A diversity index is mathematical measure of species diversity in the community. Shimpson's Diversity Index is a measure of diversity which takes into account both richness and evenness.
Dear Guirgio
Please go through these links
http://www.webpages.uidaho.edu/range357/notes/Diversity.pdf
http://www.zoology.ubc.ca/~krebs/downloads/krebs_chapter_13_2014.pdf
http://www.maths.ed.ac.uk/~tl/mdiss.pdf
This is a big question, I recommend: Magurran, A. E. 2004. Measuring biological diversity.
In pdf online: http://www2.ib.unicamp.br/profs/thomas/NE002_2011/maio10/Magurran%202004%20c2-4.pdf
Hi, there is no single 'best' measure for species diversity. Each index measures a different component of species diversity.
Species richness only counts the number of species, while evenness indices only look at the equality in abundances between species. Shannon and Simpson indices take both into account.
The measure you want to use depends on your research question. A lot of research study more than one index.
And of course, you also have functional diversity and phylogenetic diversity measures...
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