World Aquaculture 9 Exercise 1 – Pond Inventory Using Marked Simulated Fish This involves counting marked individuals and estimating the size of the population after releasing the marked simulated, in this case, fish back into the pond. To start, we’ll use a 0.45 kg bag of large dry lima beans; these beans will be our fish. Count out 80 beans and mark each of them with an X on both sides (Figure 2). Then, mix them with the unmarked beans in a small bucket (our pond). Use you hand to mix the marked and unmarked beans completely. After the beans are mixed up, reach in and get a handful. Count the number of marked and unmarked beans, and then return all the beans to the bucket. Repeat this procedure three times. Show your answers on Table 1. Table 1. Estimated beans in the bucket using one handful samples. Sample Total number Total number Total number of Estimate of total number of marked of beans in marked beans number of beans beans (a) sample (n) in sample (r) in bucket (N) 1 80 2 80 3 80 Fig. 2. Lima beans in a bucket. Some are marked with X. Photo by M. Landau. Solve for N using the equation above; do this for all three samples. The value of a will be the original number of marked beans (80). Finally, count all the beans in the bucket to find out how good the estimate (N) was of the true total. Student Question – You now know how many beans were really in the bucket. Why did you get different values for N each time you sampled? Answer – Even though the beans were mixed in the bucket, this doesn’t mean that they had a perfectly uniform distribution. That is the reason that one handful is not exactly the same as another. Therefore, since each (n) and (r) were different, each (N) was different. To increase the accuracy of (N) you can either increase the number of marked beans, increase the sample size or both. This results in more marked beans being counted, which should result in less sample variation. To test this, mark 20 more beans and mix them in with the rest of the beans, so now (a) is 100. Now, rather than taking one handful of beans, take two handsful for each sample. Repeat the experiment above to see if (N) is now a better estimator of the true number of beans in the bucket. Put your answers in Table 2. Table 2. Estimated beans in the bucket using two handful samples. Sample Total number Total number Total number of Estimate of total number of marked beans (a) of beans in marked beans number of beans sample (n) in sample (r) in bucket (N) 1 100 2 100 3 100
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