A fish population in a lake follows the logistic growth model dN/dt = rN(1 - N/K) - H, where r is the intrinsic growth rate (per month) and K is the carrying capacity (fish). The intrinsic rate is r = 0.4 per month and the carrying capacity is K = 5 000 fish.

(a) Determine the maximum constant harvest H_max (fish per month) that still allows a non‑zero equilibrium population.

(b) If the actual harvest is set at 800 fish per month, calculate the equilibrium population size (if any).

(c) Based on your results, state whether the harvest of 800 fish per month is sustainable.

Question

A fish population in a lake follows the logistic growth model dN/dt = rN(1 - N/K) - H, where r is the intrinsic growth rate (per month) and K is the carrying capacity (fish). The intrinsic rate is r = 0.4 per month and the carrying capacity is K = 5 000 fish.

(a) Determine the maximum constant harvest H_max (fish per month) that still allows a non‑zero equilibrium population.

(b) If the actual harvest is set at 800 fish per month, calculate the equilibrium population size (if any).

(c) Based on your results, state whether the harvest of 800 fish per month is sustainable.

Accepted Answer

Maximum sustainable harvest = 500 fish per month; with a harvest of 800 fish per month the equilibrium population is 0 (extinction); therefore the harvest is not sustainable.

Waec Model Questions Vol1 2025 Biology Question 6

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