Environmental Engineering Reference
In-Depth Information
accumulation rate for
i
, while
M
0
i
is the “other mortality” rate for
i
.
P
i
is calculated as
the product of
B
i
the biomass of
i
and (
P
/
B
)
i
, the production/biomass ratio for
i
. The
(
P
/
B
)
i
rate under most conditions corresponds to the total mortality rate,
Z
(see Allen
1971), commonly estimated as part of fishery stock assessments. The “other mortal-
ity” is all mortality not included elsewhere, and is internally computed from (5.2)
P
i
ð
1
EE
i
Þ
M
0
i
¼
(5.2)
;
B
i
where
EE
i
is called the “ecotrophic efficiency” of
i
, and can be described as the
proportion of the production that is utilized in the system. The predation term,
M
2,
in (5.1) serves to link predators and prey as
X
n
Q
j
DC
ji
B
i
M
2
i
¼
(5.3)
;
j¼
1
where the summation is over all
n
predator groups
j
feeding on group
i
,
Q
j
is the
total consumption rate for group
j
, and
DC
ji
is the fraction of predator
j
's diet
contributed by prey
i
.
Q
j
is calculated as the product of
B
j
, the biomass of group
j
and (
Q
/
B
)
j
, the consumption/biomass ratio for group
j
. For parameterization Eco-
path sets up a system with (at least in principle) as many linear equations as there
are groups in a system, and it solves the set for
one
of the following parameters for
each group, biomass, production/biomass ratio, consumption/biomass ratio, or
ecotrophic efficiency. The other three parameters along with the following para-
meters must be entered for all groups, catch rate, net migration rate, biomass
accumulation rate, assimilation rate and diet compositions (for more details see
Christensen and Walters
2004
).
Within each group energy balance is ensured using the following master equa-
tion two:
Master equation two:
Consumption
¼
production
þ
respiration
þ
unassimilated food
(5.4)
:
This equation is in line with Winberg (1956), who defined consumption as
the sum of somatic and gonadal growth, metabolic costs and waste products.
In Ecopath it was chosen to estimate respiration from the difference between
consumption and the production and unassimilated food terms. This reflects the
focus on application for fisheries analysis, where respiration rarely is measured
while the other terms are more readily available. Besides units of wet weight
biomass, Ecopath models can be constructed using energy as well as with nutrient
related currencies. If a nutrient-based currency is used in Ecopath the respiration
term is excluded from the above equation (as nutrients are not respired), and the
unassimilated food term is estimated as the difference between consumption and
production.
