How does estimation of environmental carrying capacity for bivalve culture depend upon spatial and temporal scales?

The simplest computational approach for estimating environmental carrying capacity (CC) for bivalve suspension-feeders is to compare the combined rate of filtration with rates of processes that contribute to food renewal. More realistic approaches are based on mathematical models that take into account complex sets of feedbacks, both positive and negative, whereby cultured organisms interact with ecosystem processes. Each of these methods requires spatial and temporal integrations. Yet densities of cultured animals and rates of ecological processes vary in space and time. We illustrate strong dependencies of estimated CC on the spatial and temporal scales chosen for associated integrations. Where food availability is the primary limitation upon CC, low resolution models may lead to overestimates of CC, when the potential for error increases in positive relation with the spatial scale resolved by a model. Considering both spatial and temporal integrations, we recommend a procedure to help evaluate the maximum appropriate scale for the situation at hand, thereby avoiding bias in estimates of CC stemming from any "dilution" of bivalve densities.