Game Wardens and Wildlife Managers are often called upon to make an accurate estimate of the population of certain species within a defined area. This investigation is a simulation of the process (tag and release) used by Fish & Game Scientists to estimate the number of fish in a lake.Materials:

Each group will need a lake (paper sack) full of fish (cheddar fish and parmesan fish) and a net (a small cup).Problem:

Make a reasonable prediction of the number of goldfish in a lake by drawing samples and releasing a fixed number of tagged fish. Use the chart provided to record your findings following the procedures on the next page.

Number of Tagged Fish in SampleTotal Number of Fish in Sample. . . . . . . . . . . .

Total Number of Tagged Fish in Sample _______________Procedure:Estimated Number of Fish in Lake _______________

Actual Number of Fish in Lake_______________

- Wash your hands before handling the fish. Scientists are careful not to spread disease to a population with which they are working.

- Fill your sack almost full of cheddar fish.

- Use your “net” to take out a sample (cupful) of fish.

- Count the number of fish you netted in your sample. To “tag” the netted fish, replace each one with a parmesan fish. Record the number of tagged fish as the “total number of tagged fish”.

- Put all the tagged fish back into the lake. Be careful not to let any of the fish jump out onto the floor. If a fish is spilled, remove it from the experiment. This could simulate migration. If you would like to sample a fish, go ahead. This is called predation and you have identified yourself as a predator. Gently shake the bag to thoroughly mix all the fish in the lake. Try not to bruise them.

- Use your net to take out another cupful of fish. Count the number of tagged fish in the sample and record this number as “number of tagged fish in sample”. Count and record the “total number of fish in sample” also. This is called sampling.

- You now have three pieces of information: the total number of tagged fish in the lake, the number of tagged fish in the sample and the total number of fish in sample. Use this information to write two equivalent ratios. Then use the equation you wrote to estimate the total number of fish in the lake.
Use this proportion to estimate the total number of fish in the lake.

Tagged Fish in Lake : Total Fish in Lake = Tagged Fish in Sample : Total Fish in SampleYour estimate of the total fish in the lake is ____________.

- Return your sample of fish to the lake, gently mix the fish, and take another sample. Repeat the counting procedure of part (6) and the use of ratios in part (7) to get another estimate of the lake’s fish population.

- It is important to get an accurate count of the fish population, but each time you net a sample it costs the taxpayers $500 for your time and equipment. So far your samples have cost $1000. If you feel your estimate at this point is accurate, record it on the class chart with your cost. If you think you should try another sample for better accuracy, do the same steps as before. Draw as many samples as you feel you need, but remember each sample costs $500.

- Enter the number of tagged fish in each sample in L1 and the total number of fish in each sample in L2. Place the cursor at the top of L3 and enter L1/L2. This will give you the ratio of the number of tagged fish to total fish for each sample. Compute the average of these ratios in L3 (STAT, CALC, 1 - Var Stats, L3, enter).
Estimated Number of Fish in Lake = Total Tagged Fish in Lake / Average of L3 Ratios- After all data is recorded, count the fish in your lake to find the actual population. Record that actual population.

- Was your estimate close? What might have thrown it off? What do you think of this method for estimating fish populations?

Copyright 1997 by Vicki Fortson Shirley

Corinth High School

Academic & Performing Arts Center

Corinth, MS

vfshirley@tsixroads.com

http://www.ti.com/calc/docs/act/shirley14.htm

Return to Exploring Data with the TI-83