Question

Fox’s Surplus production model implies

• A. Yield per effort increases with increase in fishing effort
• B. Yield per effort decreases and never approaches zero even at high fishing effort
• C. Yield per effort decreases and reaches zero at certain higher level of fishing effort
• D. Yield per effort remains same at all levels of fishing effort

Hint:

Remember:
1. Schaefer = Linear CPUE vs Effort $\rightarrow$ Hits zero.
2. Fox = Logarithmic/Exponential CPUE vs Effort $\rightarrow$ Asymptotic to zero (never touches).
Fox model is preferred when the CPUE data shows a slow, prolonged decline.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question refers to Fox's (1970) surplus production model, which is an alternative to the linear Schaefer model used in fisheries stock assessment.
Key Formula or Approach:
1. Schaefer Model: Assumes a linear relationship between Catch Per Unit Effort (CPUE) and Effort (f): \( U = a - bf \). Here, CPUE hits zero when effort is high.
2. Fox Model: Assumes an exponential relationship: \( \ln(U) = a - bf \) or \( U = e^{a-bf} \).

Step 2: Detailed Explanation:

• Relationship between CPUE and Effort: In the Fox model, as fishing effort (\( f \)) increases, the yield per effort (\( U \)) decreases exponentially.

• Asymptotic behavior: Because the relationship is exponential (\( U = e^{a-bf} \)), the value of \( U \) (yield per effort) will get smaller and smaller as effort increases, but mathematically it will approach zero asymptotically. This means it never actually reaches zero, unlike the linear Schaefer model where the CPUE line intersects the X-axis.

• Biological implication: This model implies that even at extremely high levels of effort, some residual catch might always be possible, representing a more "conservative" or persistent view of stock depletion compared to the Schaefer model.

• MSY in Fox Model: The Maximum Sustainable Yield (MSY) in the Fox model occurs at a lower level of biomass (\( B_{MSY} = B_{\infty} / e \)) compared to the Schaefer model (\( B_{MSY} = B_{\infty} / 2 \)).

Step 3: Final Answer:
The Fox model implies that yield per effort decreases but never reaches zero at high effort levels.