Lots and lots of literature on this. in a quick (perhaps too quick) reaction I would say that the fact that you get similar diversity/evenness values is because the relative abundances of the taxa (species, genera, whatever) in each sample is rather similar, regardless of the absolute abundance or density even. You could use "Estimated number of species" (can also be used for higher-level taxa) as defined by Sanders and corrected by Hurlbert 1971 using actual counts rather than relative proportions (and hence includes the actual abundance of your sample). Care should be taken with the different underlying properties of the different samples and the scale you're looking at, however. sampling effort (in terms of numbers of samples used or numbers of individuals samples) and the species-area relationship may confound your results... key here is also identifying whether you are anywhere near the diversity asymptote in rarefaction curves or species-accumulation curves (collector's curves), because the slope of the curve that represents your samples' diversity represents the eveness to an extent. You also have to distinguish clearly between species or taxon richness (just the number of taxa present, regardless of their abundance and hence evenness) and heterogeneity diversity (including abundances and hence including an evenness component).

In short, be careful in comparing diversity... diversity in itself is very diverse!

A few references which may be of use.

Have a look for books by Anne E Magurran on Biological Diversity

Olszewski, T.D., 2004. A unified mathematical framework for the measurement of richness and evenness within and among multiple communities. Oikos 104, 377-387.

Gotelli, N.J., Colwell, R.C., 2001. Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. Ecology Letters 4, 379-391.

Colwell, R.K., Coddington, J.A., 1994. Estimating Terrestrial Biodiversity through Extrapolation. Philosophical Transactions of the Royal Society of London Series B-Biological Sciences 345, 101-118.

Gray, J.S., 2000. The measurement of marine species diversity, with an application to the benthic fauna of the Norwegian continental shelf. J. Exp. Mar. Biol. Ecol. 250, 23-49.

Thank you very much for your answer. A key assumption of my study is that all species are completely sampled and all sample sites have the same size, thus sampling effort and species-area relationships are not a main issue. I'll have a look at the suggested literature.

Sample size differences are particularly critical when it comes to quantifying species RICHNESS. Then, rarefaction or extrapolation methods may be required to control for samples size effects.

With regard to 'DIVERSITY' measures in a more narrow sense, that address the geometry of the species-abundance distributions, sample size issues are not as critical, as long as all samples to be compared are large enough. For example, Fisher's alpha parameter of the logseries distribution may be rather robustly estimated from samples, as soon as these comprise a few hundred individuals.

For Shannon diversities, it may be very useful to integrate the bias-correction that has been formulated by Anne Chao and co-workers a few years ago. This bias correction at least partially alleviates problems arising from undersampling.

See for example:

Beck J, Schwanghart W (2010) Comparing measures of species diversity from incomplete inventories: an update. Methods Ecol Evol 1:38–44

Thank you Konrad. As I stated above, my assumption is that there is no undersampling, so that such a correction may introduce a bias rather than a correction.

then it seems to me that they are the same communities in terms of heterogeneity diversity using relative abundance, only each taxon is represented by more individuals whilst relative proportions are maintained within the assemblage you are investigating... that or the assumptions need to be looked at to see whether they are the reality

Best wishes,

Jeroen

A lot of recent bibliography explained the importance of consider also other aspects of the population diversity: the most simple is of course the species richness. But a more deepest approach could consider also the taxonomic diversity, genetic diversity and functional diversity. In this way, you can made a right confronting between several sites. See this interesting paper of Devictor (Devictor et al., 2010. Spatial mismatch and congruence between taxonomic, phylogenetic and functional diversity: the need for integrative conservation strategies in a changing world. Ecology Letters, 13:1030-1040.)

Good research!

There is also nice review related to this topic:

https://www.researchgate.net/publication/5995878_Species_abundance_distributions_moving_beyond_single_prediction_theories_to_integration_within_an_ecological_framework

Article Species abundance distributions: moving beyond single predic...

We obtained interesting results by comparing evenness data even though species composition and community structure varied considerably.

https://www.researchgate.net/publication/227367007_Assessment_of_yeast_diversity_in_soils_under_different_management_regimes

Article Assessment of yeast diversity in soils under different manag...

Thank you very much for the useful comments and literature. Andrew, I just would like to ask you if you did not have trouble in comparing eveness between samples that differed a lot in the number of species present. For exemple eveness may be much higher for samples with 2 occurring in similar proportion than for samples with much more species, but I am not sure that I can say that a community with only 2 species is more even. Maybe I am thinking to much but anyway it sounds quite illogical to me.

I must say I was lucky enough having the total number of species being in the same range. We did not have cases when we had to compare a community with 10 and 2 species only.

