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 will analyze each option provided and determine which ones are associated with him.

### Step-by-Step Solution:

1. **Understanding Alexander von Humboldt's Contributions:**
- Alexander von Humboldt was a prominent naturalist and geographer known for his extensive research on the relationship between biodiversity and area, particularly in South America.

2. **Analyzing Option (a): Species - Area Relationship**
- Humboldt is indeed associated with the species-area relationship, which states that the number of species increases with the area explored. This is a fundamental concept in ecology and aligns with his research.

3. **Analyzing Option (b): Log S = Log C + z Log A**
- This equation represents the relationship between species richness (S) and area (A) in logarithmic form. Humboldt's findings led to this equation, where C is a constant and z is the slope of the line. Thus, this option is also correct.

4. **Analyzing Option (c): Within a region, species richness increases with the increasing limited explored area.**
- This statement reflects Humboldt's observations that species richness increases with area, but only up to a certain limit. Therefore, this option is also correct.

5. **Analyzing Option (d): Increased diversity contributes to higher productivity.**
- This statement is not associated with Humboldt. While it is a concept in ecology, Humboldt did not specifically study the relationship between biodiversity and productivity.

6. **Analyzing Option (e): Species diversity increases with the loss of keystone species.**
- This statement is incorrect in the context of Humboldt's work. The loss of keystone species typically leads to a decrease in biodiversity, not an increase. Humboldt did not focus on this aspect.

### Conclusion:
Based on the analysis, the options associated with Alexander von Humboldt are:
- (a) Species - area relationship
- (b) Log S = Log C + z Log A
- (c) Within a region, species richness increases with the increasing limited explored area.

Thus, the correct answer is **(a), (b), and (c)**.

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