The relation between species richness and area is described on a logarithmic scale by the equation [where S = species richness, A = area, Z = slope of the line (regression coefficient ), C= Y - intercept]

Options

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

Answer

To solve the question regarding the relationship between species richness (S) and area (A) using a logarithmic scale, we can follow these steps:

### Step-by-Step Solution:

1. **Define Species Richness**:
- Species richness (S) refers to the number of different species present in a given area (A).

2. **Understanding the Logarithmic Relationship**:
- The relationship between species richness and area can be expressed in a logarithmic form. This means that as the area increases, the species richness also tends to increase, but this relationship can be modeled logarithmically.

3. **Equation Representation**:
- The relationship can be represented by the equation:
\[ \log S = \log C + Z \log A \]
- Here, \(C\) is the y-intercept, \(Z\) is the slope of the line (regression coefficient), and \(A\) is the area.

4. **Interpreting the Equation**:
- In this equation:
- \( \log S \) represents the logarithm of species richness.
- \( \log C \) is the logarithm of the constant \(C\), which indicates the baseline level of species richness when the area is at a specific reference point.
- \(Z \log A\) indicates how much the species richness increases with the logarithm of the area.

5. **Graphical Representation**:
- If we were to graph this relationship, we would plot \( \log S \) on the y-axis and \( \log A \) on the x-axis. The slope of the line would be \(Z\), and the y-intercept would be \( \log C \).

6. **Conclusion**:
- The final equation \( \log S = \log C + Z \log A \) shows that species richness is positively correlated with area, meaning that larger areas generally support a greater number of species.