Biological Signals as Handicapsby Alan Grafen

Alex Kiam and Josh Elkington

QuestionAre biological signals honest?

In other words, do animals’ signals or “advertising” reflect their actual quality?Are

Question

Are biological signals honest?

Earlier biologists disagreed as to whether this is true

Paper creates model to try to resolve this conflictAre

Game Theory: The study of strategic decision making

Can occur naturally without conscious decisions made by players (i.e. evolutionarily)

The “game” in question is attracting female mates, the players are males, and the strategies are how much to advertise one’s biological fitness

Nash equilibrium: a game is in Nash equilibrium when no player can improve its payoff by switching strategies

Equilibrium Stable Strategy

Nash equilibrium for a population that occurs through evolution

Zahavi Handicap Principle

Each organism maximizes their own fitness with honest signals

In the mating game, signalling is costly and is more so for low quality males

Receivers know that the signal indicates quality because inferior quality signallers cannot afford to produce such wastefully extravagant signals

Model● q is true quality of male● a is level of advertising by male● p is perceived value of male by female● fitness (w) of males depends on a, p, and q

A* is the male’s best level of advertising

Model● fitness (D) of females depends on discrepancy between p and q

P* is female’s best level of assessment

Model● For Equilibrium Stable Strategy of males and females, signals

are honest, advertising is costly, and more efficient for better males to advertise more

Main ResultsSurprisingly, the model shows that over time, the optimal strategy for all players is to advertise honestly

● Males begin with quality that increases with high advertising

● Male fitness depends on number of mates (p^r where r>0)

● As r increases, the level of advertising for all males increases

ESS of A and P

Fitness of Males

Main ResultsOne interesting conclusion is that the lower the fitness of the lowest male, the more the highest male has to advertise

Importance● The paper proves that the Zahavi Handicap Principle can be

satisfied for an ESS model● The model can be applied to many types of signalling other than

mating

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ImportanceModel can also be used to describe competition between birds in a nest being fed by a parent and predator-prey interaction

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Model shows that signalling requires waste, such as the cost of jumping high, in order to ensure honesty

Assumptions/Limitations● Males who advertise more are perceived more highly by

females, and being perceived more highly improves fitness● Advertising is costly, and is costlier for lower quality animals● Males with more mates are fitter● Animals can’t tell each other’s level of fitness without

advertising

Summary

1. Animals pay a cost of advertising2. This cost of advertising ensures honest communication3. This principle is a good way to model many types of animal interactions beyond mating