Alternative mechanisms alter the emergent properties of self-organization in mussel beds

Abstract

Theoretical models predict that spatial self-organization can have important, unexpected implications by affecting the functioning of ecosystems in terms of resilience and productivity. Whether and how these emergent effects depend on specific formulations of the underlying mechanisms are questions that are often ignored. Here, we compare two alternative models of regular spatial pattern formation in mussel beds that have different mechanistic descriptions of the facilitative interactions between mussels. The first mechanism involves a reduced mussel loss rate at high density owing to mutual protection between the mussels, which is the basis of prior studies on the pattern formation in mussels. The second mechanism assumes, based on novel experimental evidence, that mussels feed more efficiently on top of mussel-generated hummocks. Model simulations point out that the second mechanism produces very similar types of spatial patterns in mussel beds. Yet the mechanisms predict a strikingly contrasting effect of these spatial patterns on ecosystem functioning, in terms of productivity and resilience. In the first model, where high mussel densities reduce mussel loss rates, patterns are predicted to strongly increase productivity and decrease the recovery time of the bed following a disturbance. When pattern formation is generated by increased feeding efficiency on hummocks, only minor emergent effects of pattern formation on ecosystem functioning are predicted. Our results provide a warning against predictions of the implications and emergent properties of spatial self-organization, when the mechanisms that underlie self-organization are incompletely understood and not based on the experimental study.

Pattern formation at multiple spatial scales drives the resilience of mussel bed ecosystems

“…This function expresses a scale-dependent effect of mussel density on individual movement, where L 1 and L 2 represent the density of other mussels in the neighbourhood at a scale of 1.5 and 6 cm, respectively. The large-scale populationand ecosystem-level processes are represented as partial differential equations (PDE), describing the local growth and mortality of mussels as determined by algal consumption, sediment accumulation and a density-dependent mortality rate 13,20,25 . Let A(x, y, t) describe the algal concentration in the benthic boundary layer, M(x, y, t) the mussel density and S(x, y, t) the sediment elevation at location (x, y) and time t. This part of the model is then given by:…”

“…As time progresses, the small-scale clumps develop into a reticulate network, while banded patterns develop at larger spatial scales due to differential growth and mortality. Increased sedimentation triggered by mussel feeding leads to the development of hummocks underneath mussel patches, which become raised from the seabed 25 (Fig. 2b,e).…”

“…To study how pattern formation at multiple spatial scales affects the resilience of mussel beds, we developed a model that combines a mathematical description of large-scale pattern formation in mussel beds 25 with an individual-based, numerical model for aggregative movement of mussels at small spatial scales 13 . In this model, large-scale population growth and losses processes are described by three partial differential equations, one describing changes in algal concentration in the benthic boundary layer A(x, y, t), one for mussel density on the bottom M(x, y, t) and one for sediment elevation S(x, y, t), each at location (x, y) and time t. Therefore, the model can be written as equation (1).…”

“…At the ecosystem level, pattern formation is driven by the interplay of two scale-dependent processes. Mussels compete for algae in the water column at large spatial scales (41 metre) due to high flow rate of the tidal water, but facilitate each other at smaller scales (o1 metre) by locally accumulating sediment (a form of ecosystem engineering) within elevated hummocks of 1-4 metres width, which improves individual feeding efficiency 25 . This interplay between facilitation and competition explains the banded patterns occurring at the 5-10-metre scale 20 .…”

The role of shore crabs and mussel density in mussel losses at a commercial intertidal mussel plot after seeding

“…Seeding practice in bottom culture leads to a highly heterogeneous distribution of mussels on culture plots, with high mussel densities within the space occupied by mussels (Capelle et al 2014). Mussels are gregarious organisms and aggregate in patches, thereby competing for food and space (Fréchette and Bourget 1985;Liu et al 2012).…”