I am working with species richness on a plant group and for my discussion, I would like to compare my results with the results obtained in different published studies. Do you know any statistical method to do it?
Most of the papers just give the number of species, other provide a species list but only with a number of total individuals.
I have just tried comparing the species richness/total area (sum of plots) and then extrapolate it to 1 ha to have the same measure in all the studies.
Why do you suggest?
Unfortunately it is not possible to directly compare species richness across sites if they refer to different areas. and you do not have additional information. Without that, comparisons are meaningful only if the inventories to be compared were drawn from samples of equal size.
The relation btw species and sample area is not linear. That prevents meaningful estimate of a "species per unit area" concept. Simply put, if you have an inventory of S species from an area of size A, the sub-inventory of the area of size A/2 will NOT be S/2. This is due to the distribution of the species' abundances which is virtually never uniform. Usually it is somewhere between logarithmic and log-normal.
The species-area curve is a well-known-to-exist, but difficult to harness, feature of biological diversity. There is a host of statistical work, mostly done by Chao, Magurran, Tuomisto, and many others on how they might behave.
Key to be able to compare richness is the availability of sample size and/or species abundances. This allows you to build the species-area curves. Rarefaction techniques have been widely used to get an estimate of the number of species in a sample of arbitrary size that is smaller than your inventory, and then compare that with the richness for the same size of another inventory (which may have been rarefacted to that same size as well). But you need the individual species abundances to build the curve. The rarefaction formula and that of its confidence interval is a bit messy but you may use good packages to work the for you; I'd recommend EstimateS and PAST. Rarefaction only works "backwards" (i.e. you rarefact to a smaller sample size).
To compare richness for samples greater than that of your inventory (i.e. to estimate richness for a fixed size) bootstrap and jacknife techniques do exist too. These can yield a pseudo-variance, that can in turn be used to construct a confidence interval and thereon allow statistical comparisons. EstimateS can do that, to, for a number of richness and diversity estimators.
Possibly, the most widely used estimators are Anne Chao's total richness S. As any of the techniques discussed above, they rely on knowing the distribution of the inventories. Both use the concept of "singleton" and "doubleton": species so rare that they yield only one (singletons) or two (doubletons) individuals in a sample, or, if you have a number of inventories, they just occur in one or two inventories.
You can find all the appropriate formulae in the literature. A lecture-type, summary overview for simple diversity comparisons (in the context of spatially-explicit diversity) can be found here: https://www.researchgate.net/publication/271012760_Beta_diversity. You'll find a list of general references at the end, but a very good manual discussing rarefaction and bootstrapping is Krebs C.J., 1989: Ecological Methodology. HarperCollins.
Regards.
Conference Paper Beta diversity
Arturo gave a very good and detailed answer. Here I am just reinforcing something he says near the beginning of his answer: it is important that you do not divide species richness by area and then compare between sites of different areas. The non-linearity of the species-area relationship is such that the number of species rises much faster on the left of the curve (i.e. as area increases from very small to small) than on the right (from large to very large). That is, species richness is a decelerating function of area. So if you divide species richness by area you will find that the smallest sites are apparently the richest ones - but that is purely an artefact of the calculation.
As Arturo said, there is no way (that I know of) to do the calculation in a way that avoids bias.
Richard and Arturo have warned you of the pitfalls. Even in studies based on the same area in each case, the sizes of the samples and the abundance or frequency distributions of the species concerned will affect comparisons. Some of this bias may be removed by rarefaction, but you are then no longer comparing actual or observed richness. Sometimes, you can be confident on other grounds that inventories are nearly complete, and you can make at least qualitative assessments of differences.
Here is a simple paper (I am not good with the sophisticated maths of others) that examined this in the context of land molluscs.
Thank you very much for your suggestions. I am very surprised about there is not standardized method to compare results of the studies, which at the end is the goal of every research.
For my study, I just use the "taxonomic diversity index" proposed by Squeo et al. 1998:
B= ni/ln Ai
Where:
ni = number of taxa (species, genus or families)
ln Ai= natural logarithm of the study area (in km2)
http://rchn.biologiachile.cl/pdfs/1998/4/Squeo_et_al_1998.pdf
Since you are unable to standardize the sampling (is that true?) it will only be a result compromised by the sampling irregularity. For comparison of biodiversity quality see my paper on Research Gate. Why do you want to compare species richness ? It is not a very meaningful measure?
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