The theoretical foundations for size spectrum models of fish communities

Size spectrum models have emerged from 40 years of basic research on how body size determines individual physiology and structures marine communities. They are based on commonly accepted assumptions and have a low parameter set, which make them easy to deploy for strategic ecosystem oriented impact assessment of fisheries. We describe the fundamental concepts in size-based models about food encounter and the bioenergetics budget of individuals. Within the general framework three model types have emerged that differs in their degree of complexity: the food-web, the trait-based and the community model. We demonstrate the differences between the models through examples of their response to fishing and their dynamic behavior. We review implementations of size spectrum models and describe important variations concerning the functional response, whether growth is food-dependent or fixed, and the density-dependence imposed on the system. Finally we discuss challenges and promising directions