Diversity index - Quiz
  • 1. What is the Rényi entropy a generalization of?
A) Herfindahl index
B) Shannon entropy
C) Simpson index
D) Gini coefficient
  • 2. Who introduced the Simpson index in 1949?
A) Albert O. Hirschman
B) Edward H. Simpson
C) Hunter–Gaston
D) Orris C. Herfindahl
  • 3. What is the economic term for the Simpson index?
A) Gini index
B) Herfindahl–Hirschman index
C) Rényi index
D) Shannon index
  • 4. What does the Simpson index (λ) represent?
A) The mean of the proportional abundances
B) The inverse of the total richness
C) The probability that two entities taken at random represent the same type
D) The total number of species in a dataset
  • 5. What is the value of 1/λ equivalent to in terms of true diversity?
A) True diversity with q = 0
B) True diversity with q = 2
C) True diversity with q = 1
D) True diversity with q = 3
  • 6. In the formula for the Simpson index, what does R represent?
A) Richness
B) Rényi entropy
C) Random sampling constant
D) Ratio of types
  • 7. What is the name of the Simpson index form used in microbiology?
A) Hunter–Gaston index
B) Hirschman–Simpson index
C) Herfindahl–Gaston index
D) Shannon–Hunter index
  • 8. What happens to the value of λ in datasets of high diversity?
A) It obtains small values
B) It obtains large values
C) It remains constant
D) It becomes undefined
  • 9. Which of these is a common transformation of λ that increases with diversity?
A) Square root of λ
B) Gini–Simpson index (1 − λ)
C) Sum of λ
D) Logarithm of λ
  • 10. What assumption is made for the standard interpretation of λ as a probability?
A) Entities are sampled with replacement
B) Entities are sampled without replacement
C) The number of types must be equal to the number of entities
D) The dataset must be infinitely large
  • 11. Who introduced the square root of the Simpson index in 1945?
A) Albert O. Hirschman
B) Edward H. Simpson
C) Claude Shannon
D) Orris C. Herfindahl
  • 12. What is the range of the minimum value for λ?
A) λ ≥ 0
B) λ ≥ 1/R
C) λ ≥ 1
D) λ ≥ R
  • 13. What is a diversity index used for?
A) Calculating the total biomass of a community
B) Identifying individual organisms by name
C) Measuring different types in a dataset
D) Predicting the future growth of a population
  • 14. What is meant by the term 'richness' in the context of a diversity index?
A) A count of the number of types in a dataset
B) The total weight of all organisms
C) The proportional abundance of the rarest type
D) The geographical spread of a species
  • 15. In information science, what entities are typically measured using diversity indices?
A) Characters
B) Hardware components
C) Network nodes
D) Digital signals
  • 16. What are Hill numbers also known as?
A) Shannon entropy constants
B) Effective number of species
C) Phylogenetic averages
D) Categorical variation counts
  • 17. What does the parameter 'q' define in the calculation of true diversity?
A) The geographical size of the site
B) The sensitivity to rare versus abundant species
C) The total number of types in the dataset
D) The unit of measurement used for the diversity
  • 18. What is the Shannon index called in the field of machine learning?
A) Perplexity
B) Information gain
C) Entropy reduction
D) Diversity gain
  • 19. What is the value of the Shannon index when there is only one type in a dataset?
A) One
B) Negative one
C) Zero
D) Infinity
  • 20. What does the Rényi entropy add to diversity measurement?
A) The ability to count rare species only
B) A way to calculate biomass
C) The ability to freely vary the kind of weighted mean used
D) The inclusion of phylogenetic relatedness
  • 21. What is the relationship between the Shannon index (H') and true diversity (1D)?
A) H' equals 1/1D
B) H' equals the square of 1D
C) H' equals 1D
D) H' equals ln(1D)
  • 22. What are indices that account for phylogenetic relatedness called?
A) Phylogenetic richness counts
B) Species-relativity indices
C) Genetic diversity indices
D) Phylo-divergence indices
  • 23. How is the Berger–Parker index defined?
A) The weighted arithmetic mean of types
B) The maximum proportional abundance
C) The inverse of the Simpson index
D) The sum of squared proportional abundances
  • 24. The Berger–Parker index is equal to the inverse of which diversity order?
A) Order 0
B) Order infinity
C) Order 2
D) Order 1
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