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)] With unlimited resources, populations undergo exponential growth, expanding rapidly without environmental constraints.
   • [(ii)] The mathematical representation of exponential growth is: \[ \frac{dN}{dt} = rN \] with \( N \) representing population size, \( r \) denoting the intrinsic rate of natural increase, and \( \frac{dN}{dt} \) signifying the rate of population change over time.
   • [(iii)] This growth pattern is characterized by a J-shaped curve, illustrating a steep and continuous rise without reaching a plateau.
2. • [(i)] Alexander von Humboldt observed that species richness within a geographical area increases with the area's size, but this trend has an upper boundary.
   • [(ii)] The Species-Area relationship is described by the equation: \[ \log S = \log C + Z \log A \] where \( S \) is species richness, \( A \) is the area, and \( C \) and \( Z \) are empirically determined constants.
   • [(iii)] The relationship is visually depicted through a graph.
   •