Hello Zu Dienle Tan, 

As you say, the Sørensen index is for presence / absence data. The Bray-Curtis is a very similar index, but that can be used with abundance data. 

What about similarity, dissimilarity and distances index? 

It depends if you want to stress on the differences or the similarities of the communities you are comparing. 

Both Sørensen and Bray-Curtis indices take values from 0 to 1. If we are using the dissimilarity or distance indices, then a value of 0 means that the communities have exactly the same species composition, and a value of 1 means they don't share any species. If we are using a similarity index, then the interpretation is the opposite: 0 means that they are not similar at all (that is, they don't share any species) and 1 means that the communities are 100 % similar. 

(Sørensen or Bray-Curtis) dissimilarity is equal to 1 minus (Sørensen or Bray-Curtis) similarity. 

As far as I understand, dissimilarity and distance are used interchangeably. However, the Wikipedia article about the Bray-Curtis dissimilarity (https://en.wikipedia.org/wiki/Bray%E2%80%93Curtis_dissimilarity) says that it is incorrect to call it a distance because it does not satisfy the triangle inequality. The triangle inequality states that the sum of the length of two sides of a triangle will always be greater than the length of the third side. Distances behave like the sides of triangles. If the Bray-Curtis dissimilarity was  a "real" distance, then the dissimilarity between communities A and B plus the dissimilarity between communities A and C should be greater than the dissimilarity between B and C. 

if you want to read more about this, I found this two links that could be useful:

http://www.planta.cn/forum/files_planta/chapter_8_analysis_of_differences_in_species_composition_172.pdf 

http://www.zoology.ubc.ca/~krebs/downloads/krebs_chapter_12_2014.pdf

Hello Zu Dienle Tan,

The Bray-Curtis and Sorensen indices are very similar. The difference, as you say, is that the Bray-Curtis index is based on abundance data, while the Sorensen index is based on presence/absence data. Both indices have similarity and dissimilarity (or distance) versions. 

Dissimilarity = 1 - Similarity 

Both indices take values from zero to one. In a similarity index, a value of 1 means that the two communities you are comparing share all their species, while a value of 0 means they share none. In a dissimilarity index the interpretation is the opposite: 1 means that the communities are totally different. 

Distance and dissimilarity are sometimes used interchangeably. However, the Wikipedia page of the Bray-Curtis dissimilarity (https://en.wikipedia.org/wiki/Bray%E2%80%93Curtis_dissimilarity) says that it is incorrect to call it a distance, since it doesn't satisfy the triangle inequality (the sum of the lengths of two sides of a triangle is always greater than the length of the third side). That is, the sum of the dissimilarities between communities A and B and communities A and C is not necessarily greater than between communities B and C.

For more information, you can check:

http://www.econ.upf.edu/~michael/stanford/maeb5.pdf

http://www.planta.cn/forum/files_planta/chapter_8_analysis_of_differences_in_species_composition_172.pdf

Just to add to what has been already said, if you have presence/absence data and you apply a Bray-Curtis dissimilarity, you'll get exactly the same result as if you had applied Sorensen. However, if you have abundances, and apply Sorensen, it ignores the abundances and your result is as if you had presence/absence. The usage of one or the other depend thus on your data, and in the case you have abundances, how you want to treat your species, that is, if you want them to be treated equally and ignore abundances (Sorensen) or you want them to be weighted by their abundance (Bray-Curtis).

About the triangle inequality of either measure (ie, they are semi-metric in nature), this is a very desirable condition, especially when you are dealing with species composition, given that you'll never be 100% sure that a zero in your data is a true absence. The species could be present in the site where the sample came from but you failed to observe/collect it, and thus two sites with a bunch of shared zeros end up being more similar to each other that two sites that share a few species if you use a metric measure (such as Euclidean distance). Therefore, these semi-metric distances ignore the double absences when comparing dissimilarities among sites and correctly assess similarities in your data. 

Hope this helps and good luck with youranalyses!

http://biodiversity-pro.software.informer.com/2.0/ can help you to analysis the data.

Hi Sebastian Block,

The comments were very instructive. Where are the chapters you sent the links, published?

Happy 2016 for all!

Hello Helena, 

I am glad you found the answer instructive, and sorry for not specifying the source of the chapters.

The first one is Chapter 5 of the book Multivariate Analysis of Ecological Data, by Michael Greenacre and Raul Primicerio. 

https://books.google.com.au/books?id=0H6IAgAAQBAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

The second one is chapter 8 of the book "Tree diversity analysis: A manual and software for common statistical methods for ecological and biodiversity studies" by Roeland Kindt and Richard Coe, published by the World Agroforestry Center. Here is a link to complete book. 

http://www.worldagroforestry.org/downloads/Publications/PDFS/b13695.pdf

Happy 2016!

