First Test: Sustained Population
Imagine that the model developers present the test simulation in Figure 2 as evidence that the simplified model provides a reasonable measure of the magnitude of the brine shrimp population under conditions prevailing in the mid 1980s. The test assumes that the lake elevation is constant at 6380 feet. Botkin (1988, p. 13) reports that the salinity depends on the elevation in a nonlinear manner, and the model uses the following graph function to capture the nonlinear relationship:
salinity = GRAPH(elevation)
(6330, 250), (6335, 210), (6340, 190), (6345, 170), (6350, 155), (6355, 140),
(6360, 130), (6365, 120), (6370, 110), (6375, 97.0), (6380, 88.0)
With the elevation fixed at 6380 feet, the salinity remains constant at 88 g/L (grams per liter). The populations are measured in thousands of shrimp per square meter, a unit of measure used to report shrimp concentrations at measuring stations (NRC 1987, p. 74). The model projects that the nauplii and juveniles would appear each spring at around 35 ks/sm (thousand shrimp per square meter). No losses are assumed for this stage of the life cycle. Consequently, around 35 ks/sm adult shrimp appear each summer. Predation from birds lowers the adult population during the course of the summer.
Figure 2. Test of the Brine Shrimp Model with Constant Elevation.
Figure 2 is presented as evidence that the model provides a reasonable simulation under conditions in the 1980s. The model developers are pleased that the projected level of 35 ks/sm agrees with measurements taken from the lake in 1985 (NRC 1987, p. 74). They are also pleased that the model shows a sustainable brine shrimp population from one year to the next because the shrimp are expected to do well if the salinity is maintained at 88 g/L (Botkin 1988, p. 13).
Second Test: Declining Population
Now, imagine that you are shown the test results for a 100 year simulation in Figure 3. The test begins with the elevation held constant at 6380 feet as before. The salinity is at 88 g/L, and the adult population appears as a spike on the graph with the height of each spike at around 35 ks/sm. After 120 months, the elevation is lowered by 5 feet. This raises the salinity to 97 g/L, and the model responds with a downward adjustment of the adult population that would appear in the lake each summer. With 97 g/l, the population is still above 30 ks/sm. After another ten years, the elevation is lowered to 6370 feet causing the salinity to increase to 110 g/L. Figure 3 shows another downward adjustment in the number of adults to appear in the lake each summer. During this part of the test, the brine shrimp population is between 20 and 25 ks/sm. This is the general vicinity of the "threshold" density for the grebes (NRC 1987, p. 98). (When the shrimp density falls this low, feeding is sufficiently difficult that the grebes could have trouble putting on weight. )
Figure 3. Test of the brine shrimp with increasing salinity.
The remainder of the simulation continues to "step down" the elevation in increments of five feet. By the end of the test, the elevation is at 6350 feet, and the salinity has climbed to 155 g/l. With these conditions, the model shows a negligible population. You are told that this final portion of the test agrees with Botkin's (1988, p. 10) view that a salinity level of 150 g/L would lead to the "demise of the lake ecosystem" because of reduced brood size and reduced hatching survival. Botkin (1988, p. 10) warns that "at this point, the present aquatic ecosystem will have been destroyed except perhaps for small refuge populations of shrimp and flies where fresh water is flowing into the lake."