Cellular automata (CA) models have been used to model the dynamics of disturbances in marine mussel beds, Mytilus californianus. These models usually consider transitions among a small number of states, for example, “empty,” “occupied,” and “disturbed”, and assume a homogenous spatial environment without boundaries. On the other hand, more complex CA models have also been used to study mussel bed boundary formation. These models consider mussel settlement and growth and predator-prey dynamics within gradients of tidal height and wave exposure. We present results from a model that combines these approaches. Small “patches” of the mussel bed are modeled using a mean field ODE approximation to the complex CA model. Each patch represents an area of constant tidal height and wave exposure. Adjacent patches are linked through local interactions to form a “quilt” that spans gradients of tidal height wave exposure. Patches are vulnerable to random disturbances that can propagate to neighboring patches, forming gaps in mussel cover. The probabilities of disturbance and propagation increase as functions of mussel biomass.
Results/Conclusions
Using this model, we report preliminary results on how the frequencies of disturbance and the size distribution of gap sizes vary with tidal height, wave exposure, and intensity of predation. We also show how healing gaps from previous disturbances influence the dynamics of gap formation.