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Q.(a)

(i) Describe the Species-Area relationship as observed by Alexander von Humboldt, for a wide variety of taxa in nature.
(ii) Draw the graph showing Species-Area relationship for S = CA^Z. What is the significance of 'Z' in Species-Area relationship ?
(OR)
(b)
(i) Describe the logistic population growth curve with the help of a suitable graphical representation.
(ii) Write the equation of Verhulst-Pearl logistic growth curve and explain what 'K' and 'r' suggest in the given equation.
CBSECBSE Class XII Board 2025Subjective· 5mImportance★★★★★
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Part (a): Humboldt found species richness increases with area (hyperbola, straight on log-log) as S = C.A^Z, where Z is the slope (regression coefficient).

Part (b): A resource-limited population follows the S-shaped logistic curve; in the Verhulst-Pearl equation dN/dt = rN[(K-N)/K], K is the carrying capacity and r the intrinsic rate of natural increase.

Part (a)

  1. Humboldt's species-area relationship Alexander von Humboldt observed, during his exploration, that within a region species richness increases with the area explored — but only up to a limit, after which the increase slows. For a very wide variety of taxa (angiosperm plants, birds, bats, freshwater fishes), the relation of species number to area is a rectangular hyperbola.
    The species-area relationship: species richness plotted against area is a rectangular hyperbola that becomes a straight line, of slope Z, on a log-log scale.
    The species-area relationship: species richness plotted against area is a rectangular hyperbola that becomes a straight line, of slope Z, on a log-log scale.
  2. Graph, equation and significance of Z The relation is described by: S = C cdot A^{Z} Taking logarithms gives a straight line: log S = log C + Z log A.
log S |        .
      |      .
      |    .
      |  .
      |________ log A
  • S = species richness, A = area, C = intercept (constant). …

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