Probabilistic causal inference for coordinated movement of pigeon flocks

One of the most striking examples of natural animal behavior is the highly ordered coordinated group movement, where inter-agent interaction is considered as a key factor tuning the coordination. To understand the interaction mechanism, a long-standing challenge is to reveal the causal relationship among the group individuals. In this study, we propose a causal inference method from the viewpoint of information theory. More precisely, we extend conditional information entropy of pairwise individuals with time delay, and subsequently induce causation entropy which quantifies the causal dependence of two individuals subject to a condition set consisting of other neighbors. Moreover, we analyze the high-resolution GPS data of three pigeon flocks to construct the interaction networks accordingly. We dynamically analyze the interaction characteristics and interestingly observe that the individuals closer to the mass center and the average velocity direction are more influential to the others. This study may shed some light onto the research of collective behaviors