If you have:

observed_richness: total number of different species, singletons: number of species with a single representative, and multitons: number of species with two or more representatives, then you can calculate the Chao-1 index as follows:

Chao1 = observed_richness + singletons2/( 2 * multitons)

Also, I strongly recommend a must-read article about diversity indexes:

"Tuomisto, Hanna. "A consistent terminology for quantifying species diversity? Yes, it does exist." Oecologia 164.4 (2010): 853-860."

I hope that helps. Best regards.

To estimate/predict species richness you can use Michaelis-Menten model, fitting the rarefaction curve. See in PAST software manual (p. 123).

http://www.nhm2.uio.no/norlex/past/pastmanual.pdf

I agree with Salvador Ramirez-Flandes 

Whilst it depends on the nature of your data there are four methods that can be used: Chao 1 & 2, bootstrap and jackknife all of which can be found on the Pisces programme (along with other options).  Michaelis-Menten is not helpful as it is a retrospective model fitting technique beloved by engineers!

See my papers for examples of SR estimations with real data.

Good luck 

Alan

I agree with Salvador. however be careful because sometimes (like my friend's) you might get the estimated number of the species, MORE than the existed total number of described species. Unless you are dealing with organisms which has thousand of species number like moth or butterflies.

Ok. Michaelis-Menten (in Pisces software included) is an extrapolation method for expected species richness. Predict species richness for further sampling.

This gives a range of estimators, including one for species richness, q=0.

https://chao.shinyapps.io/SpadeR/

Hi all.

I agree with Salvador and David.

I also recommend seeing the works of Hill, Jost and Chao, and employ Hill numbers or the effective number of species.

Success and regards.

https://dash.harvard.edu/bitstream/handle/1/11148822/Chao2013.pdf?sequence=1

http://onlinelibrary.wiley.com/doi/10.1111/j.2006.0030-1299.14714.x/full

http://biocomparison.ucoz.ru/_ld/0/78_hill_obzor.pdf

remiss of me not to have included Lou Jost's excellent blog post of Effective numbers of Species, so it is here for you :)

http://www.loujost.com/Statistics%20and%20Physics/Diversity%20and%20Similarity/EffectiveNumberOfSpecies.htm

I agree with Salvador Ramirez-Flandes