Hierarchical structure of bivalve culture systems and optimal stocking density

Bivalve culture systems are hierarchical, with culture units being nested within culture gear, which are nested within farms, and so on. The possibility that processes acting at the scale of individual culture units may interact with high-level processes has been overlooked in carrying capacity models, although basin-scale patterns are generated at the scale of culture units. Here I study the effect of increasing basin-scale loading on unit-scale optimal stocking density (OSD). I find a curvilinear relationship, with OSD decreasing with basin-scale loading. Clearly basin-scale models should incorporate culture-unit effects. This may be achieved by using experimental studies of the clearance rate of whole culture units to complement estimates of ecophysiological processes of individuals. Such culture-unit information, along with knowledge of associated local phytoplankton depletion at various current speeds and culture-unit stocking levels, may be used to generate submodels to be included in basin-scale models. To facilitate experimental testing of across-scale effects, I develop a simple food-regulated growth model combining density dependence at the scale of individual culture units and at the scale of basins.