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Question

Q.(a)

(i) Describe the population growth curve applicable in a population of any species in nature that has limited resources at its disposal.
(ii) Give the equation of this growth curve.
(iii) Name the growth curve and depict a graphical plot for this type of population growth.
(OR)
(b)
(i) Explain the Species-Area relationship within a natural forest and also predict the nature of graph when species richness is plotted against the area for a wide variety of taxa.
(ii) Depict the graphical relationship between species richness and area.
(iii) Give the equation of the Species-Area relationship for a wide variety of taxa on a logarithmic scale.
CBSECBSE Class XII Board 2025Subjective· 5mImportance★★★★★
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Figure — OR-alternative (a) asks to name and 'depict a graphical plot' of the resource-limited (logistic) growth curve;
Figure — OR-alternative (a) asks to name and 'depict a graphical plot' of the resource-limited (logistic) growth curve;

Part (a): A population with limited resources follows the logistic (sigmoid) growth curve, dN/dt = rN[(K-N)/K], levelling off at the carrying capacity K.

Part (b): The species-area relationship shows species richness rising with area (a hyperbola, straight on a log-log plot) described by log S = log C + Z log A.

Part (a)

(i) The growth curve under limited resources

No natural habitat has unlimited resources, so a population cannot grow exponentially for long. Growth follows a logistic pattern:

  • a slow initial lag phase,
  • a phase of rapid (acceleration/exponential) growth,
  • deceleration as resources (food, space) become limiting and competition rises,
  • stabilisation around the carrying capacity (K) — the maximum number the habitat can support.

(ii) Equation

dN/dt = rN[(K − N)/K]

where N = population size at time t, r = intrinsic rate of natural increase, and K = carrying capacity. When N is small, (K-N)/K is near 1 and growth is almost exponential; as N approaches K the term approaches 0 and growth stops.

(iii) Name and graph

This is the logistic growth curve (Verhulst-Pearl logistic curve), giving a sigmoid / S-shaped plot:

N |            ________ K (carrying capacity)
  |          /
  |        /
  |      /
  |____/________________ time (t) …

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