Modeling activity rhythms in fiddler crabs

Burrowing crabs of the genus Uca inhabit tidal mudflats and beaches. They feed actively during low tide and remain in their burrows when the tide is high. The timing of this activity has been shown to persist in the absence of external light and tidal cues, indicating the presence of an internal timing mechanism. Researchers report the persistence of several variations in locomotor activity under laboratory conditions that cannot be explained by a single circatidal clock. Previous studies supported two alternative hypotheses: the presence of either two circalunidian clocks, or a circadian and circatidal clock to regulate these activity rhythms. In this paper, we formulate mathematical models to describe and test these hypotheses. The models suggested by the literature contain some important differences beyond the frequency of proposed clocks, and these are reflected in the mathematical formulations and simulation results. One hypothesis suggests independent phase oscillators, while the other hypothesis suggests that they are coupled in anti-phase. Neither model is able to recover all of the variations in locomotor acitivity observed under laboratory conditions. However, we propose a new model that incorporates aspects of both existing hypotheses and is able to reproduce all laboratory observations.