Your RDA result appears to show a horseshoe effect, which means that the linearity assumption of the RDA is not fulfilled, and that the data is more likely to be distributed unimodally. My suggestion is to use CCA, which is the unimodal equivalent of RDA.

Thanks Ofir, who has suggested that the triangle is simply a 'horseshoe' effect and suggests that I should run a CCA instead - but the CCA produces a very similar triangle ordination. 

Interesting problem... the recurring issue of the arch or horseshoe effect. What it means it that at the extremes of the spp X site matrix you get sites that don´t have species in common. These sites ended up being similar due to joined dissimilarities, or zeros in the matrix spp X sites... Usually, this happens b/c the similarity matrix is based on euclidian distances and could be non-linear. Any chances you could use a different similarity matrix or a transformation? How about using a similarity matrix based on indices of spp overlap? The horseshoe effect shows that there is an ecological explanation for the artifact although the analysis is not efficient capturing the actual pattern since dissimilarity does not reach a maximum value when 2 or more sites don´t have species in common. I have seen this happening -in my case- when you get lots of sites but relatively few species and few individuals -lots of zeroes-.  If you get noisy data like this perhaps doing a multivariate analysis indiscriminately for all sites is not very efficient. Going over your data and selecting sites that are interesting, dropping sites that are not very informative, could improve the type of meaningful ecological information you want to extract from this. Best of luck. GA

thanks Geraldo,

running a CCA also produces the horseshoe effect. I will look into other ways of calculating a similarity matrix that deals with all the zeros-  nice idea. thanks!

I belong to very old school of ordination , but still feel you  at least try simple three dimensional ordination using dissimilarity matrix and see how habitats are behaving in hyperspace.I feel that would give you some insight to explain your problem ,

Dear Tania, please consider transforming your species data using Hellinger distance. Find attached a paper by Legendre & Gallagher discussing about that. Good luck!

According to you graphs, NMDS-axis1 does a relatively good job at separating A from B and C, whereas B and C are overlapping. On the other hand NMDS-axis 2 contributes next to nothing to the separation of the 3 groups. So there is actually very little "linearity" in the first graph.

RDA does an excellent job at separating all 3 groups. If you can interpret these axes ecologically I would not bother about the arch-effect (unless the non-linear relation between the two axes compromises your interpretations).

I do agree with Irene. From what I have seen, you have conducted a two-dimensional non-metric multi-dimensional scaling (nMDS) ordination of species in habitat type spaces. I am not sure of the software you have used to do the nMDS ordination. I guess it is R. However if one uses PCORD of which I am familiar with, the variance explained can be interpreted by looking at % values with respective to the axises(1 & 2). That means that one will be able to know which axis explains more variance than the other. Further explanation of the differences should be done in the context of ones research objective(s). It is also important to report the stress value, final instability as well as the number of iterations for your ordination. My take is, you can decide to use either nMDS or RDA but not necessarily interpreting the two graphs, since both of them essentially visualize similarities and dissimilarities in patterns displayed. But if that what is relevant for answering your research question(s), you can still go ahead to do so. Please also bear in mind that your interpretation should reduce complexities for a wide range of your audience. All the best in your analysis.  

good knock 

Mr Gerardo Avalos Explain well

Thanks everyone for your answers: 

Jhonny - These graphs were both created from data that is already hellinger transformed. So perhaps the 'horseshoe' effect is in fact an actual difference along the y axis of habitat B from the others?  

Irene - thanks for your interpretation but Im not sure I understand- is there not linearity along the x axis even if there is no trend seen along the y in the nmds?  

John-Baptist, thanks also I didnt specify how many dimensions for the NMDS -which I did in R.. I believe the default n dimensions = no. species -1? In which case its around 50 dimensions although only two are shown.

Anyway I have decided to stick with just the NMDS for now to avoid this issue. 

As I understand it linearity means a linear relationship between variables, e.g. as the values of one variable the values of the other variable increase or decrease in a monotonous way.

best wishes for your work! 

I feel you are going in right direction.Perhaps in habitatt B there are definitely some component or importance value of prominant species in relative terms have less impact than that in habitat A:C.Just try to see dissimilarity matrix of different habitats .

you right

thanks dear J. C. Tewari 

Thank you Dr. Khan.

Hi Tania,

You can download these manuscripts, they include PCA, NMDS, CCA , AHC and other multivariate and ordination technique.

They are free, you can download them from Heliyon Journal or science direct.

You can use the following URL as well:

The impact of five environmental factors on species distribution and weed community structure in the coastal farmland and adjacent territories in the northwest delta region, Egypt

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

Comparative view for the impact of five eco factors on species distribution and weed community structure in Isthmus of Suez and adjoining farmland east Nile delta, Egypt

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

Diversity and Biostatistics of the plant life in the Northwest of the Delta, Egypt

https://www.academia.edu/36696721/Diversity_and_Biostatistics_of_the_plant_life_in_the_Northwest_of_the_Delta_Egypt

Best regards,

what is the difference between Non-metric multidimensional scaling and Agglomerative Hierarchical Cluster (AHC)