavi, A. 1977. The cost of honesy (further remarks on the handicap principle). J. theor. Biol. 67, 603-605. Grafen, A. 1990a. Biological signals as handicaps. J. theor. Biol. 144, 517-546 Grafen, A. 1990b. Sexual selection unhandicapped by the Fisher process. J. theor. Biol. 144, 475-516 Johnstone, R.A. 1998. Game Theory and Communication, Chapter 5 (pp 94-117) of Game Theory and Animal Behavior (editors L.A. Dugatkin and H.K. Reeve, OUP) Maynard Smith, J and Harper, D. 2003. Animal Signals. (Oxford Series in Ecology and Evolution). Oxford University Press.