Modeling the dynamics of disturbance in mussel beds

Background/Question/Methods Realistic approaches to modeling disturbances in complex ecological systems could aid in the conservation and management of natural resources. Cellular automata (CA) models have been used to study 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 with periodic 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. I formulate and analyze a model that combines these approaches to allow a consideration of the effects of mussel growth, size-dependent predation, and environmental gradients on disturbance dynamics. Small “patches” of the mussel bed are modeled using a deterministic mean field ordinary differential equation (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 and 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 I investigated how the distribution of gap sizes varied with frequency of disturbance and predation intensity in both homogeneous environments and in gradients of tidal height and wave exposure. I also examined how recovering gaps from previous disturbances influence the dynamics of gap formation. As with simpler models, the gap size frequency distribution varied according to a power law in homogenous mussel beds. In simulations with environmental gradients, the highest frequencies and largest sizes of disturbances occurred in interior areas of highest biomass. When As disturbances became more likely, the historical effects from previous gap formations had a greater influence on the dynamics of disturbance. The hybrid deterministic-stochastic quilt model provides a novel paradigm for studying ecological disturbances. These types of predictive models could advance our knowledge of disturbance mechanisms and be adapted for the management of other complex biological systems, such as forests.