Confidence Sharing: An Economic Strategy for Efficient Information Flows in Animal Groups

Social animals may share information to obtain a more complete and accurate picture of their surroundings. However, physical constraints on communication limit the flow of information between interacting individuals in a way that can cause an accumulation of errors and deteriorated collective behaviors. Here, we theoretically study a general model of information sharing within animal groups. We take an algorithmic perspective to identify efficient communication schemes that are, nevertheless, economic in terms of communication, memory and individual internal computation. We present a simple and natural algorithm in which each agent compresses all information it has gathered into a single parameter that represents its confidence in its behavior. Confidence is communicated between agents by means of active signaling. We motivate this model by novel and existing empirical evidences for confidence sharing in animal groups. We rigorously show that this algorithm competes extremely well with the best possible algorithm that operates without any computational constraints. We also show that this algorithm is minimal, in the sense that further reduction in communication may significantly reduce performances. Our proofs rely on the Cramér-Rao bound and on our definition of a Fisher Channel Capacity. We use these concepts to quantify information flows within the group which are then used to obtain lower bounds on collective performance. The abstract nature of our model makes it rigorously solvable and its conclusions highly general. Indeed, our results suggest confidence sharing as a central notion in the context of animal communication.Author Summary: Cooperative groups are abundant on all scales of the biological world. Despite much empirical evidence on a wide variety of natural communication schemes, there is still a growing need for rigorous tools to quantify and understand the information flows involved. Here, we borrow techniques from information theory and theoretical distributed computing to study information sharing within animal groups. We consider a group of individuals that integrate personal and social information to obtain improved knowledge of their surroundings. We rigorously show that communication between such individuals can be compressed into simple messages that contain an opinion and a corresponding confidence parameter. While this algorithm is extremely efficient, further reduction in communication capacity may greatly hamper collective performances.