Question

Answer the following questions:

• [(i)] Describe the population growth curve applicable in a population of any species in nature that has unlimited resources at its disposal.
• [(ii)] Explain the equation of this growth curve.
• [(iii)] Name the growth curve and depict a graphical plot for this type of population growth.
• [(i)] Explain the conclusion drawn by Alexander von Humboldt during his extensive explorations in the wilderness of South American jungles.
• [(ii)] Give the equation of the Species-Area relationship.
• [(iii)] Draw a graphical representation of the relation between species richness and area for a wide variety of taxa such as birds, bats, etc.

Hint:

Exponential (J-shaped) growth occurs only under ideal conditions. In nature, due to limited resources, most populations follow logistic (S-shaped) growth patterns.

Answer 1

1.  
   • [(i)] When unlimited resources are available, populations exhibit exponential growth. The population size increases rapidly without any environmental resistance.
   • [(ii)] The equation for exponential growth is: \[ \frac{dN}{dt} = rN \] where:
     • \( N \) = population size
     • \( r \) = intrinsic rate of natural increase
     • \( \frac{dN}{dt} \) = change in population size per unit time
   • [(iii)] The growth curve is called the J-shaped curve. It shows rapid increase initially and continues rising steeply without a plateau.
2.  
   • [(i)] Alexander von Humboldt observed that within a region, species richness increases with increasing area but only up to a certain limit.
   • [(ii)] The Species-Area relationship equation is: \[ \log S = \log C + Z \log A \] where:
     • \( S \) = species richness
     • \( A \) = area
     • \( C \) and \( Z \) = constants
   • [(iii)] Graphical Representation:
   •