Of course, the case of very species-poor communities is difficult. However, I think you might be still able using SAD-diagrams to illustrate some trends. Furthermore, there are quite a few well-known examples of climax species-poor communities such as boreal forests. I feel you can find studies having data-setup similar to your case in plant ecology. You can imagine that a large-scale comparison across terrestrial biomes (e.g. boreal vs. tropical forests) will ultimately face same problems.

I'm not sure if it matters whether you are looking at bacterial metagenomic sampling or other samples, but a very nice software package is CatchAll. This combines several different models for estimation of species or OTU within a sample and compares it to actual abundance then it calculates a best fit model. The author was very helpful to me also and explained what the terms meant and which parts were relevant. I'm working at Agroscope near Zürich, so not too far away. Another one was the rarefaction curve analysis.

I also suggest EstimateS software: http://viceroy.eeb.uconn.edu/estimates/

It estimates species richness but also provides beta-diversity data.

Thank you. Indeed there are a lot of ecological papers mentioning EstimateS, but I've never used it, What would be the advantage of using EstimateS instead of R? I don't know if it is a good way to analyse my data with several different softwares, because of the risk to get lost or have trouble with incompatibilities, unless there are good reasons (i.e., calculations provided only by one software)? Anyway I will have a look at EstimateS and CatchAll.

Dear Valérie, don't forget to look at the data! Always look at the data!

If you are comparing a 2-species sample and a 40-species sample, there is little meaning in using an evenness index, so don't get too hung up on comparing and discussing indices in such a case... the data itself tells you what the difference is. The logical question to ask in such an example is what is causing the 2-species assemblage as opposed to the 40-species one. Your example illustrates the importance of treating richness and evenness together as well.

Best wishes,

Jeroen

Dear Jeroen, that's true that the main point should be to find about ecological meaning of the differences between the data, not to blindly apply mathematical formulas. The thing is that I would like to compare 30 sites with three degrees of isolation (10 of each). I'd like to know what is the difference in the mean species richness, which is quite straightforrward, but I found it interesting to look at eveness and diversity as well, as it could give me useful indication if for example isolated sites are less even, that is some species strongly dominate the community. However I maybe should take out the sites with very low number of species or individuals, but I don't really know what should be the threshold, so that I confidently can compare the different sites.

Dear Valérie, I found Estimates friendly enough and input files are easy to format. This program works fast and it is stable.

Hi,

I don´t think is a problem to compare evenness in species-poor communities since this metric compare the RELATIVE PROPORTION of individuals/abundances occupied by each species. This should not be a problem in general, although a community formed by 3 individuals (doesn´t matter the number of species) seems too poor for doing this, maybe you should focus in those sites with at least 5-10 individuals (a minimum number to consider it representative). Why is the reason of this extremely low number of individuals?

Be careful with the species richness. When comparing differences in species richness among sites which also differ strongly on the number of individuals you may confound your results simply by the difference in the sampling effort (see Gotelli & Colwell 2001-Ecology letters). I would recommend using the rarefaction curves to measure differences in species richness, and the Hulbert´s PIE index to measure evenness. Both are provided by EstimateS (recommended in this conversation before). You can see very interesting reviews in this topic in Nick Gotelli´s website (http://www.uvm.edu/~ngotelli/PubList.html).

hope it helps

Oh, yes. Among- and within-sites heterogeneity is an interesting issue. In addition to "traditional" rarefaction curves and diversity estimations, I suggest to take a look at curves showing species-area relationships. These may be extremely useful in case of low species richness on a single site but high between-sites heterogeneity. See also:

https://www.researchgate.net/publication/216850205_The_speciesaccumulation_curve_and_estimation_of_species_richness

Article The species-accumulation curve of estimation of species richness

Thank you very much for suggesting me the studies of Nick Gotelli, I should find quite a lot of interesting inputs for my study. Species-area relationships are maybe not so useful if all my sites have the same area.

I am looking at the colonization of different sites by trap-nesting Hymenoptera and there are some sites colonized by a very large number of individuals and some sites with only sporadic individuals, such that I may end with less than 5 individuals/species. I always fear to loose useful information when I disregard certain sites or to bias my results. Anyway, keeping sites with too low number of individuals would bias my results as well. Trade-offs always occur.

Good statistical criterion for comparison Shannon index values exist . It's Hutcheson criterion which are modifies Student's t-criterion. This criterion was realized in programm PAST (free software can be download from http://folk.uio.no/ohammer/past/.

Valérie, studying species area relationships can be good coupled with beta-diversity parameters. While, species richness estimators provide expected number of species for the entire sampling, estimations performed for any 1, 2, 3, 4, etc. sites give good overview on how different are these sites and how the inclusion of additional sites may change expected diversity values. Thereby, you can extrapolate estimations to a certain area or biotope. You can also assess diversity (species richness) dynamics depending on the sampling intensity.

