Dear Piotr,

While I have found incidence-based ecological indices useful for biomonitoring purposes (even more useful than abundance/density-based ones), I am not aware of incidence-based diversity indices sensu strictu.  When incidence (i.e., presence/absence) is involved, typically richness is invoked.

You might find some info (and a lot of ecological and theoretical reasoning) in the following book:

Magurran Anne E. & Brian J. McGill (Eds.), 2011.  Biological Diversity -- Frontiers in Measurement and Assessment.  Oxford University Press, New York, NY, 345 pp.  ISBN (paperback version): 978-0-19-958067-5.

I obtained this book via Amazon.com, quick and easy.  It is an excellent reference book on the topic, and a recent one too.

I admit that the highly theoretical and mathematically complex chapters were too much for me -- I am a "practical" ecologist and I leave the more sophisticated academic exercises to the real experts.  However, I find this book useful for my purposes.  I haven't found any mention of an incidence-based diversity index, though; unless of course this topic is discussed in the more sophisticated chapters, which are out of my intellectual reach.

About your other question (the first), I think that whether calculating species diversity at every location makes or doesn't make sense depends on your scientific question, which I do not know.

I hope that my answer helps you a little bit...  Sorry for not having anything better than this.  Please feel free to contact me directly if you have more questions or if my explanation was somehow suboptimal.

Good luck with everything!

-Paola

Stress Index can give a best reflection of present/absent data of species

Hi Piotr,

have you ever tried the so-called "Taxonomic Distinctness". A certain form exists which only needs presence-absence data. It describes the taxonomic diversity within a dataset (of course phylogenetic diversity would be even better, but the true phylogeny is often unknown).

You would need a matrix not only of your species, but also of their taxonomic properties, like genus, order, and so on. But it would be best to also have a dataset from a kind of larger reference area if you want to see whether your obtained diversity is significantly higher or lower than that of the reference area. Otherwise you just get a value without much meaning.

This index is implemented in the software Primer.

The theory is published in Clarke & Warwick 1998 (see article).

All the best

Armin

with simple presence absence data, your options are fairly limited.  the most useful quantitative indices require count data by species and sample.  if your comparative sample are large enough, simple species richness - the count of distinct species or entities - works fairly well.  you could also build a species rarefaction curve plotting number of species on the Y axis against number of samples on the X axis.  Again, only legitimate if number of samples is large enough to have captured the full suite of species in each of the comparative sampling areas.  The software EstimateS could be applied to evaluate statistically significant differences identified by space between the respective rarefaction curves for two samples, within their 95% CIs.

Although it is considered an indicator of beta diversity, I recommend using a similarity index as Sorensen. Additionally it must be show on a cluster of Bray-Curtis where similarity and difference between habitats can be expressed  at the same time.

Hi there,

as written at another question, clustering is not a good idea for comparisons of sampling areas. If you want to do similarity analyses, ordination and nMDS methods should be applied instead of cluster methods.

One reason is that during the process of clustering encaptic groups are built out of the samples which are then treated as entities in the further process. This is not valid. Secondly, samples from nature are not inherently of hierarchical nature, but instead should be treated as being on the same level. Clustering, however, requires a hierarchical structure within the data. But this is rarely considered in biological studies. Ordination and nMDS treat ecological samples in a more adequate way. Better use these.

Best regards

Armin

Dear Colleagues,

Thank you for a very interesting discussion. However, I’m more interested in “alpha” diversity (characteristics of a sample/site) rather than indices describing the beta-diversity. Armin Rose – I was thinking about something very similar. In meanwhile, I have stumbled across the paper you attached, thank you. This index seems to be exactly what I can do with my dataset. I also realized that I may calculate some indices of functional diversity too (but I havent gathered information on species properties yet).

Best wishes

Piotr

Hi Piotr,

I also once tried this index (see paper below; sorry, the abstract is in German, but the rest in English). In the first paragraph I wrote some sentences about it and provided some citations. Maybe it is useful for you.

I think this is a really interesting index, since it covers a totally different aspect of diversity.

All the best

Armin

Article The „taxonomic distinctness“, a diversity index from marine ...

Dear Armin, I think it will be very useful :). Thank you!

Best wishes,

Piotr

Piotr, 

I think there is no good species diversity to a 0-1 data.  You might work with a only species number and a qualitative analysis. If you want to compare areas use UPGMA or WPGMA clustres (or both). 

A usefull  reading could be 

Krebs, C.J. 2014. Ecological Methodology, 3rd ed. (in prep)

Chapters revised to date (14 March 2014) are available to download for evaluation and review (PDF files).

With on line access at: http://www.zoology.ubc.ca/~krebs/books.html.

or :

Zar, J. H .Biostatistical Analysis, 5th ed,  Illinois: Pearson, 2009

I am no whizz on the statistics, but with advice from more able co-authors, I have come to distrust simple indices of similarity or difference like the Jaccard index. I would personally prefer the Sorensen, or its modification in the Simpson index which takes the species in common as a proportion of the less rich of two samples. 

Apart from the complication of having different richnesses in samples, I found that dendrograms using UPGMA or similar are not really satisfactory. I am convinced that ordination is a better process, and I know that there are methods that accommodate presence/absence data.

