Based upon r or Ro, is the population growing, declining, or stable? How often do we get a new generation of fish? Justify your answer.

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Based upon r or Ro, is the population growing, declining, or stable? How often do we get a new generation of fish? Justify your answer.

**Table Analysis and Interpretation: Fish Population Dynamics**

**Question: B6. Based upon \( r \) or \( R_0 \), is the population growing, declining, or stable? How often do we get a new generation of fish? Justify your answer.**

**Data Table**

1. **Age Class Intervals (\( x \))**: 
   - The intervals range from 0 to 7.99.

2. **Frequency (\( g(x) \))**: 
   - Total count of fish within each age class.
   - Values: 15, 9, 11, 13, 25, 15, 7, 1.
   - Total sum: 106.

3. **Percentage (\( \%g(x) \))**:
   - Percentage makeup within the population.
   - Values range from 1% to 24%.

4. **Survivorship (\( l(x) \))**:
   - Proportion of the original cohort surviving to each age class.
   - Starts at 106 and decreases with age.

5. **Survivorship Proportion (\( l(x) \% \))**:
   - Expresses survivorship as a percentage of the initial cohort.
   - Begins at 100% and drops to 1%.

6. **Reproduction (\( l(x) \times m(x) \))**:
   - Product of survivorship and reproduction at each interval.
   - Values vary, with highlights like 32 and 6.29.

7. **Reproductive Rate (\( x^*(l(x) \times m(x)) \))**:
   - Integrated measure considering age and productivity.
   - Peaks at 48.23 and varies across intervals.

**Summary Values**
- **\( R_0 \) (Net Reproductive Rate)**: 24.78
- **\( T \) (Generation Time)**: 3.80 months
- **\( r \) (Intrinsic Rate of Increase)**: 0.84

**Conclusion**
- **Population Status**: The population is growing since \( R_0 \) is greater than 1 and \( r \) is positive.
- **Generation Turnover**: A new generation of fish appears approximately every 3.80 months. This indicates rapid turnover and supports the growth trend given the positive \( r \).

This data implies an active reproductive cycle contributing
Transcribed Image Text:**Table Analysis and Interpretation: Fish Population Dynamics** **Question: B6. Based upon \( r \) or \( R_0 \), is the population growing, declining, or stable? How often do we get a new generation of fish? Justify your answer.** **Data Table** 1. **Age Class Intervals (\( x \))**: - The intervals range from 0 to 7.99. 2. **Frequency (\( g(x) \))**: - Total count of fish within each age class. - Values: 15, 9, 11, 13, 25, 15, 7, 1. - Total sum: 106. 3. **Percentage (\( \%g(x) \))**: - Percentage makeup within the population. - Values range from 1% to 24%. 4. **Survivorship (\( l(x) \))**: - Proportion of the original cohort surviving to each age class. - Starts at 106 and decreases with age. 5. **Survivorship Proportion (\( l(x) \% \))**: - Expresses survivorship as a percentage of the initial cohort. - Begins at 100% and drops to 1%. 6. **Reproduction (\( l(x) \times m(x) \))**: - Product of survivorship and reproduction at each interval. - Values vary, with highlights like 32 and 6.29. 7. **Reproductive Rate (\( x^*(l(x) \times m(x)) \))**: - Integrated measure considering age and productivity. - Peaks at 48.23 and varies across intervals. **Summary Values** - **\( R_0 \) (Net Reproductive Rate)**: 24.78 - **\( T \) (Generation Time)**: 3.80 months - **\( r \) (Intrinsic Rate of Increase)**: 0.84 **Conclusion** - **Population Status**: The population is growing since \( R_0 \) is greater than 1 and \( r \) is positive. - **Generation Turnover**: A new generation of fish appears approximately every 3.80 months. This indicates rapid turnover and supports the growth trend given the positive \( r \). This data implies an active reproductive cycle contributing
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