Question

Beverton and Holt's fish stock-recruitment model suggests that the relationship between parent stock and recruitment is

• A. Positive linear
• B. Negative linear
• C. Bell shape
• D. Asymptote

Hint:

Stock-Recruitment Curves:
Beverton-Holt Model $\rightarrow$ ASYMPTOTE (Plateau Saturation curve).
Ricker Model $\rightarrow$ BELL DOME-SHAPED (Peaked with density-dependent crash).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Mathematical stock-recruitment relationships (SRR): Beverton-Holt model describes density-dependent juvenile mortality approaching a horizontal asymptotic plateau at high spawner biomass, whereas Ricker's model is dome/bell-shaped.
Key Formula or Approach:
\[ R = \frac{\alpha S}{1 + \beta S} \quad \implies \quad \lim_{S \to \infty} R = \frac{\alpha}{\beta} = R_{\max} \quad \text{[Asymptotic Saturation Curve]} \]

Step 2: Detailed Explanation:
Comparing mathematical Stock-Recruitment Models in fisheries science:
1. Beverton and Holt Model (1957) (D): Assumes density-dependent juvenile mortality during pre-recruit stages (competition for food/space). As parent stock ($S$) increases, recruitment ($R$) initially rises steeply and then levels off smoothly to a horizontal Asymptote (saturation plateau, $R_{\max} = \alpha/\beta$).
2. Ricker Model (1954): Assumes cannibalism or density-dependent predation ($R = \alpha S e^{-\beta S}$), producing a dome-shaped bell-shaped curve where recruitment crashes at high stock densities.

Step 3: Final Answer:
Hence, Beverton and Holt's model suggests an Asymptote relationship, matching option (D).