‘Z’ in the given equation refers to: log S = log C + Z log A

The correct answer is Option (4) → Regression coefficient

The equation shows the species-area relationship found by Alexander von Humboldt. Within a region, the number of species (species richness, S) goes up as the area explored (A) goes up, but only up to a limit. On a log scale this relationship becomes a straight line. Z is the slope of this line, called the regression coefficient. It tells how fast the number of species rises with area. Z is usually 0.1 to 0.2, but for very large areas such as whole continents it is much steeper (0.6 to 1.2).

(1) Area — Incorrect. Area is A in the equation.

(2) Species Richness — Incorrect. Species richness is S in the equation.

(3) Carrying Capacity — Incorrect. Carrying capacity (K) is the largest population that an environment can support. It belongs to the logistic growth of populations and does not appear in this equation.

(4) Regression coefficient — Correct. Z is the slope of the line, that is, the regression coefficient.

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”