Here Im addressing your questions in the order you posted them:

-Diversity: since you have 11 reefs and I am guessing that each has different number of species, you have to use an index that takes into account the number of species. Shannon and Simpson diversity are helpful but are one step short from accomplishing that goal. Use Hill's numbers instead which is the exponent of Shannon and the inverse of Simpson; I highly recommend you to read this paper so you understand this point Article Jost, L. Entropy and diversity. Oikos

anosim and adonis compare the community composition and not diversity. For example, you may have similar richness and diversity indices but totally different communities in terms of species composition, so anosim and adonis come in handy. If you read the "See Also" section of anosim in the vegan R package, they suggest adonis.

-Composition: anosim and adonis address composition. Bray-Curtis is perhaps the most popular (and one of several) distance method to compute communitiy dissimilarity. From my experience, these techniques dont tell you the percentage % by which these communities differ, but will tell you if the community composition of Reefs are different or not. If you want to compare each reef, then do a pairwise adonis comparison https://github.com/pmartinezarbizu/pairwiseAdonis

-simper gives you "the contribution of each species to overall dissimilarities" read "Details" section carefully in vegan package.

In summary, diversity is a combination of richness and evenness but doesnt tell you much. Perform adonis to compare community composition (dont forget to run 'betadisper' which is the assumption prior to adonis), and run pairwiseAdonis if needed. Then plot your nmds for sites, which is helpful to interpret/visualize you adonis (the default distance is Bray-Curtis but you can find the best distance using 'rankindex' in vegan). Then you can use SIMPER to identify what are the species contributing the most to such differences among sites. You could also add environmental variables to your nmds using the 'envfit' function.

Here Im addressing your questions in the order you posted them:

-Diversity: since you have 11 reefs and I am guessing that each has different number of species, you have to use an index that takes into account the number of species. Shannon and Simpson diversity are helpful but are one step short from accomplishing that goal. Use Hill's numbers instead which is the exponent of Shannon and the inverse of Simpson; I highly recommend you to read this paper so you understand this point Article Jost, L. Entropy and diversity. Oikos

anosim and adonis compare the community composition and not diversity. For example, you may have similar richness and diversity indices but totally different communities in terms of species composition, so anosim and adonis come in handy. If you read the "See Also" section of anosim in the vegan R package, they suggest adonis.

-Composition: anosim and adonis address composition. Bray-Curtis is perhaps the most popular (and one of several) distance method to compute communitiy dissimilarity. From my experience, these techniques dont tell you the percentage % by which these communities differ, but will tell you if the community composition of Reefs are different or not. If you want to compare each reef, then do a pairwise adonis comparison https://github.com/pmartinezarbizu/pairwiseAdonis

-simper gives you "the contribution of each species to overall dissimilarities" read "Details" section carefully in vegan package.

In summary, diversity is a combination of richness and evenness but doesnt tell you much. Perform adonis to compare community composition (dont forget to run 'betadisper' which is the assumption prior to adonis), and run pairwiseAdonis if needed. Then plot your nmds for sites, which is helpful to interpret/visualize you adonis (the default distance is Bray-Curtis but you can find the best distance using 'rankindex' in vegan). Then you can use SIMPER to identify what are the species contributing the most to such differences among sites. You could also add environmental variables to your nmds using the 'envfit' function.

In addition to the clear explanation provided by Yvan, If you are not familiar with R software, you can use PAST software to run the analysis. For the beginners, I usually advise the use of this software for analysing diversity data. its two components namely "Multivar" and "Diversity" are very powerful as tools.

Hi, Brid,

Here is an alternative to the Bray-Curtis index: https://odajournal.com/2014/11/09/unioda-vs-bray-curtis-dissimilarity-index-for-count-data/

This alternative gets you an exact p (with no assumptions), maximizes the accuracy of the model, assesses cross-generalizability to other random samples taken from the reefs, and reveals specifically where the dissimilarities lie.

With 11 reefs you'd have to do a novometric (Latin: new measurement) analysis. Conducting the analysis requires learning the methodology--and the information is freely available (https://www.ODAJournal.com).

