J
15.3. Model Assumptions
347
where a, B , and c. are habitat-specific constants, x is a measure of the
I
I
I
I
density of juvenile cod in region i, and Z j is a scaling factor.
We assume a relation between local density (of juvenile fish) and natural
mortality. Specifications for the functional response curves are based on the
relative differences in habitat-specific mortality observed in laboratory experiments (Lindholm et al. 1999). Lindholm et al. (999) quantified relative
differences in habitat-mediated juvenile cod mortality at the microhabitat
scale, focusing on the proce sses governing predator-prey-habitat interactions at the scale of individual fish. The model uses these relative differences to scale-up the role of habitat in mediation of survivorship of juvenile
fish to a scale of kilometers. Juvenile mortality for habitats with lowest complexity (unprotected areas) is given a maximum value of 0.98. Mortality for
habitats with highest complexity (MPAs) was given a maximum value of
0.32. Juvenile fish in unprotected areas lack adequate cover to seek refuge
from predation. Therefore , they experience a corresponding increase in
natural mortality over regions within an MPA.
In Equation 1, M; is the net movement from any region i to surrounding
regions j month -} and is given by
M; = I v jN j - YiNi'
(5)
j
where v. is the percentage of individuals moving each month from region j
to i and Vi is the percentage of individuals leaving region i. Movement occurs in a "rook" pattern in a 4 X 4 matrix such that individuals randomly
move to any adjacent cell (e.g. up , down , to either side, but not diagonally).
15.3. Model Assumptions
We make a number of simplifying assumptions in the model that allow us
to focus on habitat-mediation of juvenile cod survivorship and the role of
MPAs. Juvenile cod settlement occurs in a single pulse in the first month ,
and settlement is uniform within any region or cell, and between all. Juvenile mortality is a density-dependent function of predation, mediated by sea
floor habitat quality. The model does not consider variation in food availability, water temperature, salinity, and other biological and physical parameters affecting juvenile fish. Differences between an MPA and surrounding areas with respect to mortality are constant for the duration of a model
run . Fishing activity directly influences habitat quality. High natural mortality is interpreted as low habitat quality due to fishing alteration of the sea
floor, whereas low natural mortality is interpreted as high habitat quality
with little to no alteration by fishing. The effect of fishing activity on sea
floor habitat is uniform across any area in which it occurs. Habitat hetero -
geneity is considered relative only to differences between an MPA and surrounding areas, with habitat quality uniform within a cell. Movement rates
are constant for the duration of a model run.
15.3. Model Assumptions
347
where a, B , and c. are habitat-specific constants, x is a measure of the
I
I
I
I
density of juvenile cod in region i, and Z j is a scaling factor.
We assume a relation between local density (of juvenile fish) and natural
mortality. Specifications for the functional response curves are based on the
relative differences in habitat-specific mortality observed in laboratory experiments (Lindholm et al. 1999). Lindholm et al. (999) quantified relative
differences in habitat-mediated juvenile cod mortality at the microhabitat
scale, focusing on the proce sses governing predator-prey-habitat interactions at the scale of individual fish. The model uses these relative differences to scale-up the role of habitat in mediation of survivorship of juvenile
fish to a scale of kilometers. Juvenile mortality for habitats with lowest complexity (unprotected areas) is given a maximum value of 0.98. Mortality for
habitats with highest complexity (MPAs) was given a maximum value of
0.32. Juvenile fish in unprotected areas lack adequate cover to seek refuge
from predation. Therefore , they experience a corresponding increase in
natural mortality over regions within an MPA.
In Equation 1, M; is the net movement from any region i to surrounding
regions j month -} and is given by
M; = I v jN j - YiNi'
(5)
j
where v. is the percentage of individuals moving each month from region j
to i and Vi is the percentage of individuals leaving region i. Movement occurs in a "rook" pattern in a 4 X 4 matrix such that individuals randomly
move to any adjacent cell (e.g. up , down , to either side, but not diagonally).
15.3. Model Assumptions
We make a number of simplifying assumptions in the model that allow us
to focus on habitat-mediation of juvenile cod survivorship and the role of
MPAs. Juvenile cod settlement occurs in a single pulse in the first month ,
and settlement is uniform within any region or cell, and between all. Juvenile mortality is a density-dependent function of predation, mediated by sea
floor habitat quality. The model does not consider variation in food availability, water temperature, salinity, and other biological and physical parameters affecting juvenile fish. Differences between an MPA and surrounding areas with respect to mortality are constant for the duration of a model
run . Fishing activity directly influences habitat quality. High natural mortality is interpreted as low habitat quality due to fishing alteration of the sea
floor, whereas low natural mortality is interpreted as high habitat quality
with little to no alteration by fishing. The effect of fishing activity on sea
floor habitat is uniform across any area in which it occurs. Habitat hetero -
geneity is considered relative only to differences between an MPA and surrounding areas, with habitat quality uniform within a cell. Movement rates
are constant for the duration of a model run.