A fish population in a lake follows the logistic growth model $\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)$ with intrinsic growth rate $r=0.4$ yr⁻¹ and carrying capacity $K=200,000$ fish. A constant harvest $H$ fish per year is applied.

(a) Determine the maximum sustainable yield (MSY) and the equilibrium population size at which this yield occurs.
(b) If the fishery wants to keep the stock at least 30 % of the carrying capacity, what is the greatest harvest that can be taken while satisfying this condition?

Question

A fish population in a lake follows the logistic growth model $\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)$ with intrinsic growth rate $r=0.4$ yr⁻¹ and carrying capacity $K=200,000$ fish. A constant harvest $H$ fish per year is applied.

(a) Determine the maximum sustainable yield (MSY) and the equilibrium population size at which this yield occurs.
(b) If the fishery wants to keep the stock at least 30 % of the carrying capacity, what is the greatest harvest that can be taken while satisfying this condition?

Accepted Answer

MSY = 20,000 fish/yr (equilibrium 100,000 fish); maximum harvest with ≥30 % of K = 16,800 fish/yr

Gce Model Questions Vol1 2022 Agricultural Science Question 37

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