To follow up on Justin's comment, if you have a species-area relationship you think is robust across all political units you're interested in, you could compare units by looking at the residuals. See Guilhaumon, F., O. Gimenez, K.J. Gaston, and D. Mouillot. 2008. Taxonomic and regional uncertainty in species-area relationships and the identification of richness hotspots. Proceedings of the National Academy of Sciences USA 105:15458-15463.

You might try to include the political area as an additional variable in your analyses of richness. See for instance:

Baselga et al. 2012. Dispersal ability modulates the strength of the latitudinal richness gradient in European beetles. Global Ecology and Biogeography 21:1106-1113.

Thank you for the advice. We are currently using diversity index=no. of species/natural log of area but this is heavily weighted to the number of species and the area seems to make little difference. We are working with numbers of species in states of different sizes.

Are the species richness values already known/estimated? Or would you be surveying these data yourself?

I like Adam Smith's advice about residuals. This is a simple yet informative way of addressing your question. The residuals could then be used in other analyses.

We know the number of species and area of each state and I would like to calculate an index from this to compare diversity in different states.

I understand. So, it seems like you might be interested in asking 'Do states have higher/lower species richness than predicted by area?" If so, I think the residual approach that Adam recommend would be good. Then, you can ask what factors contribute to having higher or lower richness.

At the moment, all I need is an index of diversity based on the area and number of species, is there a formula for this?

Hi Allen,

As Justin and Adam have suggested, any index would need to account for the nonlinear relationship between species and area (aka a power function). The residual richness would be your "index."

Does that make sense, or are you hoping for something differet?

So is the formula I gave above a fair one to use? The index this gives is almost in the same order as the number of species regardless of area.

The worst thing to do is to divide richness by area. This gives complete nonsense results as richness is related to area in a non-linear way. The best way to indicate the "relative richness" for geographic entities of varying size is to find a good regression function for your dataset and then use the residuals of each point to this regression function as a comparable measure of diversity. You can try to find the best among many possible function types (e.g. Dengler 2009, J. Biogeogr.) or use even model averaging as Guilhomon et al. (2008, PNAS) did. But perhaps for your case the simple power function (which generally is among the best performing function for fitting species-area relationships) will do. And then the calculation of the residuals (call alpha-indices by Carsten Hobohm in some of his papers on that topic) is a very easy issue.

Your question does not give an indication of the size of the political areas?

To get a one degree latitude-longitude scale for a lot of the planet, you can get an idea from your computer by looking at the on-the-ground photos from http://www.confluence.org, and with photos from that site, I have stitched together a lot of photo vegetation megatransects at http://www.ecoseeds.com/mega.html.

After doing a lot of these continent-wide photo vegetation megatrasnects, it is quite shocking to see how depauperate the native vegetation understory is across the planet, especially the wildflowers and herbaceous non-grass species. The non-grass native understory, seems to getting spatially extinct, which I confirmed when I did a mile-by-mile megatransect for over 2,000 miles here in the Western USA in 1997.

If you look at http://www.ecoseeds.com/megatransect.html I drove from California to South Dakota and back, and every post mile, noted what species of grass was growing at that spot. For example, in California portion of the transect, the native understory was 99% gone, replaced by exotic plants. In Colorado, South Dakota, Wyoming, Nevada and Utah, the native understory was 55-68% spatially extinct, and the portion of Idaho that I surveyed, the native understory was 94% gone.

So, to survey a whole continent, the Confluence.org photos seem to be a good place to start--then if you are working on a smaller area, a roadside mile-by-mile or kilometer-by-kilometer megatransect survey might give you some insights, and cost the least amount of money and time.