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.
Highlights
Over the past decade, a number of studies have reported on self-organized spatial patterns from a wide range of ecosystems [1]
The process of spatial self-organization is the central explanation for the occurrence of regular or otherwise coherent spatial patterns in ecosystems lacking underlying abiotic heterogeneity [1]
Most theoretical studies currently focus on the explanations for observed spatial patterns, following the first mathematical model proposed by Klausmeier [2]
Summary
A number of studies have reported on self-organized spatial patterns from a wide range of ecosystems [1]. Van de Koppel et al [7] explained the formation of these patterns by the interplay of local facilitation and large-scale competition for algae, inducing spatial self-organization This model assumes that facilitation between mussels, resulting from aggregation, reduces losses owing to predation and wave dislodgement, as mussels bind to each other using byssus threads to form strong clusters and mats. The first mechanism involves a positive effect of mussel density on mussel survival rates, as clumping and attachment to other mussels with byssus threads reduces chances of predation and wave dislodgement This mechanism is the central hypothesis of a prior paper on self-organized pattern formation in mussel beds [1,7]. The second mechanism involves a positive relation between feeding efficiency and sediment accumulation, which is based on the results of the field survey presented in the prior section Both models involve the same large-scale negative feedback arising from algal depletion by the mussels. We describe the rate of change of mussel biomass per square metre with the expression:
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