Biological diversity estimation and comparison: problems and solutions

1. Biological diversity estimation and comparison: problems and solutions W.B. Batista, S.B. Perelman and L.E. Puhl

2. 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

3. d, local diversity a, arrival rate e, local-extinction rate , among-location diversity (heterogeneity) Conceptual model S, total diversity

4. d, local diversity Conceptual model S, total diversity

5. Conceptual model

6. Conceptual model

7. frequency d S-d RURAL CORE SATELLITE URBAN density Conceptual model

8. S, total diversity 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

9. Diversity estimation

10. Diversity estimation

11. Diversity estimation

12. Diversity estimation

13. Decreases with increasing density • Increases with increasing aggregation • High for urban and satellite species • Low for rural and core species 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

14. Non- Parametric Estimation • Depend on no assumptions about the probability distributions of species densities e.g. First order Jackknife Chao estimator 1 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.

15. If all species had equal density, and therefore 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

16. 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

17. Assessment of diversity estimators: a modeling exercise • 4 scenarios of species density distribution • 20 samples of size N=20 per scenario • Using program SPADE by Anne Chao to calculate different diversity estimators • Summary of estimator performance under all 4 scenarios

18. Modeling exercise Scenario 1 S=100, few rare species, no aggregation pattern

19. Modeling exercise Scenario 2 S=100, many rare species, no aggregation pattern

20. Modeling exercise Scenario 3 S=100, few rare species, with aggregation pattern

21. Modeling exercise Scenario 4 S=100, many rare species, with aggregation pattern

22. Modeling exercise Scenario 1

23. Observed species number • Jackknife • Chao • ICE • Bayesian

24. 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.

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