Name:
Stocking Lake Corpus Christi
Exploring Recursive Models for Fish Populations
» A Fishy Business
Lake Corpus Christi is a large lake (18,256 surface acres) with a lot of fish. Starting in 1972, the
Texas Parks and Wildlife Department has occasionally stocked Lake Corpus Christi with fish to
support recreational fishing and a balanced ecosystem.
Some examples of annual numbers of new fish stocked in Lake Corpus Christi include:
 2,000,000 walleye in 1973

533,172 palmetto bass in 1995

456,349 largemouth bass in 2009

1,500 rainbow trout in 2010
Officials could track the new fish using radio frequency tags, but in practice they use
mathematical and statistical models for estimating the fish population levels in the lake.
walleye
largemouth bass
palmetto bass
rainbow trout
1. Why do you think the Texas Parks and Wildlife Department decided to introduce so
many new walleye into Lake Corpus Christi in 1973?
2. The Texas Parks and Wildlife Department has stocked between 1,000 and 2,500 new
rainbow trout into Lake Corpus Christi nearly every year since 1993. Why do you think
they’ve stock the lake with this number of trout each year?
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Some Hypothetical Fish Population Models
For simplicity, let’s suppose the four example fish stocking levels are initial populations of the
walleye, palmetto bass, largemouth bass, and rainbow trout in Lake Corpus Christi. In addition,
suppose officials are considering the following possible models for the fish populations.
Model 1: The walleye population could be decreasing steadily by approximately 75,000 fish per
year. The decrease might reduce to a more manageable 40,000/yr after the population reaches
about 1.5 million.
Model 2: The palmetto bass population might initially decrease, but by smaller amounts each
year. The annual change in palmetto bass might follow the pattern
−50,000, −42,000, −34,000, −26,000, −18,000, … and so on.
Model 3: The largemouth bass population might be decreasing by about 18% each year.
Model 4: The largemouth bass population could be related to the number of fertile females. The
annual population increase could be 3 times the number of fertile females, which might have
started around 200,000 and be dropping by about 25% each year.
Model 5: The rainbow trout population might change each year according to amount 300 −
60𝑛, where 𝑛 stands for the number of years since the trout were first introduced.
Model 6: The palmetto bass population could be decreasing rapidly. Based on reports from
fisherman, perhaps the fish population will decline each year by about 83%.
Model 7: Suppose we count the rainbow trout in Lake Corpus Christi in thousands, so the trout
population was 1.5 in 2010, and the lake can support up to 500. In addition, the population next
year might be proportional to both the population this year and the difference between the
capacity and the population. If 𝐿 stands for the number of largemouth bass in a given year (in
thousands), then the number of largemouth bass the following year might be:
. 00765 ∗ 𝐿 ∗ (500 − 𝐿)
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Name:
Group Activity
Work in a small group to complete Tasks 1-3:
Task 1: Understand the Model
Use separate paper to complete the following:
1. Select one of the hypothetical models for the fish populations.
2. Using your chosen model, create a table of population estimates for 20 years after the
initial stocking of your species. Label your table values and round appropriately.
3. List some reasons that might have led the officials to propose your population model.
4. Consider the time-frame for which your model might be appropriate (this is called the
domain of the model). Do your model’s predicted values seem reasonable for years prior
to the stocking of the lake (negative years)? How many years after the initial stocking
might it be reasonable to extrapolate?
5. What are the limitations of your model? What changes would you consider making to the
model if you had access to more data?
Task 2: Create a Poster for Your Model
After you get a handle on your model in Task 1, your next job is to communicate your
understanding through a poster. Include each of the following:
1. A brief description of your model in words
2. A table of population estimates based on your model
3. One or more equations that describe your model
4. A graph describing the short and long-term population change in the fish population
5. A few “Findings and Recommendations” based on your group’s explorations
Task 3: Present your Model to the Class
Choose one or two group members to deliver a brief summary of your groups’ model and its
predictions for the fish population.
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