“…Other important research questions include 120 the sources of diversity (Tsimring et al, 1996;De'ath, 2012), extensions of diversity to include a concept of species distance Chao et al (2010); Leinster and Cobbold (2012);Feoli (2012);Scheiner (2012), and techniques for measuring diversity (Chao and Shen, 2003;Schmera and Podani, 2013;125 Gotelli and Chao, 2013), despite the well-known difficulties in estimating entropy in an unbiased fashion (Harris, 1975;Paninski, 2003). Beyond ecology, the study of diversity is also important in economics (Garrison and Paulson, 1973;Hannah and Kay, 1977;Attaran and Zwick, 1989;Malizia 130 and Ke, 1993;Drucker, 2013), immunology (Tsimring et al, 1996), neuroscience (Panzeri and Treves, 1996;Strong et al, 1998), and genetics (Innan et al, 1999;Rosenberg et al, 2002;Falush et al, 2007). This paper is organized as follows.…”