Theoretical models highlight that spatially self-organized patterns can have important emergent effects on the functioning of ecosystems, for instance by increasing productivity and affecting the vulnerability to catastrophic shifts. However, most theoretical studies presume idealized homogeneous conditions, which are rarely met in real ecosystems. Using self-organized mussel beds as a case study, we reveal that spatial heterogeneity, resulting from the large-scale effects of mussel beds on their environment, significantly alters the emergent properties predicted by idealized self-organization models that assume homogeneous conditions. The proposed model explicitly considers that the suspended algae, the prime food for the mussels, are supplied by water flow from the seaward boundary of the bed, which causes in combination with consumption a gradual depletion of algae over the simulated domain. Predictions of the model are consistent with properties of natural mussel patterns observed in the field, featuring a decline in mussel biomass and a change in patterning. Model analyses reveal a fundamental change in ecosystem functioning when this self-induced algal depletion gradient is included in the model. First, no enhancement of secondary productivity of the mussels comparing with non-patterns states is predicted, irrespective of parameter setting; the equilibrium amount of mussels is entirely set by the input of algae. Second, alternate stable states, potentially present in the original (no algal gradient) model, are absent when gradual depletion of algae in the overflowing water layer is allowed. Our findings stress the importance of including sufficiently realistic environmental conditions when assessing the emergent properties of self-organized ecosystems.
Keywords: biogenic gradients; ecosystem functioning; emergent properties; mussel beds.