557
32.2.5 Growth and Mortality Effects
Change in biomass (B, in units of mg N) for each polygon, depth layer, and age class
of functional group i is determined following the Atlantis model application
described by Ainsworth et al. (2018), as defined in Eq. 32.1:
dB
dt
R T
T
M
P
F g G
G
i
i
I MM i
E M i
i
j
i j
i
i s
ir
=
+
−
−
− ∑
−
⋅
+
,
,
,
,
,
1
oil
(32.1)
R is entry of new individuals into the age class from recruitment or aging, T IMM,i and
T EM,i are immigration and emigration, F i is fisheries catch, and P i,j is predation by
predator j on group i. G i,s and G i,r are growth in structural and reserve nitrogen,
which are functions of assimilation efficiency, growth rate, and total consumption.
M1 summarizes natural mortality from non-predation sources as in Eq. 32.2:
M m m m
l
q
1 = +
+ oil
(32.2)
where m l and m q are linear and quadratic mortality parameters set iteratively during
model calibration and m oil is mortality caused by oil exposure derived from the
dose-response model in Eq. 32.3. g oil is the modifier on growth rate caused by oil
exposure defined in Eq. 32.4:
m
m
B m
B
oil
p elagic
benthic
=
⋅ −
(
)+
⋅
1
(32.3)
g
g
B g
B
oil
p elagic
benthic
=
⋅ −
(
)+
⋅
1
(32.4)
The m oil term represents a weighted average of a pelagic mortality modifier (m pelagic )
and a benthic mortality modifier (m benthic ) that reflects the proportion of B in the
affected group’s diet that comes from either benthic or pelagic prey. Growth rate g oil
is similarly weighted based on pelagic and benthic diet. These modifiers were calculated from the dose-response models developed by Dornberger et al. (2016) to
describe the effects of polycyclic aromatic hydrocarbons (PAH) on growth and mortality rates in fishes. The most parsimonious and best fit by Dornberger et al. (2016)
were “hockey-stick” models that imply the existence of a PAH concentration threshold below which there are no adverse effects and above which there is a log-linear
increase in mortality (Eq. 32.5) and decrease in growth (Eq. 32.6):
m t
t
= ⋅
⋅
α
ϕ β
log
1
(32.5)
g t
t
= − ⋅
⋅
1
1
γ
ϕ δ
log
(32.6)
These dose-response models (Eqs. 32.5 and 32.6) estimate the mortality and growth
as a function of the amount of bioavailable oil (φ t ) at time step t. The estimates,
32 Comparing Ecosystem Model Outcomes Between Ixtoc 1 and Deepwater...
32.2.5 Growth and Mortality Effects
Change in biomass (B, in units of mg N) for each polygon, depth layer, and age class
of functional group i is determined following the Atlantis model application
described by Ainsworth et al. (2018), as defined in Eq. 32.1:
dB
dt
R T
T
M
P
F g G
G
i
i
I MM i
E M i
i
j
i j
i
i s
ir
=
+
−
−
− ∑
−
⋅
+
,
,
,
,
,
1
oil
(32.1)
R is entry of new individuals into the age class from recruitment or aging, T IMM,i and
T EM,i are immigration and emigration, F i is fisheries catch, and P i,j is predation by
predator j on group i. G i,s and G i,r are growth in structural and reserve nitrogen,
which are functions of assimilation efficiency, growth rate, and total consumption.
M1 summarizes natural mortality from non-predation sources as in Eq. 32.2:
M m m m
l
q
1 = +
+ oil
(32.2)
where m l and m q are linear and quadratic mortality parameters set iteratively during
model calibration and m oil is mortality caused by oil exposure derived from the
dose-response model in Eq. 32.3. g oil is the modifier on growth rate caused by oil
exposure defined in Eq. 32.4:
m
m
B m
B
oil
p elagic
benthic
=
⋅ −
(
)+
⋅
1
(32.3)
g
g
B g
B
oil
p elagic
benthic
=
⋅ −
(
)+
⋅
1
(32.4)
The m oil term represents a weighted average of a pelagic mortality modifier (m pelagic )
and a benthic mortality modifier (m benthic ) that reflects the proportion of B in the
affected group’s diet that comes from either benthic or pelagic prey. Growth rate g oil
is similarly weighted based on pelagic and benthic diet. These modifiers were calculated from the dose-response models developed by Dornberger et al. (2016) to
describe the effects of polycyclic aromatic hydrocarbons (PAH) on growth and mortality rates in fishes. The most parsimonious and best fit by Dornberger et al. (2016)
were “hockey-stick” models that imply the existence of a PAH concentration threshold below which there are no adverse effects and above which there is a log-linear
increase in mortality (Eq. 32.5) and decrease in growth (Eq. 32.6):
m t
t
= ⋅
⋅
α
ϕ β
log
1
(32.5)
g t
t
= − ⋅
⋅
1
1
γ
ϕ δ
log
(32.6)
These dose-response models (Eqs. 32.5 and 32.6) estimate the mortality and growth
as a function of the amount of bioavailable oil (φ t ) at time step t. The estimates,
32 Comparing Ecosystem Model Outcomes Between Ixtoc 1 and Deepwater...