A fish population in a lake follows logistic growth described by $\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)$ where the intrinsic growth rate $r = 0.6\ \text{year}^{-1}$ and the carrying capacity $K = 8000$ fish. A constant harvest of $H$ fish per year is introduced.

(a) Determine the maximum sustainable harvest (MSY) that can be removed without causing the population to collapse.
(b) If a harvest of 1500 fish per year is implemented, state whether this harvest is sustainable and, if not, explain the expected outcome.

Question

A fish population in a lake follows logistic growth described by $\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)$ where the intrinsic growth rate $r = 0.6\ \text{year}^{-1}$ and the carrying capacity $K = 8000$ fish. A constant harvest of $H$ fish per year is introduced.

(a) Determine the maximum sustainable harvest (MSY) that can be removed without causing the population to collapse.
(b) If a harvest of 1500 fish per year is implemented, state whether this harvest is sustainable and, if not, explain the expected outcome.

Accepted Answer

Maximum sustainable harvest = 1200 fish / year; a harvest of 1500 fish / year exceeds this limit, so the population will decline toward extinction (not sustainable).

Neco Model Questions Vol1 2021 Biology Question 43

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