Size-based models of marine ecosystems and fishing - Michael Plank (University of Canterbury)

Many marine fish species can grow in body mass more than seven orders of magnitude over their lifetime. As fish grow, their target prey and their growth, mortality and reproduction rates change drastically with body mass. This means that body mass is a crucial variable in any mathematical model. Size-spectrum models put body mass foremost by doing a bookkeeping of biomass as it flows from prey to predator, and from parent to offspring. This is a different paradigm from the classical species-based predator-prey model.

This talk will give an overview of size-spectrum models and the insights they have given us into marine community dynamics. Size-spectrum models are based on a generalisation of the McKendrick-von Foerster equation to a nonlinear, partial integro-differential equation. I will show some theoretical results about the equilibrium size structure and stability, as well as applications in fisheries management and fisheries-induced evolution. Size-spectrum models are particularly suited to investigating the effects of different distributions of fishing mortality over body mass and species, which is a key question for ecosystem-based fisheries management.