Dear Frederik, each asymptotic species richness curve is a result of an specific sampling effort in terms of time, sample units, area, baits, traps types and other variables that are totally different for each group. If you have different sampling efforts that will affect definitively your response. So, it is necessary to standarize your samplings if you want to compare them.

Dear Frederik, statistical programs don´t all use the same algorithms to calculate their values and so slightly different values using different programs are quite possible. Check through the parameters you need to put into each one and the options they have (this is especially true for some R routines). Make sure that its all set up the way you want it to avoid too much discrepancy.

Response to 1:

As Jorge says, sampling effort needs to be corrected for else you will get misleading results. So standardization is a must for comparisons across sites.

Response to 2:

Yes R packages may give different answers primarily due to the defaults. You should get very similar answers if you make sure all the parameters are set to the same settings across packages.

None of the conventional measures of diversity and species richness, like H and H', are truly sample size independent.   They are advertised as such, but fail when sample  sizes are low.  Species rarefaction curve analysis is perhaps the best way to compare species richness - if you have a number of samples from each study area to enable rarefaction curve analysis.  There is excellent, inexpensive, and easily usable software to apply to the analysis.  This is EstimateS.  I recommend it very strongly.  Easy to use, can dump Excel or flat data files straight in, and 95% confidence bounds are calculated.  The fundamental rationale is that a large number of random draws are made upon the grouped data for each comparative study site.  When the ESPP curve becomes asymptotic at X species, you can determine a Y number of pooled specimens that provides a solid estimate of species richness at that group sample size - for comparison with other pooled samples from other sites.  You can plot the 95%CIs around the curves, evaluate for overlap.  If not overlap at the selected Y number of specimens, then the two sites are significantly different.   There are other softwares out there to do the same thing - but none is so easy to use.

To those who answered my first question: Can you give any references that support your statement? I'm unable to find a paper that explicitly states that you can only compare diversity between sites that were sampled equally. In fact, I see a lot of papers that don't do it.

No - it is not necessary to standardize your input data. As per the original rarefaction curve concept of Sanders, the idea is simply to combine all samples into a common pool, then make random draws upon that pool at different sample sizes. The curve is simply a plot of species encountered (expected species) as a function of sample size. Certain data standardizations could actually defeat the elegant simplicity of the underlying concept. That is not to say that sampling methods employed to get the data should not follow a common standardized protocol. Certainly they should. But, equal sample size is not a requirement at all for rarefaction curve analysis. Indeed that is one of the beauties of this method.

Dear Ken, thanks for your quick reply. I think I haven't been clear; my previous comment still applied to my initial question about sampling effort. So with '...sampled equally' I meant 'in terms of sampling effort'.

What I mean with sampling effort has to do with the methodology; the amount of time spent, the number of traps set, etc. Sample size is the result of the sampling; in case of individual-based data, the amount of specimens caught.

Indeed rarefaction is made to compare samples with differences in sample size. My question is whether these samples should be (or should have been) collected with equal sampling effort. Can you say that, after correcting for sample size, one sample is more diverse than the other when the effort to get to this sample was not equal? Same counts for the comparison of asymptotic species richness estimators.

You actually already answered it 'Certainly they should'. But so far I have never read this explicitly in any of the (recent) papers on rarefaction, that's why I'm still doubting.

Frederik -

I was first attracted to rarefaction methodology in the 1970s because using a number of test data sets, it became apparent to my that H" was not sample size independent.  This is particularly true when individual samples are too small to approximate the 'mean diversity' of the community being sampled.  I was concerned with trawl samples from very deep ocean waters - samples which typically yielded a few tens of specimens.  Pooling large numbers of such standard-methodogy samples, then applying rarefaction, demonstrated an asymptote at a certain minimum pooled 'N'.  Then the goal was to sample different areas, and contrast two or more pooled samples using the old Fortran program 'Rarify' of M. M. Yong at a selected pooled sample 'N' size well above the asymptote.   I think you do need to do all you can to standardize sampling methods to obtain individual 'n' data to form the pooled 'N' samples and 'N' specimens in forming the overall pooled sample to which rarefaction is applied.  I would not think, for example, of pooling trawl, trap, and angling samples since individual methods are selective in terms of which species they extract from the overall community.   That situation shows up  the problems of sticking with one preferred sampling method, however standardized.  In the situation for deep demersal fishes on the ocean floor, we can now employ videography to obtain much more catholic 'samples' that are more inclusive of the total suite of species comprising the community.  Still we encounter problems because there are crpytic species in the fauna, as well as a changeover in which fishes are active diurnally versus nocturnally.  Getting a handle on the total fauna is challenging.   However, I have found that the application of rarefaction via EstimateS is very instructive.  In contrast numerical diversity indices values are not only sample-size dependent at low sample sizes, but are difficult to interpret.  I hope these comments prove helpful.