Consider a case where 400 fish are tagged and released during a first outing. During a second outing in the same area, 400 fish are again caught and released, of which half are already tagged. Estimate N, the total number of fish in the entire sampling area.

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Consider a case where 400 fish are tagged and released during a first outing. During a second outing in the same area, 400 fish are again caught and released, of which half are already tagged. Estimate N, the total number of fish in the entire sampling area.

### Mark-Recapture Method for Estimating Wildlife Populations

**Instructions:**

1. **Research and Report:** 
   - Explore methods used to estimate wildlife populations in a region.
   - Focus on studies that utilize the "catch and release" method.
   - Note the study titles, locations, and the type of wildlife counted.
   - Cite each study with appropriate URLs and page titles where applicable.

2. **Calculating Population Estimates:**
   - **Scenario 1:** Tag and release 400 fish in a first outing. During a second outing in the same area, recapture 400 fish, with half of them previously tagged. Estimate the total number of fish, \( N \), present in the sampling area.
   - **Explain your reasoning** for the estimate calculated in #3.

3. **Different Estimation Scenario:**
   - **Scenario 2:** Again, tag and release 400 fish. In the second outing, 400 are recaptured, but this time only one fourth are already tagged. Calculate \( N \), the total number of fish.
   - **Provide reasoning** for this calculation as in #5.

4. **Generalization:**
   - Develop a formula \( N = f(p) \), where \( p \) is the fraction of tagged fish caught during the second outing.

5. **Graphical Representation:**
   - **Graph the Function:** Create a detailed graph of the function from #7.
   - Determine the **domain** (possible values of \( p \)) and the **range** (possible values of \( N \)) from your graph.
   
6. **Comparison and Analysis:**
   - Choose one study from your research that aligns with tasks #3-10.
   - Compare and contrast its methodology with this exercise. Discuss accuracy and alignment with theoretical expectations.

This procedure is designed to enhance understanding of population estimation techniques, specifically focusing on practical and theoretical applications of the mark-recapture method.
Transcribed Image Text:### Mark-Recapture Method for Estimating Wildlife Populations **Instructions:** 1. **Research and Report:** - Explore methods used to estimate wildlife populations in a region. - Focus on studies that utilize the "catch and release" method. - Note the study titles, locations, and the type of wildlife counted. - Cite each study with appropriate URLs and page titles where applicable. 2. **Calculating Population Estimates:** - **Scenario 1:** Tag and release 400 fish in a first outing. During a second outing in the same area, recapture 400 fish, with half of them previously tagged. Estimate the total number of fish, \( N \), present in the sampling area. - **Explain your reasoning** for the estimate calculated in #3. 3. **Different Estimation Scenario:** - **Scenario 2:** Again, tag and release 400 fish. In the second outing, 400 are recaptured, but this time only one fourth are already tagged. Calculate \( N \), the total number of fish. - **Provide reasoning** for this calculation as in #5. 4. **Generalization:** - Develop a formula \( N = f(p) \), where \( p \) is the fraction of tagged fish caught during the second outing. 5. **Graphical Representation:** - **Graph the Function:** Create a detailed graph of the function from #7. - Determine the **domain** (possible values of \( p \)) and the **range** (possible values of \( N \)) from your graph. 6. **Comparison and Analysis:** - Choose one study from your research that aligns with tasks #3-10. - Compare and contrast its methodology with this exercise. Discuss accuracy and alignment with theoretical expectations. This procedure is designed to enhance understanding of population estimation techniques, specifically focusing on practical and theoretical applications of the mark-recapture method.
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