Appendix A. Proofs of all the mathematical results. Tom Leinster Christina A. Cobbold 10.6084/m9.figshare.3552705.v1 https://wiley.figshare.com/articles/dataset/Appendix_A_Proofs_of_all_the_mathematical_results_/3552705 Proofs of all the mathematical results. 2016-08-09 11:45:43 effective number biodiversity diversity microbial diversity entropy quadratic entropy species similarity model diversity profile Environmental Science Ecology