Which of the following equation correctly represent species-area relationship?

Options

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

Answer

To solve the question regarding which equation correctly represents the species-area relationship, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Species-Area Relationship**:
The species-area relationship describes how the number of species (S) increases with the area (A) surveyed. This relationship is often expressed mathematically.

2. **Identify the General Equation**:
The general equation for the species-area relationship is given by:
\[ S = cA^z \]
where:
- \( S \) = species richness (number of species)
- \( A \) = area
- \( c \) = a constant
- \( z \) = the slope of the relationship

3. **Convert to Logarithmic Form**:
To analyze this relationship further, we can take the logarithm of both sides:
\[ \log S = \log c + z \log A \]
This transformation is useful because it allows us to interpret the equation in terms of a linear relationship.

4. **Compare with Linear Equation**:
The logarithmic form resembles the equation of a straight line \( y = mx + b \), where:
- \( y \) corresponds to \( \log S \)
- \( m \) corresponds to \( z \)
- \( x \) corresponds to \( \log A \)
- \( b \) corresponds to \( \log c \)

5. **Identify the Correct Option**:
Based on the derived logarithmic equation \( \log S = \log c + z \log A \), we can conclude that the correct representation of the species-area relationship is:
\[ \log S = \log c + z \log A \]
Therefore, the correct option is **Option 4**.

### Final Answer:
The equation that correctly represents the species-area relationship is:
\[ \log S = \log c + z \log A \quad \text{(Option 4)} \]

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