A krill–predator–fishery model for evaluating candidate management procedures

The CCAMLR has recognised the need to subdivide the precautionary krill catch limit for Statistical Area 48 amongst smaller spatial units in order to minimize the localized depletion of krill in predator foraging areas. These smaller spatial units, termed small-scale management units (SSMUs), have been defined, and six candidate procedures for subdividing the catch have been identified. It is now necessary to evaluate these procedures in terms of their likely effects on krill and predator populations as well as fishery performance. This evaluation must be conducted in the context of considerable uncertainty about how the krill-predator- fishery system operates. We describe a model designed to investigate the performance of these procedures and their sensitivity to numerical and structural uncertainty. The model is spatially resolved to the level of SSMUs and surrounding oceanic areas, and it includes the transport of krill between these areas. Krill and predator population dynamics are implemented with coupled delay-difference models, which are formulated to accommodate various assumptions about the recruitment and predation processes. The fishery is represented as a simultaneous and equal competitor for available krill. Straightforward Monte Carlo simulations are used to integrate the effects of numerical uncertainty, and structural uncertainty can be assessed by comparing and merging results from multiple such simulations. We present a range of performance measures that can be used to evaluate catch-allocation procedures and assess tradeoffs between predator and fishery performance. We provide basic instructions on running the model in S-Plus and illustrate its use. Finally, we conclude that although our model necessarily simplifies a complex system, it provides a flexible framework for investigating the roles of transport, production, predation and harvesting in the operation of the krill-predator-fishery system.