Employing Relative Entropy Techniques for Assessing Modifications in Animal Behavior

In order to make quantitative statements regarding behavior patterns in animals, it is important to establish whether new observations are statistically consistent with the animal's equilibrium behavior. For example, traumatic stress from the presence of a telemetry transmitter may modify the baseline behavior of an animal, which in turn can lead to a bias in results. From the perspective of information theory such a bias can be interpreted as the amount of information gained from a new measurement, relative to an existing equilibrium distribution. One important concept in information theory is the relative entropy, from which we develop a framework for quantifying time-dependent differences between new observations and equilibrium. We demonstrate the utility of the relative entropy by analyzing observed speed distributions of Pacific bluefin tuna, recorded within a 48-hour time span after capture and release. When the observed and equilibrium distributions are Gaussian, we show that the tuna's behavior is modified by traumatic stress, and that the resulting modification is dominated by the difference in central tendencies of the two distributions. Within a 95% confidence level, we find that the tuna's behavior is significantly altered for approximately 5 hours after release. Our analysis reveals a periodic fluctuation in speed corresponding to the moment just before sunrise on each day, a phenomenon related to the tuna's daily diving pattern that occurs in response to changes in ambient light.