Class 12th Biology 2017 Set1 Outside Delhi Board Paper Solution

Question 25

Compare, giving reasons, the J-shaped and S-shaped models of population growth of a species.

Answer

(a) There are 2 models of population growth :

(i) The exponential growth

(ii) Logistic growth

(i) Exponential growth :

This growth occurs where the resources (food + space) are unlimited. The equation can be represented as

dN / dt = (b – d) × N

Let (b – d) = r

dN / dt = rN

N_t = N₀ert

N = population size

Nt = population density after time t.

N₀ = population density at time zero

r = growth rate

b = birth rate

d = death rate

In this growth, when N in relation to time is plotted on graph, the curve becomes J-shaped.

(ii) Logistics growth model :

This is a realistic approach as the resources become limited at a certain point of time.

(a) J-shaped curve ⇒ exponential growth

(b) S-shaped curve ⇒ logistics growth

Every ecosystem has limited resources to support a particular maximum carrying capacity (K).

When N is plotted in relation to time t, a sigmoid-S-shaped curve is obtained & is also called as VERHULST-PEARL logistic growth. The equation is :

dN / dt = rN (K − N) / N

N = population density at time t.

r = growth rate

K = carrying capacity.