Balanced exploitation and coexistence of interacting, size-structured, fish species

This paper examines some effects of exploitation on a simple ecosystem containing two interacting fish species, with life histories similar to mackerel (Scomber scombrus) and cod (Gadus morhua), using a dynamic, size-spectrum model. Such models internalize body growth and mortality from predation, allowing bookkeeping of biomass at a detailed level of individual predation and growth and enabling scaling up to the mass balance of the ecosystem. Exploitation set independently for each species with knife-edge, size-at-entry fishing can lead to collapse of cod. Exploitation to achieve a fixed ratio of yield to productivity across species can also lead to collapse of cod. However, harvesting balanced to the overall productivity of species in the exploited ecosystem exerts a strong force countering such collapse. If balancing across species is applied to a fishery with knife-edge selection, size distributions are truncated, changing the structure of the system and reducing its resilience to perturbations. If balancing is applied on the basis of productivity at each body size as well as across species, there is less disruption to size-structure, resilience is increased, and substantially greater biomass yields are possible. We note an identity between the body size at which productivity is maximized and the age at which cohort biomass is maximized. In our numerical results based on detailed bookkeeping of biomass, cohort biomass reaches its maximum at body masses