On an isolated island, the immigration rate of a species is I(N)=I₀(1-N/S) and the extinction rate is E(N)=E₀(N/S), where N is the number of species present, S=50 is the maximum possible species number, I₀=12 species Myr⁻¹ and E₀=4 species Myr⁻¹.
(a) Find the equilibrium number of species (N₁) where immigration equals extinction.
(b) After a new predator is introduced, immigration is reduced by 20% and the extinction constant rises to E₀'=6 species Myr⁻¹. Find the new equilibrium number of species (N₂). Give both answers to the nearest whole species.

Question

On an isolated island, the immigration rate of a species is I(N)=I₀(1-N/S) and the extinction rate is E(N)=E₀(N/S), where N is the number of species present, S=50 is the maximum possible species number, I₀=12 species Myr⁻¹ and E₀=4 species Myr⁻¹.  
(a) Find the equilibrium number of species (N₁) where immigration equals extinction.  
(b) After a new predator is introduced, immigration is reduced by 20% and the extinction constant rises to E₀'=6 species Myr⁻¹.  Find the new equilibrium number of species (N₂).  Give both answers to the nearest whole species.

Accepted Answer

N₁≈38 species; N₂≈31 species

Waec Model Questions Vol1 2025 Biology Question 37

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