Ecological Archives M084-003-A4
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. http://dx.doi.org/10.1890/13-0133.1
Appendix D. Proof details for some formulas (Eqs. 5, 8, 9b, 11a, and 11b of the main text) and a replication principle.