Wild fish, farmed fish and sea lice—a big-box model with spatial effects

The Anderson-May dynamical model for host-macroparasite systems is extended to include resource limitation and the distribution of both resource limitation effects and parasite pathogenicity over host mortality and natality. When the equilibrium host population is regarded as a fixed fraction of the environmental capacity, an important concept that emerges is the regulatory budget of wild hosts. This machinery is used to model a system consisting of wild fish, sea lice and free-living larvae. An analogous dynamical model for sea-cage fish farms is constructed and then coupled to the wild system by cross-infection rates from farm to wild and wild to farm. If the wild, farm, and cross-infection rates are similar, wild fish decline nearly linearly with the addition of farm fish to the system, independent of most system parameters other than lice natality and mortality. If cross-infection rates are low, the initial decline of wild fish is slight, but the decline steepens as farm fish approach pre-farm levels of wild fish. Short grow-out times and frequent treatment of farm fish for parasites reduce the decline of wild fish, but a reduction in cross infection rates is a more effective, and apparently essential, strategy. Three treatment protocols are studied: fixed treatment rate, adaptive treatment to keep farm abundances at a fixed fraction of ambient wild abundance, and adaptive treatment to keep farm abundances at a fixed fraction of pre-farm wild abundance. Spatial effects are incorporated by a new integral for infection rate, then used to examine several sea-cage farming scenarios. Sea-cages located in fiords appear to be worse for wild fish than open-ocean sea-cages because a “good-flush” in a fiord reduces the farm infection rate only a little, and the farm-to-wild infection rate not at all.