Question

(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 the 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.

Hint:

Population growth curves are essential to understand how populations respond to environmental limitations. The species-area relationship helps ecologists predict biodiversity patterns across regions and scales.

Answer 1

(a) (A) When a population of any species grows in a habitat with limited resources, it follows a logistic growth curve. Initially, the population grows exponentially due to abundant resources, but as resources become limited, the growth rate slows and finally stabilizes at the carrying capacity (\(K\)) of the environment. (B) The equation for logistic growth is: \[ \frac{dN}{dt} = rN \left( \frac{K - N}{K} \right) \] where,
\(N\) = Population density at time \(t\), 
\(r\) = Intrinsic rate of natural increase, 
\(K\) = Carrying capacity. (C) The name of this curve is the Logistic Growth Curve (S-shaped curve). Graphical representation of Logistic Growth Curve

OR 
(b) (A) The Species-Area Relationship states that the number of species (species richness) increases with increasing area, but at a decreasing rate. In a natural forest, as we explore larger and larger areas, we find more species. When plotted, this forms a rectangular hyperbola. However, for a wide variety of taxa, the graph becomes a straight line on a logarithmic scale. (B) The graph between species richness and area is: (C) The equation for the Species-Area Relationship on a logarithmic scale is: \[ \log S = \log C + Z \log A \] where, 
\(S\) = Species richness, 
\(A\) = Area, 
\(C\) = Y-intercept constant, 
\(Z\) = Slope of the line (regression coefficient).