  Animal behavior is shaped by a myriad of mechanisms acting on a wide range of
scales, which hampers quantitative reasoning and the identification of general
principles. Here, we combine data analysis and theory to investigate the
relationship between behavioral plasticity and heavy-tailed statistics often
observed in animal behavior. Specifically, we first leverage high-resolution
recordings of C. elegans locomotion to show that stochastic transitions among
long-lived behaviors exhibit heavy-tailed first passage time distributions and
correlation functions. Such heavy tails can be explained by slow adaptation of
behavior over time. This particular result motivates our second step of
introducing a general model where we separate fast dynamics on a
quasi-stationary multi-well potential, from non-ergodic, slowly varying modes.
We then show that heavy tails generically emerge in such a model, and we
provide a theoretical derivation of the resulting functional form, which can
become a power law with exponents that depend on the strength of the
fluctuations. Finally, we provide direct support for the generality of our
findings by testing them in a C. elegans mutant where adaptation is suppressed
and heavy tails thus disappear, and recordings of larval zebrafish swimming
behavior where heavy tails are again prevalent.
