Grasshopper communication

What do they have to talk about?

Are you a male or a female?Are you receptive to mating?

Are you a grasshopper?

Do you belong to my species?

Go away

I’m still here!

Behavioral Repertoire Approach Flick Walk away Flutter Chirp Femur-raise Wave-off Mount Jump Fly silently Crepitation Groom antennae Null act

What is communication?

• How do we know that animals are communicating?

•We know there is communication between 2 animals when the probability of an act being performed by one of them changes as a result of an act by the other.

Information Theory

• A way to determine whether the probabilities have changed.

• Measures uncertainty (H)• H can be applied to behavior also• Transmission (T)• Normalized transmission (t)

Bits of information

• Suppose you have 2 flowers and want to know on which of the 2 a bee has landed. You can ask only questions that can be answered by yes or no (these are binary questions and the answer is measured in bits). With 2 flowers there will be one question and you will receive 1 bit of information.

Now suppose you have 4 flowers. On the average, you can find the bee in 2 questions. This situations has 2 bits of information in it.

How many bits will there be if there are 16 flowers? Ans.

Our uncertainty about the location of the bee depends on the number of flowers there are. We use H as the symbol for this type of information.

H is a measure of our uncertainty about an outcome.

When the alternatives are equally probable H(X) = log2n bits. This means that there are log2n bits of information gained when we know which choice has been selected and our uncertainty about the choice has been removed.

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16

8 8

4 4

2

4 4

2 2 2

2

2

21 1 1 1

1

So there are 4 questions to get the right flower.

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The number of choices can be the number of acts in the repertoire of the animal. Since all of the acts are not equally probable H(act) must be weighted by the probability of that act occurring.

This leads us to the horrible looking formula: H(X)=Σp(i) log2p(i) where X is made up of acts in the animal’s repertoire (x1,x2,…xn) and p(i) is the probability of any single act in that repertoire. H(X) is never less than 0 or greater than log2 n.

H(X) will = 0 when an animal always sends the same message. In that case there is no uncertainty about what it will do and no information when the animal does it.

For an active communicator, however, freely choosing among many possible messages, there is much more uncertainty about which will be chosen and more information conveyed with each signal.

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Transmission• The transmission, T(X;Y) is a measure of relatedness. It shows

the amount of constraint on the behavior of a second animal (Y) put on it by the behavior of the first (X). T(X;Y)= H(Y)-H(Y/X)

• The transmission would be 0 if the behavior of animal 2 is statistically independent of the behavior of animal 1. In such a case there is no apparent communication between the two.

• The transmission would be equal to H(Y) if the action of Y were to be strictly determined by the immediately preceding act of X.

• So the amount by which T(X;Y) exceeds zero and approaches H(Y) can be thought of as the amount of information X transmits to Y by X’s behavior.

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Normalized Transmission

H(Y) (the upper limit of the transmission between X and Y) is itself bounded by the number of categories used in its calculation.

This makes the number of categories, behavioral acts, used to calculate H(Y) extremely important. This can vary from observer to observer and each will calculate a different value for T.

For example, of two workers independently observing the same animals, one might determine H(Y) to be 2 bits and the other might find it to be 1 bit

This could happen if the two observers divided the behaviors into

different numbers of categories. It makes the choice of categories extremely important in informational analyses.

To avoid this difficulty a normalized transmission is calculated from the ratio: t(X;Y) = T(X;Y)/H(Y). This measure will always fall between 0 and 1 and is largely independent of the number of categories used in its calculation.

The normalized transmissions can be thought of as the % of uncertainty reduction.

Back to Grasshoppers

• I extended this to 3 dimensional analyses. In these cases I calculated T(XY:Z). What do we learn when we examine the combined effects of an act by animal 1 and an act by animal 2 on what animal 1 will do next?

• It turns out that there was an 18-22% increase in predictability of what the first male will do if we know both what he had just done and what his partner had just done.

• Surprisingly, 60% of the information that made this uncertainty reduction possible was contained in the first male’s own previous act, 30% was due to the act of his partner and 9% to some interaction between the two. Sounds like people in an argument.

• Male-male interactions are unpredictable because they are trying to convey a relatively simple message “go away”. The behavior of the other animal conveys the information that he is still in the contest. The order in which one male performs his acts has little effect upon the subsequent acts of the other animal.

• If it became possible to predict the end of such interactions all a male would have to do is wait it out.