Class 12th Biology 2017 Set2 Outside Delhi Board Paper Solution
Compare, giving reasons, the J-shaped and S-shaped models of population growth of a species.
(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
or
Nt = 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.
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