Alexander von Humboldt is associated with
(a.) species - area relationship
(b.) log S = log C + z logA
(C.) Within a region , species richness increases with the increasing limited explored area.
(d.) Increased diversity contributes to higher productivity.
(e.) Species diversity increases with the loss of keystone species.

Options

A. a and e
B. a , b and d
C. a,b,c
D. b,c and d

Answer

To solve the question regarding Alexander von Humboldt's contributions, we need to analyze each option provided and determine which ones are associated with his work.

### Step-by-Step Solution:

1. **Understanding Alexander von Humboldt's Contributions**:
- Humboldt was a naturalist and biogeographer known for his research in botanical biogeography. His work laid the foundation for understanding the relationship between species and their geographical distribution.

2. **Evaluating Each Option**:
- **(a) Species-area relationship**: Humboldt is indeed associated with the species-area relationship, which states that larger areas tend to support more species. This is a fundamental concept in biogeography.
- **(b) Log S = log C + z log A**: This equation is derived from the species-area relationship. It expresses the logarithmic relationship between species richness (S) and area (A), where C is a constant and z is a scaling factor. This is also associated with Humboldt's work.
- **(c) Within a region, species richness increases with the increasing limited explored area**: This statement reflects Humboldt's findings that as the area explored increases, the number of species found also increases, up to a certain limit. This aligns with his research.
- **(d) Increased diversity contributes to higher productivity**: This statement is not directly associated with Humboldt. While it may be true in ecological contexts, it does not reflect his specific contributions.
- **(e) Species diversity increases with the loss of keystone species**: This statement contradicts ecological principles and is not related to Humboldt's work. Humboldt did not focus on keystone species or their loss.

3. **Conclusion**:
- The statements associated with Alexander von Humboldt are (a), (b), and (c). Therefore, the correct answer is the combination of these options.

### Final Answer:
The correct options associated with Alexander von Humboldt are (a), (b), and (c).