Question

The species-area relationship is represented on a log scale as

• A. a hyperbola
• B. a straight line
• C. a parabola
• D. a circle

Hint:

Key Exam Tip:
Remember the logarithmic form of the species-area relationship: $\log S = \log C + Z \log A$. This equation directly shows a linear relationship between $\log S$ and $\log A$.

Answer 1

The Correct Option is B

The species-area relationship, often described by the species-area curve, postulates that as the area surveyed increases, the number of species found also increases. When this relationship is plotted on a logarithmic scale, it typically approximates a straight line. This linear relationship in log-log plots is a common observation in ecological studies and is often expressed by the equation: $\log S = \log C + Z \log A$, where $S$ is the number of species, $A$ is the area, and $C$ and $Z$ are constants. The equation in this form represents a linear relationship between $\log S$ and $\log A$.

Step 1: Understand the species-area relationship. The species-area relationship describes the pattern of how the number of species changes with the size of the area surveyed. Generally, larger areas contain more species.

Step 2: Consider the representation on a log scale. The question asks how this relationship is represented when both species richness ($S$) and area ($A$) are plotted on a logarithmic scale.

Step 3: Recall or derive the equation for the species-area relationship. A common form of the species-area relationship is given by the equation: $S = C A^Z$, where $S$ is the number of species, $A$ is the area, and $C$ and $Z$ are constants. $C$ is the y-intercept and $Z$ is the slope.

Step 4: Linearize the equation by taking the logarithm of both sides. Taking the logarithm of both sides of the equation $S = C A^Z$ gives: $\log S = \log (C A^Z)$ Using logarithm properties, this can be expanded to: $\log S = \log C + \log A^Z$ $\log S = \log C + Z \log A$

Step 5: Identify the form of the linearized equation. The equation $\log S = \log C + Z \log A$ is in the form $y = mx + c$, where $y = \log S$, $x = \log A$, $m = Z$ (the slope), and $c = \log C$ (the y-intercept). This is the equation of a straight line.

Step 6: Conclude the representation on a log scale. Therefore, when the species-area relationship is plotted on a log-log scale (i.e., $\log S$ versus $\log A$), it appears as a straight line. Final Answer: \(\boxed{\text{a straight line}}\)