How do you determine whether two, three, or four individuals are interacting? With people, it can be fairly straightforward: they talk, touch, and communicate with each other. That’s not necessarily true with other animals which can release olfactory pheromones which we can’t see. Mice (like dogs) also communicate through scent-marking. Further, interactions might occur indirectly; if you are sitting in a chair, it makes it much less likely that someone else will come and sit in that chair as well… Which leaves us again with the broad question of how to determine whether (and how many) individuals are interacting if we can’t see their interactions?
Shemesh et al. turn to the technique that is the bread-and-butter for the Schneidman lab, the maximum entropy technique. This method relies on answering a very simple question about the correlations between individuals. That is, how well can you predict where an individual will be given the probabilities of each location? And how much better can you predict if you assume that there are interactions between two, three, or four individuals?
In order to see whether these interactions existed between mice, they filmed mice for 12 hours overnight for four days and observed their locations. They then made the simplest assumption: what if the animals weren’t interacting at all? Then you can assume statistical independence. In other words, knowing the probability of each mouse’s location individually will tell you what the probability is for all four together. This, it turns out, doesn’t do so well. What about if the probability for a mouse to be somewhere was related to where the mouse observed just one other individual at a time was? There are many different models of statistics and behavior that can fit this data, but Shemesh et al. used the maximum entropy model. This uses the absolute minimal level of assumptions – just the probabilities and the order of correlations and is as uncertain [entropic] as possible about everything else. These sets of models have a long history in statistical physics. They find that using these models, interactions between multiple individuals is very important.
This also allows us to examine which are the strongest interactions. Here are three examples, the first being an important interaction between a pair of individuals, the second between a triplet, and the third being a negative interaction:
This is a nice, principled method for extracting the interactions between individuals. It’s a system that can get data quickly. I hope one of the next things that they do with it is start examining mutants (dopamine receptors, etc). I also wonder how the interactions scale with individuals. Did fourth-order interactions explain so little information because there were only four individuals in the arena? Or is there something more fundamental that is occurring?
Shemesh Y, Sztainberg Y, Forkosh O, Shlapobersky T, Chen A, & Schneidman E (2013). High-order social interactions in groups of mice. eLife, 2 PMID: 24015357