A mathematical model is developed to describe the competition for space and food among blue mussels, which adhere on cylindrical substrata. In order to develop and validate the model, field investigation is carried out for mussels growing on ropes installed around the mouth of Sumida River in Tokyo Bay. In addition to monitoring of environmental factors such as water temperature, salinity, and the concentration of dissolved oxygen, the relationship between the position of each mussel and its size in the mussel bed is examined precisely. The position of each mussel in the bed is specified by how much the gape of the shells comes out from the bed. As a result, the growth of the mussels in the inner layer is obviously slow and they are considered to continue living by consuming the reserved materials accumulated in their bodies. On the contrary, mussels can grow faster if only a part of the gape of their shells comes out from the mussel bed. These observed features are taken into account in the mathematical model. The model can predict well the size structure of mussels in the bed; the faster growth of the surface mussels and the slower growth of the inner mussels, which corresponds to observations. In the future the model will be also applied to mussels on the cylindrical substrata such as cultivation ropes, piers, and piles for aquaculture management and environmental impact assessment of the coastal structures.

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