Thank you Sebastian for two very useful links. 

The releves were also recorded according to the Braun-Blanquet (1932) method for the three-dimensional ordination technique. The Wisconsin polar ordination technique (Bray and Curtis, 1957) was used for grouping the releves and separating plant communities. This method is quite well suited to the modern interactive computer scenario. Bray and Curtis’ ordination method has been successfully used in the past, and because it is simple it highlights the problems of polar ordination quite well. To statistically support the results obtained from the Braun-Blanquet method by phytosociological studies and three-dimensional ordination, the following procedures were carried out (Sağlam, 2013). The scales of abundance-coverage of Braun-Blanquet (1932) were translated into Van der Maarel’s (1979) ordinal values (+ = 2, 1 = 3, 2 = 5, 3 = 7, 4 = 8, 5 = 9). The similarity (Is%) and dissimilarity (Id%) equivalence values of each releve were calculated using the similarity index formula of Sorensen (1948). Is%= (2 x W x 100) / (A+B), Id%= 100-Is%. The values of x, y, and z were determined by creating a correlation matrix using the index of similarity ( x= L2 +(dA) 2 +(dB) 2 / 2L, y= (L’) 2 +(dA’) 2 -(dB’) 2 / 2L’, z= (L’’) 2 +(dA’’) 2 -(dB’’) 2 / 2L’’ ).The positions of the releves on these axes were determined according to the values of x, y, and z. A three-dimensional ordination graphic was drawn according to the values obtained. Sampling areas were separated into associations according to the clusters in the ordination graphic. A software package (FG-ORD) was used for the classification of vegetation according to the method of ordination (Geven et al., 2008). The International Code of Phytosociological Nomenclature was used for naming the new associations (Weber et al., 2000). Sorensen’s similarity index was used to compare the associations with similar associations studied near the research area (Sorensen, 1948).

Bray-Curtis index is used for quantitative data (abundance) and its analogue (Sørensen index) for qualitative data. Bray-Curtis index has been shown to be one of the best for detecting gradients in species composition (see Michin PR , 1987, An evaluation of relative robustness of techniques for ecological ordination. Plant Ecol 69:89–107. doi:10.1007/BF00038690 ). Qualitative index tends to give more weight to rare species because common species tend to occur in all plots and contribute little to the differences between plots. Quantitative index tends to give more weight to common species, which have more numerical variation between plots.

Check out the Morisita-Horn index and the discussion in chapter 5 and 6 of MAGURRAN, Anne E.; MCGILL, Brian J. (ed.). Biological diversity: frontiers in measurement and assessment. Oxford: Oxford University Press, 2011.

The authors provide great insight into the advantages and limitations of similarity indices, as well as in the issue of beta diversity (temporal beta diversity, or the comparison of similarity in community composition over time is an aspect of diversity almost totally ignored by the literature). The above-mentioned book updates the classic book by Magurran. Best, GA

please look this also...

https://www.researchgate.net/publication/287615478_A_MODIFIED_SORENSEN%27S_INDEX_TO_COMPARE_SIMILARITY_BETWEEN_PLANT_COMMUNITIES

Conference Paper A MODIFIED SORENSEN'S INDEX TO COMPARE SIMILARITY BETWEEN PL...

See also Clarke KR, Somerfield PJ, Chapman MG (2006) On resemblance measures for ecological studies, including taxonomic dissimilarities and a zero-adjusted Bray-Curtis measure for denuded assemblages.  J. Exp. Mar. Biol. Ecol. 330:55-80.

When using similarity index you must also see the equation to see how they consider double absences (species that are no represented in any of two places, but can be in a third one). Some index consider double absences increasing similarity, others ignore double absences and consider only the species that are present in at least one of the localities. Using one kind of index or other would depend of the biological sense of your study.

Angel, and what about the niche overlap? In your logic, the Bryan and Curtis is better than Morisita, because in this last only the coincident species count. On the other hand, in the Bryan & Curtis the exclusive species contribute to the final value. 

In my oppinion, to compare niche overlap we need an index that not consider double absences increasing simmilarity. The fact that two species being absent in marine environments does not involves that they share or overlap the niches. One can leave in the top of mountains and the other in lakes. 

this is quite interesting and approaches it slightly differently

http://chao.stat.nthu.edu.tw/wordpress/paper/97.pdf

Earlier I tried to point people to a paper (Clarke et al 2006) that covers most of the points people have made, which folks could look at on ResearchGate if they wished.  In that paper we lay out some guidelines for properties that a good resemblance measure for biological data should have, and which Bray-Curtis and related measures have: 

Coincidence:  coefficient = 0 only when two samples are identical (talking about dissimilarity here)

Complementarity:  takes its max value (100) when two samples have no species in common

Relative invariance:  scaling change does not affect relative values of resemblances

Independence of joint absence:  taxa not present in both samples do not contribute to the resemblance (note the asymmetry: joint presence implies similarity, absence opposite presence implies dissimilarity, joint absence implies nothing)

Localisation:  each pairwise resemblance depends only on data for those two samples

Dependence on totals:  coefficient is able to combine relative composition and change in totals.