Using this approach we have compared expected species diversity in natural versus managed forests, see https://www.researchgate.net/publication/51587009_Species_accumulation_curves_and_incidence-based_species_richness_estimators_to_appraise_the_diversity_of_cultivable_yeasts_from_beech_forest_soils

Article Species Accumulation Curves and Incidence-Based Species Rich...

I agree with Santiago that also small sample sizes can be meaningful for calculations of evenness indices. You might want to check some properties of evenness indices. Some are directly related to species richness at its lower range. Hurlberts PIE is closely related to 1-D, but was corrected for small sampling sizes. But you should avoid Pielous J'.

Smith and Wilsons review might give you a good overview and some ideas, which kind of index might work best for your purpose:

http://www.jstor.org/discover/10.2307/3545749?uid=3737864&uid=2&uid=4&sid=21101280141241.

Dear Valérie Coudrain

I would take caution on small samples, if it is possible (in case you have only few samples with for example less then 10 specimens) just delete them from the dataset. There is good method which allow for comparing biodiversity between small and large samples - rarefaction (avialable e.g. on PRIMER software). You may read about it in: H.J.B. Birks, J. M. Line (1992): The Holocene 2.1 (The use of rerefaction analysis for estimating palynological richness from Quaternary pollen-analyticla data).

Sorry for my late answer to your comments, I was a few days away. I always used Pielous J' and I recently read some papers mentioning Hurlberts PIE. So according to the suggestion of Erich, this index is certainly better suited for my study. I will certainly have to delete some site, but I don't have a very large sample site, so that I will have to be cautious about unbalance in my design. I think that one good way is to discuss in parallel diversity, species richness, and abundance of individuals, while insuring to control for sampling intensity.

It is possible that my review of diversity indices could be helpful (Measures of species diversity in ecology: an evaluation. Folia Zoologica 49: 241-260, 2000; attached). For species richness for example, the samples should be approximately equal though sometimes Hurlberts rarefaction method can be applied. I will exclude samples with very low number from the analysis at all. The use and interpretation of evenness indices in ecology is doubtful.

Thank you very much. Your paper is very interesting and give a wide and very useful view of the different indices.

I would have an additional question. Diversity indices are derived from both abundance and species richness. Is there a use to discuss(in a paper) diversity, richness and abundance, or should we rather include only diversity, or richness and abundance? Which of these mesures give mostly redundant information and which complement each other?

I would prefer just a reliable index of species diversity, while species richness might also be added but only in the case of similar size of the samples.

Z - you might try the diversity methods of L. Jost for measures/indices that can account for differences in samples sizes among areas. You can try this as a start - Jost, L., P. J DeVries, T. Walla, H. Greeney, A. Chao & C. Ricotta 2010. Partitioning diversity for conservation analyses. Diversity and Distributions 16: 65-76. Hope this helps.

Thank you very much. I did not know about this paper, seems very interesting approach.

I think the important thing is to consider and to be able to identify the same number of species or taxa in the analysis of the different sites.

I agree that rarefaction would be a good index for such comparisons. But the assumptions (including normality of distributions) under which such an index is used are hard to meet and in most cases impractical

I don't know a lot about rarefaction. I think that regarding my study it is not the best option anyway. I have standardized sites and time, such that it is the same in all sites and the sampled are thus not biasd by sampling effort.

Dear Valerie,

Since you mentioned Shannon and Simpson Indexes and the issue of different numbers of individuals and species, here is a tip.

These indexes have a maximum value. For instance, the H'max is the maximum value of Shannon index. H'max = lnS, where S is species richness,

If you have two Shannon Indexes one being 2.3 and another one 2.7 for respective H'max 2.6 and 5.6. Which comunity is the most diverse? The first one, because H' was closer to the maximum, despite of being the smallest Shannon Index. That could be an interpretation. Simpson index has also a maximum value. Think of that...

Valerie -

You might find rarefaction is quite a powerful tool when comparing richness among sites that have had equal sampling effort. It will allow you to statistically compare among sites that may have different sample sizes. I am attaching a paper that uses rarefaction (and other metrics) to compare diversity among several spatial and temporal partitions. Phil

Article Similarity and difference among rainforest fruit-feeding but...

Thank you very much. But is rarefaction not mainly useful for sites that contain a lot of species? Can we use this method when some sites have only one species? Maybe I get my answer in your paper. Best

Shannon index has it bias on rare species and we need to be careful with the intepretation of data when using this index

I read the very useful paper of Jost (2007): "PARTITIONING DIVERSITY INTO INDEPENDENT ALPHA AND BETA COMPONENTS". It tells about "true" diversity indices, which base on the "number equivalents" (related to Hill numbers) instead of the diversity indices generally used. Comparisons between communities based on this method is also good for small sample sites. The calculations are implemented in the R package "vegetarian". It is quite new, but maybe does somebody know about it? Best

Hi Valérie,

I don't really know more about this method.

