Question

The correct equation depicting species-area relationship is

• A. log S = log C + Z log A
• B. log C = log S + Z log A
• C. log A = log C + Z log S
• D. log Z = log C + S log A

Answer 1

The Correct Option is A

The species-area relationship describes the relationship between the area of a habitat (or part of a habitat) and the number of species found within that area. It was observed by naturalist Alexander von Humboldt.

The relationship is typically expressed by the power function:

\[ S = C A^Z \] 

Where:

• \( S \) = Number of species
• \( A \) = Area
• \( Z \) = Slope of the line (regression coefficient)
• \( C \) = Y-intercept (a constant)

This equation describes a curve on a standard plot of S versus A.

To analyze this relationship as a straight line, it is common to plot it on logarithmic scales. Taking the logarithm (base 10 or natural log) of both sides of the equation:

\[ \log(S) = \log(C A^Z) \]

Using the properties of logarithms (\(\log(xy) = \log x + \log y\) and \(\log(x^p) = p \log x\)):

\[ \log(S) = \log(C) + \log(A^Z) \]

\[ \log(S) = \log(C) + Z \log(A) \]

This equation is in the form of a straight line \( y = mx + c \) on a log-log plot, where:

• \( y = \log(S) \)
• \( c = \log(C) \) (the y-intercept)
• \( m = Z \) (the slope)
• \( x = \log(A) \)

Comparing this derived equation with the given options:

• log S = log C + Z log A (Matches the derived equation)
• log C = log S + Z log A
• log A = log C + Z log S
• log Z = log C + S log A

The correct equation depicting the species-area relationship in its logarithmic form is log S = log C + Z log A.

Answer 2

The species-area relationship describes the relationship between the area of a habitat and the number of species it supports. The correct mathematical representation of the species-area relationship is:

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

Where:

S is the number of species,

A is the area of the habitat,

C is a constant, and

Z is a coefficient that reflects the rate at which species number increases with area.

This equation suggests that the logarithm of species number (S) is related to the logarithm of the area (A), with a constant factor and a scaling exponent (Z).

The correct answer is (A) : log S = log C + Z log A.