Mathematical derivation of fishing mortality in fisheries population dynamics:
In fish stock assessment, fishing mortality rate ($F$) is directly proportional to nominal fishing effort ($f$) through the catchability coefficient ($q$):
$F = q \times f$
Given data:
$f = 8000\text{ vessels}$
$q = 5 \times 10^{-4}\text{ vessel}^{-1}\text{ year}^{-1}$
Calculation:
$F = (5 \times 10^{-4}) \times 8000$
$F = 5 \times 10^{-4} \times 8 \times 10^3 = 40 \times 10^{-1} = 4.0\text{ year}^{-1}$
Evaluating options:

• 0 would result if effort were 4000 vessels.
• 0 matches the exact calculated value.
• 6 and (D) 3.2 are incorrect.