 PCA, DCA, CCA or like can use both binary (presence/absence) and abundance data. If you have many samples, ordination bases on these multivaroate tools can be the most informative way of analyses

Dear Piotr,

I have just run into this paper:

Evangelista et al. (2012): Comparison of Diversity Indices Applied to Macrophyte Incidence-Based Data

which is available on ResearchGate at Sidinei Thomaz's profile page.  It might provide the answer that you are looking for.

I have also noticed that the Jaccard index has been mentioned in this Q&A session.  I thought that the Jaccard index is used to compare diversity (as species composition) between two sites/samples/communities, rather than to quantify diversity at any one site.  Probably a multivariate (PCA or similar) may be the best solution for you, as suggested by Zaal just above.

-Paola

Dear Piotr,

1. I suggest the indices below which help you to evaluate the species diversity of your research area in nature conservation and ecological points of view.

2. Do not use to much mathematic, since it may easily cover your message instead of highlighting! The following methods I can suggest.

3. Ecological tolerance index: Ratio of stenök (narrow tolerance)/euryök species (wide tolerance) in point of view eremophylous or hylophylous species.  See the stenbionty: http://pl.wikipedia.org/wiki/Stenobionty

If the proportion of stenök (narrow tolerance) species is high: it suggests: high proportion of indicator species: the habitat in nature conservation point of view:

a.  in  good conditon

b. need to be protected

c. probably this is a core area (nature conservation categories)

For instance, in pollinator and aculeata hymenoptera species (bees, sphecoids, etc. etc.)  these categories has already very well established (publications of Zsolt Jozan) and you need only to apply these. In other groups, at first you need to establish these categories like stenök hylophylous, stenök eremophylous, euryök hylophylous, euryök eremophylous and intermedier than analyse your faunistic list.

4. Zoogeographical indices and evaluation. Also need to know the core-distribution of your species on your list: like pontomediterran-central european, holomediterrane-central european, atlantic central european, palaearctic, west-palaearctic, central- european, pontocaspian-central european etc. and also you may calculate the ratio of atlantic, mediterranean elements in your faunistic list. It can outline the zoogeographycal type of your area. 

5. Finally: ratio of rare, extremely rare species compared to frequent, common and sporadic species with special focus of the rare species with relatively high abundace in your area. This indicate also the condition of the research area and help you to categorise whether it can be a core area, buffer zone, corridor or degradated area which need further improvement. 

Piotr, Not sure what sort of data you have available, but if you have recorded presence-absence on multiple occasions, there are studies showing that it can be valid to use the frequency data as a surrogate for abundance. In that way you could then calculate a standard diversity index.  For example, many birdwatchers make checklists, recording all the species they see in a particular place on a particular date and time.  These checklists when collected and combined show trends comparable to point-count data collected by scientists over the years.  For reference, see Droege, S., Cyr, A., & Larivée, J. (1998). Checklists: An under-used tool for the inventory and monitoring of plants and animals. Conservation Biology, 12(5), 1134-1138.  There are several more recent papers supporting this approach, but Andre Cyr one of the first to develop it. (However, I agree with previous posters that there are other often more useful metrics than diversity.) 

There are dozens of indices, and hundreds of papers. Have a look literature by Gotelli, Ulrich, etc. Have a look at "Null Models in Ecology", by Gotelli & Graves, or to Soberon & Cavner, 2019.

All species diversity indices have limitations in their uses. The diversity indices based on the presence and and/or/ or abundance data are found in those with the greatest number of limitations. Therefore, I recommend using the taxonomic indices of distinction. These indices are a valuable tool for studying the structure of communities. Review the following manuscript to see an example method of these indices:

Article A taxonomic distinctness index and its statistical properties

Colleague, if your intention is to do beta diversity studies, the following two manuscripts can help you select the best index based on your data:

Article Beta diversity for presence–absence data

Article Preferential sampling for presence/absence data and for fusi...

Article A new conceptual and methodological framework for exploring ...

Finally, I recommend this paper:

Article Inventory, differentiation, and proportional diversity: A co...

For alpha diversity, with presence-absence data, I strongly suggest using the q=0 diversity order of Hill numbers with 95% confidence intervals. You can easily calculate it and draw cumulative curves in the iNEXT software: http://chao.stat.nthu.edu.tw/wordpress/software_download/inext-online/

Another option is the Chao 2 Richness Estimator, which you can easily explore in SPADE: http://chao.stat.nthu.edu.tw/wordpress/software_download/softwarespader_online/.

@Anne Chao has the key literature on this issue.

You can find an answer in this manuscript, you can download it from the following URL, it is free

https://www.cell.com/heliyon/fulltext/S2405-8440(18)38688-2

Is your data set just a checklist of species without any additional information? Then the length of species, or species richness is the only index you can have. You might also calculate phylogenetic relatedness if it is in your interests.

If you have many lists where species occur repeatedly, than you can calculate their frequencies of occurrence and use it as a measure of abundance, then calculate the usual indices such as Shannon and Simpson.

You can find an answer in this manuscript, you can download it from the following URL, it is free

https://www.cell.com/heliyon/fulltext/S2405-8440(18)38688-2