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

  • Date: 10/23/2006

Neil Frazer (University of Hawaii)


University of British Columbia


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.

Other Information: 

PIMS-MITACS Mathematical Biology Seminar Series 2006


Neil Frazer is a Professor of Geophysics, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa.