How do You Know that the Top Dog is Really the Top Dog? Using Elo-Ratings and Bayesian Inference to Determine Rankings in Animal Groups

Post provided by Julia Fischer

A female chacma baboon (rear) signals her submission to another female by raising her tail. ©Julia Fischer.

A female chacma baboon (rear) signals her submission to another female by raising her tail. ©Julia Fischer.

Anyone who studies social animals in the wild (or human groups, for that matter), will soon find that some individuals threaten or attack others frequently, while others try to get out of the way or signal their submission in response to aggression. Observers tally the outcome of such aggressive interactions between any given two individuals (or ‘dyads’) and try to deduce the rank hierarchy from such winner-loser matrices. One drawback of this approach is that all temporal information is lost.

Imagine Royal, a baboon, dominating over Power, another baboon, 20 times, and Power dominating over Royal 20 times as well. If we just look at these data, we might think that they have the same fighting ability and similar ranks. But, if we know that Royal beat Power the first 20 of the interactions, then Power beat Royal in all further interactions, we’d come to a totally different conclusion. We’d infer that Power had toppled Royal and a rank change had taken place.

How do Rank Hierarchies Change Over Time?

One prominent method that takes the temporal dynamics of winner-loser interactions into account was originally developed to calculate the relative skill level of chess players. This method was introduced by Arpad Elo and is hence known as Elo-Rating. Elo-Rating has also been applied to rate the relative skills in a variety of competitive fields, including Major League Baseball, video games, and Scrabble. Continue reading