Michael Lachmann
   
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butterflieCostly Signalling

Background

We encounter signalling everywhere. You are now reading a signal that I transmit to you. An alarm clock prompts us to get going in the morning. We stop at a trafic-signal when it is red.

Animals do also employ signals. Birds sing, dogs bark, butterflies have pretty patterns on their wing - among countless other examples.

The problem

Any time you have communication, there is a potential for deceit. If I write something like: "If you send me $1000, you will be happier.", you sadly infer that that is not a true statement, and I get nothing. Other times, you do believe signals that are received. Why can animals believe signals that they receive? A signal that is always false stops being a signal. So how come there are any signals that are believed in the animal world?

Alarm calls are good exmaples: the boy who cried wolf too many times when there was no wolf was ignored when his signal was actually most crucial. His signal "Wolf!" had lost its meaning. Alarm calls in the animal kingdom have not lost their meaning yet, so they must not be used too often as lies.

There are several explanations for how this could be. First, if the interests of the signaler and the receiver coincide, then signals should be honest, and heeded. The alarm calls that parents give to their kids fit into this category, because the interests of parents and kids are closely intertwined -- after all, the heritage of the parents is in the hands of their kids, and is lost if the kids are lost. But, as any teenager will confirm, even the interests of parents and kids do not always coincide.

The handicap principle

Another explanation for the prevalence of honest signalling was proposed by Amotz Zahavi in 1974. If the lie is costly to its sender, costlier then the benfit that can be gained from the lie, then signals can be believed. Consider the example of a peacock with a beautiful tail. Since peahens prefer to mate with peacocks that have more beautiful tails, it is assumed that a nice tail means something like:
" I am a strong, high quality male. You should mate with me."
But if that is true, then why don't all males grow big beautiful tails? The answer that Zahavi gave is that if a weak male grew a huge beautiful tail, it would not survive for very long. It would have a hard time runing away from predators. The benefit that the weak male would gain, mating with more females, would be smaller than the cost of lying, a higher predation risk. Strong males, on the other hand, suffer a smaller predation risk when carrying a big tail - they are still able to run/fly quite fast. For them the benefit of mating with more females does overcome the predation cost.

Mathematical modeling

It took some time till the biological world accepted Zahavi's explanation. In 1990, Alan Grafen published two papers that showed that the handicap principle could indeed work. He gave an example in which males advertise their quality, and females wish to assess this quality as precisely as possible. He showed that certain cost functions (how much does it cost to send a certain signal) will make signalling stable, i.e., that signals can be believed.

Our work

Models of the type that Grafen introduced usually had the following form: the signaller knew of some property of the world, that the listener did not know. For example, the male peacock "knows" his own quality, which the peahen does not. A cost function is introduced, which says "how much will it cost a signaller who knows that the world is x, to send a signal saying that the world is y?"
The handicap principle then gives conditions on this cost function, so that as mentioned above, the benefit from lying is smaller than the cost for lying.

So, the signaller signals, pays a cost, and the listener listens, and responds. The signals are honest and everybody benefits.
Or do they? Are the participants actually better off?
In our paper "Signalling among relatives. I. When is signalling too costly?" we compared the average benefit of the signaller, and the average benefit of the listener, to the average benefit that they would have without signalling. We did this for the case of signalling between relatives, for example offspring to mother. It turned out that for biologically plausable scenarios, signalling was actually so costly as not to be worthwhile! Because of the high cost that honesty demanded, both signaler and receiver were worse off with signalling than without!

Pools

But we do see signals in the animal world. Chicks do seem to signal their parents that they are hungry. Does it mean that in all those cases all participants would actually be better off without the signal? The answer to that is not fully known yet. It could indeed be that signalling is too costly. It could also be that there is another explanation for why signalling is not actually so costly as not to be worthwhile. In the paper "Signalling among relatives. II. Beyond the Tower of Babel" we showed one possible explanation for this paradox: previous models had assumed that the listener at the end of the interaction knows exactly what the signaller knows: Different signallers always send distinct signals. In the peacock case, it means that if one male has quality x, and another quality y (and y is different from x) then the tail length of x will on average be different from that of y. But that does not have to be true. It could be that males z, y, x, and w all have tail length a, and males v, u, t, and s all have tail length b. This is called "pooling" - the signallers are pooled into groups that send the same signal. Or, if we talk about signalling of hunger from chick to mother, it could be that chicks up to a certain hunger level send one signal, and above that level a second signal. It turns out that by pooling one can find stable signalling in which signalling is worthwhile (and in "Signalling among relatives. III. Talk is cheap among relatives" we showed that with pools one can even find stable signalling without any cost!)

Only pooling?

So, is that the answer? Can only signals using pools be worthwhile? Not neccessaraly. In the paper: "Cost and conflict in animal signals and human language" we showed that cost is not neccessary for honest signalling. As stated above, lying needs to be so costly as not to be worthwhile. But, how much do you need to pay to tell the truth? In the examples that were mentioned above, quite a lot - too much. But that is not neccessary. It is possible to construct cost functions for which signalling will be honest, but telling the truth will be very cheap.

The truth, the whole truth, and nothing but the truth

One example for such a cost function is one we all know from everyday life. For humans, it is usually very cheap to tell the truth. Lies have a chance to be detected and punished. A witness in court will not have to pay anything for telling the truth, but a lie can be very costly.

Still open

So, it all depends on the cost function. If animals managed to find one of these "magic cost functions" that make signals honest and cheap, then signalling could be worthwhile. It could be that signalling is worthwhile because of pooling. It could be that signalling is worthwile for other reasons. Or it could also be that signalling actually is detrimental. We need to find experimental methods to address these questions.