There are several software by which you are able to calculate different biodiversity parameters. For instance: Power Marker, GenAlex, Genstat, Fstat ana Past3
There are several packages (e.g., vegan, vegetarian, BiodiversityR, iNEXT, FD, and many, many more) in R that allow you to compute and/or estimate a wide suite of diversity (including functional diversity) and richness measures. You can check the documentation for each to determine what measures are available.
The free NatureServe Vista extension for ArcGIS contains this function with lots of options. It is also a full scenario-based cumulative effects assessment and planning software that can interoperate with Marxan. See www.natureserve.org/Vista.
I have used SPADE - Species Prediction and Diversity Estimation to estimate biodiversity in communities. I used an old desktop version but there is a web-based version now: https://chao.shinyapps.io/SpadeR/.
I recommend the following paper from Loiseau & Gaertner (2015) to use alternative indices that can be more appropriate or sensitive depending on your research. Functional biodiversity indices are particularly interesting for community-wide approaches. https://doi.org/10.1002/ece3.1619
R is an excellent software to perform those analysis with many packages to calculate biodiversity indices.
There are a variety of softwares/ tools that can be used to estimate biodiversity indices. for eg Estimate S is a commonly used software with which one can easily calculate/ estimate species diversity/ biodiversity indices.
Depending on the objective of your study but I think even DISTANCE software can assist you in calculating some of these indices including biodiversity survey indices. Another softwares are PRESENCE and MARK 11 softwares.
EstimateS, the vegan package in R or PAST, all are quite useful. I think EstimateS software is very good option. Here is link
http://viceroy.eeb.uconn.edu/estimates/
Also you can use SPADE - Species Prediction and Diversity Estimation to estimate biodiversity in communities and iNEXT (iNterpolation and EXTrapolation)
I have recently used Past; The program, called PAST (PAleontological STatistics), runs on standard Windows computers and is available free of charge. PAST integrates spreadsheet-type data entry with univariate and multivariate statistics, curve fitting, time series analysis, data plotting, and simple phylogenetic analysis. https://folk.uio.no/ohammer/past/
This is such a wonderful thread - really helpful and inspirational - now I want to do a Ph.D. using these stats programs. It makes me so happy that all of you folks around the world are in some field that cares about biodiversity! I just cried a little - especially seeing another Armenian in the discussion, Mr. Subramanian, (I am part Armenian)...it is so important that we keep carrying out good work in this field. : )