Inferring causal relationship in coordinated flight of pigeon flocks.

Collective phenomenon of natural animal groups will be attributed to individual intelligence and interagent interactions, where a long-standing challenge is to reveal the causal relationship among individuals. In this study, we propose a causal inference method based on information theory. More precisely, we calculate mutual information by using a data mining algorithm named "k-nearest neighbor" and subsequently induce the transfer entropy to obtain the causality entropy quantifying the causal dependence of one individual on another subject to a condition set consisting of other neighboring ones. Accordingly, we analyze the high-resolution GPS data of three pigeon flocks to extract the hidden interaction mechanism governing the coordinated free flight. The comparison of spatial distribution between causal neighbors and all other remainders validates that no bias exists for the causal inference. We identify the causal relationships to establish the interaction network and observe that the revealed causal relationship follows a local interaction mode. Interestingly, the individuals closer to the mass center and the average velocity direction are more influential than others.