But Jost has a more recent paper on the subject:

Jost, L., DeVries, P., Walla, T., Greeney, H., Chao, A. & Ricotta, C. (2010) Partitioning diversity for conservation analyses. Diversity and Distributions, 16, 65–76.

http://chao.stat.nthu.edu.tw/paper/2011_Diversity%20Distrib._16_P65.pdf

Edit: Houps ! Sorry, I realized that this had already been suggested. I leave the post for the download link in case it is helpful.

Happy new year !

Tito

Thank you! Yes in fact I came on this package just before I read the paper suggested by Philip Devries and noticed that it was indeed the method he used. Thank you Philip again for this. I am especially interested in the function calculating turnover rate, as one of the aim of my study is to investigate if turnover rate in species composition changes in space and time according to an environemental gradient and a factor coding for different levels of fragmentation. I am still in doubt about how to separate the time and space effects, but I think that these new insights will help me go forwards. Best

The purpose of rarefaction is to standardize sampling effort to a fixed number of individuals. This may or may not be appropriate, given the ecological questions you want to address. Since your sampling method already standardized sampling effort to a fixed observation period, there is no absolute need to do rarefaction: the results from your various sites are comparable, as long as you remember that since sampling effort was defined in terms of time, the variable number of observed individuals will be one factor that can explain diversity differences among sites. You can find more discussion on sampling problems in relation to diversity in the following:

Tuomisto, H. 2010. A diversity of beta diversities: straightening up a concept gone awry. Part 2. Quantifying beta diversity and related phenomena. Ecography 33: 23-45. doi: 10.1111/j.1600-0587.2009.06148.x

The paper as a whole is rather technical, but you can go straight to p. 39 for a discussion on biases and constraints. Note that "turnover" and "turnover rate" are different things; this is also discussed in the paper.

As to evenness, you may be interested in this:

Tuomisto, H. 2012. An updated consumer's guide to evenness and related indices. Oikos 121: 1203–1218. doi: 10.1111/j.1600-0706.2011.19897.x

Cheers,

Hanna

Dear all, I would like to go back to my initial question: the issue of individual abundance. I read much of the suggested papers, and I noticed, especially in Jost'spapers, that there were differences depending on samples having equal or different weights. Still I am not sure I got this right. Does equal weights mean that all sites (samples) should contain the same total amount of individuals? Then, if my sites contain different amount of individuals, according to Jost only Shannon entropy or species richness should be considered. However I know very little studies in which the total number of individuals is the same in all sites. Or is it the case after rarefaction method has been performed? Thank you

The easiest way to obtain equal weights for all sites is to express species abundances as proportions (or percentages) of the total number of individuals at a site, rather than as raw numbers of individuals. In this way, the total abundance in each site becomes unity (or 100% if you use percentages) and all sites obtain the same weight in the calculations no matter how many individuals they contained. See p. 6 in the first part of the Ecography paper I mentioned above (the doi of part 1 is 10.1111/j.1600-0587.2009.05880.x) for a discussion on how results based on relative abundances differ from those obtained through rarefaction.

Sampling unit weights are also discussed in the following, but mostly in the context of what difference it makes to use presence-absence vs. absolute abundance data:

Tuomisto, H. 2010. A consistent terminology for quantifying species diversity? Yes, it does exist. Oecologia 4: 853–860. doi: 10.1007/s00442-010-1812-0

Thank you very much for mentioning this good alternative. The discussion in the paper is quite technical. I got out to be very cautious about "stretching" effects and therefore interpretation of the results.

I agree that using data based on relative abundance values helps to overcome several problems. We also used these in our analyses as incidence data alone was certainly insufficient.

https://www.researchgate.net/publication/227367007_Assessment_of_yeast_diversity_in_soils_under_different_management_regimes

https://www.researchgate.net/publication/233862794_Aboveground_deadwood_deposition_supports_development_of_soil_yeasts

Article Assessment of yeast diversity in soils under different manag...

Article Aboveground Deadwood Deposition Supports Development of Soil Yeasts

Thank you very much. Regarding all your comments, there are obviously many ways to handle my data, I'll have to pick one out. I find the approach that base on number equivalents very relevant. I learned a lot about the different ways to interpret the different indices and way some should be used or not. It is quite difficult to get all the issues related to the different indices. I will probably base my study on two measures, species richness and one which takes species abundance into account, maybe Shannon's true diversity based on proportional abundance, since it is often cited as the most robust measure.

Valérie: although this answer comes probably really late, the R package you need is called "vegan". I believe the name means vegetation analysis.

I would suggest you to study a review paper on species diversity and eveness indices:that is attached. With compliments, Zdenek. 

Thank you very much.

@ Zdenek: your paper is really interesting and helpful