Model Details
The results in Figures 2 and 3 seem reasonable,
so imagine that you press the developers for more details. You are told
that the model is based on a simplified life cycle which ignores live births
and concentrates on births from cysts. The stock of overwintering cysts
is initialized at 250 ks/sm and is fed by cyst deposition and drained by
two outflows. The two outflows are timed to occur in the 2nd month of each
year:
potential_births = if (monthly_counter=2) then overwintering_cysts else
0
births_from_cysts = potential_births*cyst_hatching_fraction
cyst_loss = potential_births*(1-cyst_hatching_fraction)
The potential births is the entire stock of overwintering cysts that exist
when the monthly conuter reaches 2. The births flow is potential births
multiplied by the hatching fraction; the loss flow is the potential births
multiplied by (1-hatching fraction). These flows will empty out the stock
of overwintering cysts during the 2nd month of each year. (Set DT = 1 month
and select the "Euler" integration method to allow these flows
to do their job correctly.) The cyst loss flow removes cysts from the system;
the births from cysts begins the next generation of animals that will eventually
mature into adults. The cyst hatching fraction can range from zero to 60%
depending on the salinity:
cyst_hatching_fraction = GRAPH(salinity)
(50.0, 0.6), (75.0, 0.2), (100, 0.12), (125, 0.07), (150, 0.03), (175, 0.01),
(200, 0.00)
The nauplii and juveniles stages of the shrimp life cycle
are combined into a single conveyor with no losses. The transit time is
represented by the naup & juv interval which is set to 4 months. The
adult interval is set to two months, and the predation loss fraction is
set at 50%. Both of the converyors are initialized at zero. With these assumptions,
the adults will not appear until the 7th and 8th months of each year. These
are the months when the shrimp feed on planktonic algae, but the model does
not simulate the algae concentration explicitly. Rather, it defines a capacity
of the lake to accommodate the shrimp's need for food. The capacity may
vary with the month of the year and with the salinity of the lake, as shown
in the following equations:
capacity = normal_capacity*capacity__multiplier
normal_capacity = if (monthly_counter=7) then 30 else 20
capacity__multiplier = GRAPH(salinity)
(50.0, 1.00), (75.0, 1.00), (100, 1.00), (125, 0.9), (150, 0.5), (175, 0.1),
(200, 0.00)
The capacity is normally at 30 ks/sm for the 7th month and 20 ks/sm for the 8th month. These monthly levels may decline, however, if the salinity climbs above 100 g/L. At 150 g/L, for example, the monthly capacities are cut in half. The adult shrimp population is compared with the capacity to find congestion, a dimensionless variable representing the balance between the shrimp and their food supply. The congestion is then used to find the brood size. The brood size determines the cyst deposition, as shown below:
brood_size = GRAPH(congestion)
(0.00, 50.0), (0.25, 20.0), (0.5, 15.0), (0.75, 12.0), (1.00, 10.0), (1.25,
8.00), (1.50, 5.00), (1.75, 1.00), (2.00, 0.00)
congestion = if (monthly_counter=7 or monthly_counter=8) then (adults/capacity)
else .5
cyst_depostion = female_adults*brood_size/interval_between_broods
female_adults = adults*fraction_female
fraction_female = .5
interval_between_broods = 1
At this point, you know enough to build and verify the brine shrimp model.
If you study the food web in Mono Lake (NRC 1987; Botkin 1988), you may
become interested in expanding the model. You could challenge yourself to
improve the model by adding
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