According to the concept of species-area relationship.

Options

A. The number of species in an area increase with the size of the area.
B. The value of Z lies in the range of 0.3 to 0.4, regardless of the taxonomic group or the region.
C. The relationship is for a rectangular hyperbola curve is described by the equation `log S = log C + Z logA`.
D. The larger the area the greater the extinction rate.

Answer

To solve the question regarding the concept of species-area relationship, we will analyze each of the given statements step by step.

### Step-by-Step Solution:

1. **Understanding the Species-Area Relationship**:
- The species-area relationship describes how the number of species increases with an increase in the area of a habitat. This is a fundamental concept in ecology that suggests larger areas can support more species due to the availability of diverse habitats and resources.

2. **Evaluating the First Statement**:
- **Statement**: "The number of species in an area increases with the size of the area."
- **Evaluation**: This statement is correct. As the area increases, the number of species typically increases due to more available niches and resources.

3. **Evaluating the Second Statement**:
- **Statement**: "The value of z lies in the range of 0.3 to 0.4 regardless of the taxonomic group or the region."
- **Evaluation**: This statement is incorrect. The value of z in the species-area relationship typically ranges from 0.1 to 0.2, and it can vary depending on the taxonomic group and the region being studied.

4. **Evaluating the Third Statement**:
- **Statement**: "The relationship is a rectangular hyperbola curve described by the equation log S = log C + Z log A."
- **Evaluation**: This statement is also incorrect. The species-area relationship is generally described as a power function, which results in a linear relationship when logarithmic transformations are applied. It does not represent a rectangular hyperbola.

5. **Evaluating the Fourth Statement**:
- **Statement**: "The larger the area, the greater the extinction rate."
- **Evaluation**: This statement is incorrect. Generally, larger areas tend to support more species, which can lead to lower extinction rates due to higher biodiversity and more stable ecosystems.

### Conclusion:
Based on the evaluations:
- The first statement is correct.
- The second, third, and fourth statements are incorrect.