Biologists collected a sample of 600 fish from West Okoboji Lake on May 1 and tagged each of them. When they returned on June 1, a new sample of 800 fish was collected and 10 of these had been previously tagged. Use this experiment to determine the approximate fish population of West Okoboji Lake.
The intuitive solution is by ratio assuming the population can be extrapolated by the sample, thus
population
=(600*(800/10)=48000.
To determine the approximate fish population of West Okoboji Lake, we can use the mark and recapture method. This method involves tagging a specific number of fish in the first sample, releasing them back into the lake, and then collecting a second sample to see how many of the tagged fish are present. Based on this information, we can estimate the total fish population.
Let's break down the steps to calculate the estimated fish population using the mark and recapture method:
Step 1: Calculate the initial population size (N) based on the first sample.
The number of fish in the initial sample is 600 (tagged individuals).
Therefore, the size of the entire population can be estimated using the Lincoln-Petersen Index formula:
N = (M * C) / R
Where:
N = Total population size
M = Number of marked individuals in the first sample
C = Total number of individuals in the second sample
R = Number of recaptured individuals in the second sample
In this case:
M = 600 (tagged fish in the initial sample)
C = 800 (total fish in the second sample)
R = 10 (recaptured fish in the second sample)
Using the formula, we can calculate:
N = (600 * 800) / 10
N = 48,000 / 10
N = 4,800
The estimated fish population in West Okoboji Lake is approximately 4,800.
It's important to note that this method assumes certain assumptions are met, such as the marked individuals mixing randomly with the population and equal catchability for both marked and unmarked individuals. Additionally, this method provides an approximation and may not be exact.