A fish population in a lake obeys the logistic growth equation $ \frac{dN}{dt}=rN\left(1-\frac{N}{K}\right) $ with intrinsic rate $ r = 0.08\ \text{yr}^{-1} $ and carrying capacity $ K = 1.2\times10^{5} $ fish. A constant annual harvest $ H $ is imposed.

(a) Determine the maximum sustainable yield (MSY) and the equilibrium population size when the harvest equals the MSY.

(b) If a pollution event reduces the carrying capacity by 25 % while $ r $ remains unchanged, what is the new MSY?

Question

A fish population in a lake obeys the logistic growth equation $ \frac{dN}{dt}=rN\left(1-\frac{N}{K}\right) $ with intrinsic rate $ r = 0.08\ \text{yr}^{-1} $ and carrying capacity $ K = 1.2\times10^{5} $ fish. A constant annual harvest $ H $ is imposed.

(a) Determine the maximum sustainable yield (MSY) and the equilibrium population size when the harvest equals the MSY.

(b) If a pollution event reduces the carrying capacity by 25 % while $ r $ remains unchanged, what is the new MSY?

Accepted Answer

MSY = 2400 fish/yr, equilibrium = 60 000 fish; after pollution, new MSY = 1800 fish/yr

Gce Model Questions Vol1 2025 Biology Question 48

Answer Options

About This Question

Master the Exam!