The Theory of Honest Signalling

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Introduction: Part 1

Introduction: Part 2

The Basic Problem

The Basic Solution

Honest signalling in biology

Zahavi's handicap principle

Grafen's model

Attracting mates

Begging for food

Deterring predation

Contesting resources

Autumn color

Honest signalling in economics

Conspicuous consumption


The mathematics of honest signalling

Signalling as a game


Other resources

Carl T. Bergstrom

Using Mathematica

Contact Information

Department of Zoology
University of Washington
Box 351800
Seattle, WA 98195-1800

Honest signalling from prey to predator:
Alarm calls and stotting displays

How can animals use costly signals to deter predators?

When threatened with predation, animals from a wide range of species produce alarm calls; these calls are typical thought to be warnings intended for other individuals of the same species. However, several authors have offered an alternative interpretation: some alarm calls may be intended for the threatening predator itself. For example, prey may be able to deter pursuit by informing a predator that it has been detected, and thereby persuading the predator to look for an easier catch elsewhere. We consider an example of this kind of signal below. Similarly, prey may be able to deter pursuit by convincing a predator that they are particularly skilled at escape, or particularly dangerous if attcked. Some authors have suggested that this is why gazelles engage in stotting behavior - spectacular leaping displays - when they see approaching predators. The leaping displays may serve to demonstrate the athletic prowess of the stotting prey, and persuade predators that any attempts at pursuit will be futile.

In their 1997 book The Handicap Principle, Zahavi and Zahavi describe a putative example of prey signalling awareness to predators, based on their observations of Arabian babblers. When a member of a feeding babbler flock spies a predator, it lets out a shrill "barking" alarm call. The birds in the flock may initially dive for cover, but often the entire flock joins the initial signaller atop the tree, all loudly issuing alarm calls. As Zahavi and Zahavi point out, this behavior is not easily explained as a warning to other babblers. If the calls were intended for the others in the flock, why would the birds continue calling long after the entire flock has joined in? And why would the babblers employ such a loud alarm call, which may attract the further attention from predators, when a much softer call would seemingly be sufficient to alert the other members of the flock?

Zahavi and Zahavi conjecture that the answer to these questions is that the alarm calls are actually directed to the predator, rather than to conspecifics. By barking loudly, the babblers inform the predator - say, a raptor - that it has been seen, and that any attack will likely be unsuccessful.

This explanation raises an additional question, however. If alarm calls actually deter the raptor's attack, why would a babbler not gain from calling indiscriminately, even before sighting a predator, on the off-chance that one is present? Zahavi and Zahavi offer an answer to this puzzle as well:

"A babbler who would cheat by going to the top of the canopy and barking before it saw a predator would expose itself to raptors it might not have noticed. That risk helps ensure that if a babbler goes to the top of the tree and declares it has seen a raptor, it has indeed seen one"


While verbal arguments of this sort seem plausible, they are difficult to evaluate without a formal mathematical model. For this reason, Michael Lachmann and I developed a general game-theoretic model in which prey signal awareness to predators. Our analysis concentrates on signals of awareness; a number of other mathematical models have been developed to investigate signalling of escape ability, such as the stotting displays used by gazelles. These include papers by Nur and Hasson (1984), Vega-Redondo and Hasson (1993), and Yachi (1995).

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Last modified September 4, 2002
Copyright © 2002 Carl T. Bergstrom