The equation that describes species-area relationships is:

The correct answer is Option (2) → \( \log S = \log C + Z \log A \)

Alexander von Humboldt observed that, within a region, species richness increases with the area explored, but only up to a limit. On a normal graph this relationship is a curve (a rectangular hyperbola). On a logarithmic scale it becomes a straight line:

    \( \displaystyle \log S = \log C + Z \log A \)

Here S is species richness, A is area, C is the Y-intercept and Z is the slope of the line (the regression coefficient). Z tells how fast the number of species rises with area. For small areas, Z usually lies between 0.1 and 0.2; for very large areas, such as whole continents, the line is much steeper (Z about 0.6 to 1.2).

(1) \( \log C = \log S + Z \log A \) — Incorrect. S and C have changed places. The quantity worked out is species richness S, so log S must stand alone on the left.

(2) \( \log S = \log C + Z \log A \) — Correct. This is the equation of the straight line, with slope Z and intercept log C.

(3) \( \log S = \log C + A \log Z \) — Incorrect. A and Z have changed places. The slope Z must multiply log A, the log of the area.

(4) \( \log S = \log CA + Z \log A \) — Incorrect. The intercept is log C alone. There is no product CA in the equation.

NCERT Extract:
Patterns of Biodiversity – “… On a logarithmic scale, the relationship is a straight line described by the equation
log S = log C + Z log A
where
S= Species richness   A= Area
Z = slope of the line (regression coefficient)
C = Y-intercept”