  Trajectories from a pair of interacting zebrafish are used to test for the
existence of anticipatory dynamics in natural systems. Anticipatory dynamics
(AD) is unusual in that causal events are not necessarily ordered by their
temporal order. However, their causal order can still be established if the
direction of information flow (DIF) is known. In order to obtain DIF between
trajectories of the two fish, we have made use of the difference of the
transfer entropy between the trajectories with a history length established by
experiments with known DIF. Our experimental results indicate that AD can be
observed much more often in fish pairs of different genders. The use of DIF to
determine causal order is further verified by the simulation of two chaotic
Lorenz oscillators with anticipatory coupling; mimicking the interaction
between the fish. Our simulation results further suggest that the two fish are
interacting with their own internal dynamics, not by adaptation.
