In a closed lake, a fish population follows the logistic growth model $ \frac{dN}{dt}=rN\left(1-\frac{N}{K}\right) $ with intrinsic rate $ r = 0.4\ \text{year}^{-1} $ and carrying capacity $ K = 5000 $ individuals. A constant harvest of $ H = 300 $ fish per year is imposed.

(a) Determine the positive equilibrium population size(s) $ N^* $.
(b) State whether the harvest rate is sustainable (i.e., whether a stable positive equilibrium exists).

Question

In a closed lake, a fish population follows the logistic growth model $ \frac{dN}{dt}=rN\left(1-\frac{N}{K}\right) $ with intrinsic rate $ r = 0.4\ \text{year}^{-1} $ and carrying capacity $ K = 5000 $ individuals. A constant harvest of $ H = 300 $ fish per year is imposed.

(a) Determine the positive equilibrium population size(s) $ N^* $.
(b) State whether the harvest rate is sustainable (i.e., whether a stable positive equilibrium exists).

Accepted Answer

Approximately 4080 individuals; harvest is sustainable

Neco Model Questions Vol1 2023 Biology Question 43

Answer Options

About This Question

Master the Exam!