Abstract
Animals moving in groups coordinate their motion to remain cohesive. A large amount of data and analysis of movement coordination has been obtained in several species, but we are lacking theoretical frameworks that can derive the form of coordination rules. Here, we examine whether optimal control theory can predict the rules underlying social interactions from first principles. We find that a control rule which is designed to minimize the time it would take a pair of schooling fish to form a cohesively moving unit correctly predicts the characteristics of social interactions in fish. Our methodology explains why social attraction is negatively modulated by self-motion velocity and positively modulated by partner motion velocity, and how the biomechanics of fish swimming can shape the form of social forces. Crucially, the values of all parameters in our model can be estimated from independent experiments that need not relate to measurement of social interactions. We test our theory by showing a good match with experimentally observed social interaction rules in zebrafish. In addition to providing a theoretical rationale for observed decision rules, we suggest that this framework opens new questions about tuning problems and learnability of collective behaviours.
Highlights
Autonomous systems in general, and animals in particular, often benefit from coordinating their behaviour with other similar agents [1,2]
We demonstrate that control theory makes predictions about interaction rules for pairs of schooling fish which are qualitatively consistent with experimentally measured social forces in zebrafish
We present an alternative depiction of the structure of our optimal controller, where we fix to a limited range the velocity values of the focal fish in order to see the effects of varying partner fish velocity
Summary
Autonomous systems in general, and animals in particular, often benefit from coordinating their behaviour with other similar agents [1,2]. We demonstrate that control theory makes predictions about interaction rules for pairs of schooling fish which are qualitatively consistent with experimentally measured social forces in zebrafish. While our treatment is grounded in the known biology of the fish locomotor system, we do make the simplifying assumption that fish move in a quasi-one-dimensional environment This is done because in our set-up, zebrafish spend 80% of their time swimming parallel to the walls along approximately one-dimensional tracks and our access to two-dimensional data is more limited. In order to analyse the predictability of acceleration using social information, we used an artificial neural network with eight input units representing the x- and y-coordinates and the x- and y-components of the velocity of the focal and partner fish at time t. We corrected the amplitude of social forces by multiplying the observed forces by the number 1/(1 2 k), where k is the total number of observations found in a shuffled forcemap divided by the total number of observations in the non-shuffled forcemap
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