Resemblance measures in the Bray-Curtis family tick all these boxes, which is why we use them for situations where zeros in the matrix imply absence (as opposed to situations where zeros imply a position on a number-line).

The overall answer to the question is that Bray-Curtis IS Sørensen (or Dice, Steinhaus, Odum or other named measures with the same formula), the difference is how the data are (pre-)treated.  If calculated for binary (presence/absence) data the measure may be called Sørensen, if calculated using abundance data it is Bray-Curtis.  The key point to note is that, if your data are NOT binary, then you probably need to pre-treat or transform your data to balance the contributions from rare and numerically dominant taxa.  Anyway, the question here is about Bray-Curtis (similarity or dissimilarity or Sørensen or Dice or Steinhaus or Odum), so you might like to have a look at Somerfield PJ (2008) Identification of the Bray-Curtis similarity index: comment on Yoshioka 2008.  Mar. Ecol. Progr. Ser. 372:303-306. 

Hi Zu

Now you know the difference, Nevertheless i recommend:

http://onlinelibrary.wiley.com/doi/10.1111/j.1461-0248.2004.00707.x/abstract

thank you all for satisfactory answers!

Is Bray curtis the opposite of Sorenson index value? to mean

BCI= 1-SI?

Yes: Bray-Curtis = 1 - Quantitative Sorenson-Dice index

Informative discussio. Thank you I am searching same topic, fortunately I found it.

Hi dear,

The book entitled “Multivariate analysis in ecological data” written by Michael Greenacre & Raul Primicerio is often recommended in multivariate analysis context. It seems that is the best reference in this field of study.

Best,

Saeed

Thank you all for sloving my same question due to the Meaningful query.

In my summary, The Bray-Curtis index is a little same as Sorensen index. And the primary distinction is that the B-CI is applied to abundance, while the SI is applied to presence/absence, i.e. B-C I = 1 - QSI . Both indices have similarity and dissimilarity (or distance) versions, in addition Dissimilarity + Similarity=1. 

Those on this thread might find my conference paper interesting: "Why I don't use Bray-Curtis in multivariate analysis of ecological data". It's on YouTube at youtube.com/CARMEnetwork, or the direct link to the video is: https://www.youtube.com/watch?v=c7VUrViGmQU … Read more

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Hello everybody,

Each index has its own circumstances and population measures to apply, and each index is derived to solve a special problem. So it depends on your goal, whether you want to seek the effect of tiny factors or just you want general information.

Thanks.

I agree to Amin Khedher that it depends on your goal which index is most appropriate. We have been doing earthworm monitoring with repeated investigations everey few years. The aim is to detect long-term changes in soil biota communities. The abundance data can vary a lot due to short-term effects as weather conditions, tillage and fertilization. Thus, we decided to exclude the abundance data from similarity assessment and use the Sörensen index (presence / absence data) to get a general idea on similarity of communities of different sites.

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

Article Measuring the ecological preference for growth of150 of the ...

https://www.cell.com/heliyon/fulltext/S2405-8440(19)35821-9

In addition to whether they are for quantitative (abundances) or qualitative (presence-absence) data, an important aspect when considering which index to use in faunal similarity studies (for characterisation of communities or biogeographic relationships) is how they consider double absences (species that do not occur at either site). Some indices consider that not sharing a species is an indication of affinity, while others only consider species that are shared. Clearly, in the type of studies being considered in this discussion, not sharing a species does not mean that two regions or habitats are similar, so indices that consider double absences should be avoided.

The main issue on which you need to pay attention is the charateristics of the species composition (when using abundance data). I mean presence or absence of a vastly or moderately od slighlty dominant species as well as total number of species with minimun level of abundance can create problem in comparison depending on the total number of species. Meanwhile I suggest that it can be beneficial for you to consider about morisita index. Sure if it fits your goal!

The comparison of the fauna or vegetation of two sites by means of indices such as those mentioned by Zu, must take into account that this comparison is only a "snapshot", a instantaneous appreciation of the organisation of the two sites. These measures of similarity or dissimilarity are useful if both sites have identical environmental conditions, the same turnover rate of individuals and species, which is... not always the case.

Best,

JJ