Question

What is the maximum sustainable yield (tonnes) of an unexploited stock with biomass of 35 tonnes and natural mortality rate of 0.8 per year?

• A. 44
• B. 28
• C. 14
• D. 7

Hint:

Remember Gulland's Formula: \( MSY = 0.5 \cdot M \cdot B_0 \).
If the question states the stock is already exploited, the formula changes to Cadima’s formula: \( MSY = 0.5 \cdot Z \cdot B \).
Always check if the stock is unexploited before using 0.5 MB.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the Maximum Sustainable Yield (MSY) based on basic population parameters (Biomass and Natural Mortality) for an unexploited stock.
Key Formula or Approach:
For unexploited or virgin stocks, a common empirical formula used is Gulland’s (1971) equation:
\[ MSY = 0.5 \times M \times B_v \]
Where:
1. \( M \) is the Natural Mortality rate.
2. \( B_v \) (or \( B_0 \)) is the Virgin (unexploited) Biomass.

Step 2: Detailed Explanation:

• Given Data:
• Biomass (\( B_v \)) = 35 tonnes.

• Natural Mortality (\( M \)) = 0.8 per year.

• Calculation:
\[ MSY = 0.5 \times 0.8 \times 35 \]
\[ MSY = 0.4 \times 35 \]
\[ MSY = 14 \text{ tonnes} \]

• Logic: The formula assumes that MSY is achieved when the fishing mortality (\( F \)) equals the natural mortality (\( M \)) and the biomass is reduced to half of its virgin level (\( 0.5 B_v \)). Although modern fisheries science often uses more conservative multipliers (like 0.2 or 0.3), in standardized exam contexts, 0.5 is the default value for Gulland's formula.

Step 3: Final Answer:
The maximum sustainable yield is 14 tonnes.