Marine Stranding as a Reachability Transition: A Control-Theoretic Model of Tidal Coastal Capture

Coastal cetacean strandings are associated with tides, bathymetry, animal state, social behavior, and oceanographic forcing, but these factors do not by themselves specify when an animal loses the ability to escape. This study formulates stranding capture as a reachability transition: a vulnerable animal becomes trapped when its feasible movement domain no longer contains a continuous route to offshore-safe water. A reduced bathymetric implementation was applied to a NOAA 30 m Cape Cod Bay digital elevation model using a prespecified 1.5 m minimum navigable depth and a 10 m offshore-safe depth. Two distinct geometric modes emerged. In connectivity-loss capture, locally navigable cells may remain isolated from offshore-safe water after a passage closes. In domain-recession capture, no discrete bottleneck is required; offshore-connected navigable water instead retreats seaward during ebb tide. Within the frozen Wellfleet analysis, a minority of tidally relevant cells exhibited substantial topological penalty, while matched-depth cells at the same tide stage could occupy opposite reachability states. Broad tidal-flat sites showed strong seaward retreat of offshore-reachable water, reaching approximately 1.78 km at First Encounter Beach, 2.35 km at Ellis Landing, and 0.97 km at Chapin Beach at the modeled low-water stage. These results show that local depth and tidal stage alone do not uniquely determine recoverability. The framework therefore identifies offshore reachability as a distinct spatial state variable and proposes time-to-loss-of-reachability as a candidate operational measure for future stranding forecasting and response. Keywords