Question

(a) (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.

OR

(b) (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:

The J-shaped curve applies to populations with unlimited resources. The Species-Area relationship reflects biodiversity patterns: larger areas tend to support more species.

Answer 1

(a) (i) Description of the Population Growth Curve:

In nature, when resources such as food, water, and space are unlimited, the population of a species shows an exponential growth pattern. This means that the population increases rapidly over time, as every individual reproduces at its maximum potential. There are no environmental resistance factors like competition, disease, or predation to limit growth.

(ii) Equation of the Growth Curve:

The exponential population growth is mathematically described by the following equation:

\( \frac{dN}{dt} = rN \)

Where:

• N = Population size
• r = Intrinsic rate of natural increase
• \(\frac{dN}{dt}\) = Rate of change of population size over time

(iii) Name and Graphical Representation:

The curve is called a J-shaped growth curve.

OR

(b) Species-Area Relationship

(i) Conclusion by Alexander von Humboldt:

During his explorations in the South American jungles, Alexander von Humboldt observed that within a given region, the species richness (i.e., number of species) increased with increasing explored area. However, the increase was not linear — it increased rapidly at first and then slowly. This gave rise to the concept of the Species-Area Relationship.

(ii) Equation of the Species-Area Relationship:

The relationship is described mathematically by the equation:

\( S = C A^Z \)

Where:

• S = Number of species (species richness)
• A = Area
• C = Constant (y-intercept)
• Z = Slope of the line (varies for different taxa and areas)

(iii) Graphical Representation:

The graphical representation of species richness against area is shown below. It is a curve that flattens out with increasing area.