If alternative legacy methods fail to get the job done, you are aware of a superior, modern alternative.

Bray Curtis shows dissimilarity based on counts, so will compare relative abundance

Hello, Bríd O'Connor

PERMANOVA, Bray-Curtis, Sorensen, etc. there are plentiful measures and indices to analyse the data from different reef can be applied to figure out the significant distinction or not.Knowing the actual meaning before Choosing the optimal method to deconstruct the pattern , process or the mechnism hiding from the abundance data is essential in the near future.

From my angle, PERMANOVA can be used to analyze the interpretation of sample differences by different grouping factors, and displacement test can be used for significance statistics. In ecological statistics, PERMANOVA can be used (it is often used together with ranking analysis, and for PERMANOVA, it is often used together with PCoA ranking analysis to explain the problem) to see whether there are significant differences in community composition and structure in different environments.

And,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 - Quantity SI . Both indices have similarity and dissimilarity (or distance) versions, in addition Dissimilarity + Similarity=1.

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Abundance-Based Similarity Indices and Their Estimation ...

viceroy.eeb.uconn.edu › Colwell › ChaoEtAl2006

PDFresults show that the adjusted estimators significantly reduce the biases of the ... tions and arguments can be readily applied to dissimilarity indices ... cal studies, the incidence-based indices do not take species ... oped by Bray and Curtis (1957), based on abundance data ... scribing forest compositional changes with time.by A Chao - ‎2005 - ‎Cited by 484 - ‎Related articles

Assessing biological dissimilarities between five forest ...

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Jun 6, 2019 - The Bray-Curtis index, a modified version of the Sørensen index, includes species abundances (Chao et al. 2005). These three indices have ...by M Hao - ‎2019 - ‎Cited by 1

https://andrewsforest.oregonstate.edu/sites/default/files/lter/pubs/pdf/pub4827.pdf

You might want to explore Anne Chao's work in this area, and her useful online toolset http://chao.stat.nthu.edu.tw/wordpress/software_download/

Hi Brid,

Short answer is ‘yes’. More correctly, Bray-Curtis shows how similar is species composition based on relative abundances of species. There is another index – Morisita-Horn, which also calculates the distance based on relative abundances, but it undervalues rare species. So it is up to you to decide which index suits you. Consult Anne Magurran’s book “Ecological Diversity and its measurement”.

Also yes. What I see done (and do myself) most commonly is PERMANOVA done on a Bray-Curtis dissimilarity index to test for differences in community composition among places (e.g., reefs), times, or whatever the contrast of interest is. This tells you nothing about what drives any detected differences. SIMPER can help with that, but it has some limitations, notably that it can't evaluate with cause of interactions (e.g., place x time). In practice, univariate follow up analyses (e.g., ANOVA) are often used for each "important" taxon to figure out which ones are driving a significant PERMANOVA result.

If you spend an hour or less watching Keith McGuinness' excellent PRIMER tutorials (on Youtube), you will feel a lot more comfortable with what to do and why.

Dear Bríd O'Connor,

Hi, You seem to be dealing with several species on each reef. If so, you have to divide each reef into micro-habitats (specific habitat) in terms of reef floor and peak, geographical directions, the slope of each side of the reef, and the type of minerals that make up the reef and many ecological elements, then micro-colonies of each reef. Study alone as a community and in comparison with other reef colonies in terms of the type of species they form and the ecological conditions of their micro-habitat. Remember that the Shannon Wiener Diversity Index applies to more than one species. You can use PAST, NTSYS-pc, PC-Ord, CANOCO, Minitab and if you familiar by R, you can try BiodiversityR package. For more information about the multivariate analysis, I recommend you "Multivariate analysis in ecological data" book.

Best,

Saeed

Notably, if the species is known to you, you can use the NMDS technique to discriminate the ecological conditions that make up any habitat for any species. The DCA technique discriminates ecological factors for each well. Using CANOCO, communities can be divided based on constituent species.

Best,

Saeed