Scale-dependent feedbacks and regular pattern formation in mussel beds
Self-organization has been hypothesized as one of the factors explaining the emergence of regular spatial patterns of organisms in landscapes. To study scale-dependent ecological feedbacks that could explain regular banding patterns that have been observed in some mussel beds in soft-bottom habitats, van de Kopple et al. (2005) conducted field studies in the Wadden Sea to characterize spatial patterns of its mussel beds, and constructed spatially explicit models to determine if feedbacks between large-scale competition for algal resources and small-scale facilitation of conspecifics could contribute to the emergence of the observed spatial patterns. To do this, they took photographs in aerial surveys of mussel beds, and analyzed them using two-dimensions spectral analysis to determine whether the mussels exhibited regular bands with a consistent orientation and wavelengths between bands. Mussels generally exhibited regular spatial patterns with a wavelength of approximately 6m, and bands oriented in the direction of the tidal current. For the models, they modeled algal density over a position the mussel bed as a function of mussel density and the exchange of water between upper and lower water layers with different algal concentrations, and they modeled mussel biomass as a linear functional response to algal density with a given per capita mortality rate and conversion efficiency, and diffusion rate (assumed random) of mussels. Using numerical simulations on a 100 x 100 spatial grid with unidirectional water flow, they found that regular bands of mussels formed when there were any small spatial heterogeneities and the algal concentration in the upper water layer was low. Mussel bands moved upstream as new mussels established and grew on the upstream side of the bands where the highest algal densities existed, and mussels on the downstream side of the bands died due to depletion of their algal resources by the upstream mussels. Spacing between the bands water determined by distance required to allowed the two water layers to mix adequately to increase the algal concentrations in the lower water layer that the mussels used.
When using a nondimensionalized form of their models for algal density and mussel biomass to determine the sensitivity of the observed responses to parameter values, the authors found that algal concentration in the upper water layer was important for pattern formation, and above a threshold, homogenous (non-patterned) mussel beds should emerge at equilibrium. Additionally, they found that the predicted total mussel biomass was higher in beds with regular pattern formation compared to beds with homogeneous distributions (Fig.4, dashed green line vs. dashed blue line). These patterned beds could persist when upper water algal concentrations were lower than what was necessary to support homogeneous mussel beds. When they tested the resilience of mussel beds to disturbance, they found that beds that were disturbed in a manner that also homogenized the spatial distribution of mussels recovered more slowly than beds that were disturbed to the same degree, but kept their patterned spatial distribution.
Overall, authors found that self-organization resulted in regular spatial patterns of mussel beds. These patterns increased the productivity of the predators (mussels) in this predator-prey system across a range of algal concentrations, allowed the mussels to persist in more stressful environmental conditions (i.e. lower algal concentrations), and improved their resilience to disturbance. These results are similar to findings in arid ecosystems, and indicate that self-organization resulting from ecological feedbacks occurring at multiple spatial scales may be important to the spatial patterns and dynamics of organisms in many ecosystems.
Citation:
van de Koppel, J., Rietkerk, M., Dankers, N. & Herman, P. M. J. Scale-dependent feedback and regular spatial patterns in young mussel beds. Am Nat 165, E66–77 (2005).