Correct option is B
Hill numbers (also called the effective number of species) provide a unifying framework for measuring diversity. They are parameterized by an order q, which determines the sensitivity of the diversity measure to species abundance.
When q = 0, Hill number equals species richness (all species weighted equally).
When q = 1, Hill number corresponds to the exponential of Shannon entropy (weights species proportional to their abundance).
When q = 2, it relates to the inverse of Simpson’s index, giving more weight to common species.
As q increases, more weight is given to common species, and rare species are downweighted.
Conversely, lower q values (closer to 0) emphasize rare species.
Therefore:
Statement (1) is correct: As q increases, the diversity measure emphasizes dominant species.
Statement (3) is correct: Increasing q tends to decrease the diversity index, especially if species are not equally abundant.
Statement (4) is correct: For q ≥ 5, the Hill number becomes very close to the inverse of the most abundant species’ relative abundance.
Statement (2) is INCORRECT: It falsely claims that increasing q emphasizes rare species, which is the opposite of the correct trend.
