Question

Biologists need to estimate the fish population in a lake without harming the fish. They use a method of catching, tagging, and releasing 96 fish. A week later, they catch 72 fish, of which 4 are tagged. Assuming that the catch is representative, how many fish live in the lake?

Answer 1

Using the mark and recapture method, a proportion is set up with the number of tagged fish in the initial and second catches. With 96 tagged fish initially and 4 of 72 fish tagged in the second catch, the estimated fish population in the lake is 1728 individuals.

Step-by-step explanation:

Biologists can estimate the fish population in a lake using the mark and recapture method, which involves catching, tagging, and releasing a sample of the population, then later capturing another sample to see how many tagged fish are in the new catch. In this case, 96 fish were initially tagged and released. Subsequently, 72 fish were caught with 4 beings tagged. Using this information, we set up a proportion where 96 (initially tagged) is to estimated population size (N) as 4 (tagged fish in second catch) is to 72 (total second catch). Solving for N gives us 96/4 = N/72, which simplifies to N = 96*72/4, giving an estimated population of 1728. Therefore, there are an estimated 1728 total individuals in the original population.

There are some limitations to the mark and recapture method. Animals may learn to avoid capture after being tagged or may prefer to be retrapped, potentially affecting the accuracy of the population estimate. Alternative methods include electronic tracking and using data from commercial operations.