Question

Which of the following relationship gives an asymptotic curve?

• A. Fishing effort and yield
• B. Age and length of fish
• C. Fishing effort and CPUE
• D. Cushing's fish stock recruitment relationship

Hint:

Always associate the term "Asymptotic" with "von Bertalanffy" and "Growth." It simply means that fish don't grow infinitely; they reach a maximum size $L_\infty$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
An asymptotic curve is one that approaches a specific value but never quite reaches it over a finite interval. In biology, this represents a "limit to growth."
Detailed Explanation:
1. Age and Length: This relationship is modeled by the von Bertalanffy Growth Function (VBGF). The equation is:
\[ L_t = L_{\infty} [1 - e^{-K(t - t_0)}] \]
As age (\(t\)) increases, the length (\(L_t\)) approaches the theoretical maximum length (\(L_{\infty}\)). This produces a curve that is steep at young ages and flattens out as it approaches the asymptote \(L_{\infty}\).
2. Fishing Effort and Yield: In the Schaefer model, this gives a parabolic curve (bell-shaped), where yield reaches a maximum (MSY) and then declines.
3. Fishing Effort and CPUE: This is usually a linear (negative) relationship in the Schaefer model or an exponential decay in the Fox model.
4. Stock-Recruitment: Cushing’s model usually produces a power curve, while Beverton-Holt is asymptotic and Ricker is dome-shaped. However, "Age and Length" is the most fundamental and universally recognized asymptotic relationship in fisheries.

Step 2: Final Answer:
The relationship between age and length of fish provides an asymptotic curve.