Diapositiva 1

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Biological diversity estimation and comparison
problems and solutions W.B. Batista, S.B.
Perelman and L.E. Puhl
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• A simple conceptual model of plant-species
  diversity
• The rationale of diversity estimation
• Some essential diversity-estimator functions
• Parametric
• Non-parametric
• Coverage based
• Assessment of diversity estimators a modeling
  exercise

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Conceptual model
S, total diversity
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Conceptual model
S, total diversity
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Conceptual model
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Conceptual model
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Conceptual model
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Diversity estimation
N, quadrat number D, total number of observed
species ni, frequency of species i
q(k), number of species for which ni, k
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Diversity estimation
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Diversity estimation
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Diversity estimation
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Diversity estimation
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Diversity-estimator functions
S, total diversity D, total number of observed
species ni, frequency of species I q(k), number
of species for which ni, k
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Diversity-estimator functions

• Parametric Estimation
• Based on specific assumptions about the
  probability distributions of species densities
• Maximize the Likelihood of the observed q(k) as a
  function of S and the parameters of the
  probability distributions of species densities.

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Diversity-estimator functions

• Coverage-based Estimation

• Coverage is the sum of the proportions of total
  density accounted for by all species encountered
  in the sample.

• Anne Chao has developed coverage-based estimators
  by for the general case of unequal densities
  based on the coverage of infrequent species

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Diversity-estimator functions
A panoply of diversity estimators

• Parametric
• Beta binomial CMLE
• Beta binomial UMLE
• Non-Parametric
• Chao 2
• Chao 2 bias corrected
• 1st order Jackknife
• 2nd order Jackknife
• Coverage-based
• Model(h) Incidence Coverage Estimator
• Model(h)-1 or ICE1
• Model(th)
• Model(th)1
• Bayesian estimators

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Assessment of diversity estimators a modeling
exercise

• 4 scenarios of species density distribution
• 20 samples of size N20 per scenario
• Using program SPADE by Anne Chao to calculate
  different diversity estimators
• Summary of estimator performance under all 4
  scenarios

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Modeling exercise
Scenario 1
S100, few rare species, no aggregation pattern

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Modeling exercise
Scenario 2
S100, many rare species, no aggregation
pattern
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Modeling exercise
Scenario 3
S100, few rare species, with aggregation
pattern
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Modeling exercise
Scenario 4
S100, many rare species, with aggregation
pattern
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Modeling exercise
Scenario 1
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Modeling exercise

• Parametric estimators either failed to converge
  or produced extremely biased results.
• When no species were very rare and no species had
  aggregation pattern most estimators worked well,
  but then so did the naïve estimator D.
• Some of the coverage-based estimators were
  relatively robust to the differences among the
  scenarios we tested.

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• Diversity estimation is a delicate task.
• It should be aided by assessment of the patterns
  of species density and aggregation.