Anne Chao, Nicholas J. Gotelli, T. C. Hsieh, Elizabeth L. Sander, K. H. Ma, Robert K. Colwell, and Aaron M. Ellison. 2014. Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies. Ecological Monographs 84:45–67.


Appendix A: A binomial product model can incorporate spatial aggregation for quadrat sampling.
Ecological Archives M084-003-A1.

Appendix B: Rarefaction and extrapolation for species richness (abundance data).
Ecological Archives M084-003-A2.

Appendix C: Rarefaction and extrapolation for species richness (incidence data).
Ecological Archives M084-003-A3.

Appendix D: Proof details for some formulas (Eqs. 5, 8, 9b, 11a, and 11b of the main text) and a replication principle.
Ecological Archives M084-003-A4.

Appendix E: Extrapolation formulas for Hill numbers of q = 1 and q ≥ 2 based on abundance data.
Ecological Archives M084-003-A5.

Appendix F: Using simulation to test the proposed analytic estimators.
Ecological Archives M084-003-A6.

Appendix G: A bootstrap method to construct an unconditional variance estimator for any interpolated or extrapolated estimator.
Ecological Archives M084-003-A7.

Appendix H: Rarefaction and extrapolation of Hill numbers for incidence data.
Ecological Archives M084-003-A8.

Appendix I: Hill numbers and Hurlbert’s indices.
Ecological Archives M084-003-A9.

Appendix J: An example: sample-size- and coverage-based Shannon diversity curves may exhibit inconsistent patterns.
Ecological Archives M084-003-A10.

Appendix K: Probability of an Interspecific Encounter (PIE) and rarefaction.
Ecological Archives M084-003-A11.


Supplement 1: R code for the analysis of individual-based (abundance) and sample-based (incidence) species diversity data.
Ecological Archives M084-003-S1.