Dear Pedro,

Thank you so much for your kind help. But, I don't understand what you said, arch or horseshoe effect. Would you mind to explain me more?

with best regards

lynn

Hi Tin. In paper attached there explanatory information that you can serve.

Regard

CA is for a unimodal models and RDA not. You can use the book "Numerical ecology" (Chapter 9) to understand and interpret better the results of your ordination graphics. Also, in this book you can find other stadistics methods.

I suggest also that before to do the analysis you should know the correlation of your variables. If this variables have a correlation between them upper to 0.5 you should to delete one of them.

In your RDA you can see how the variables in the right side are relationed with the WL samples. In other words, in this WL samples these variables had high values. But WL samples have negative relation with Sand(%). The number of axes 1 is the % of variability explained by this axes. 

Hi Tin,

Luis is right in saying that CA is a unimodal model, while RDA is a linear model. So the assumption behind using CA is that your environmental gradients are "long" enough to display the species' optimum location along those gradients. If your environmental gradients are short, then RDA may be a more appropriate method. Also, because CA is a unimodal method, it is prone to a distortion known as "the arch effect". However, your biplot shows no signs of such an effect, so I don't think that's a concern for you.

It is also important to note that CA is an indirect gradient analysis, while RDA is a direct gradient analysis.  In indirect gradient analyses, species are arranged by their sample matrix, with environmental information being used after the analysis for interpretation. For instance, species may be arranged along gradients that we have no data for. Conversely, direct gradient analyses utilize both species and environmental data to tell us how species composition is related to our measured variables. Meaning the arrangement of species along axes is constrained by environmental gradients. If you wish to use a direct gradient analysis that is also a unimodal model, I'd recommend a Canonical Correspondence Analysis (CCA). Hope this helps.

Hi, in order to decide what kind of analysis you should use, you have to run a DCCA or CA then depeding on the length of the gradient you will know  what analysis you should use. For example, if you run a DCCA and  results suggest a  a short gradient (less than 3), then you should run  a redundancy analysis

All the best,

Cesar

Above they've cleared up the CA/RDA debate, but I'm not sure I understand the other part of the question entirely. It sounds like you're asking about a number to report on: XX% of variation in WL is explained by XX% Clay, or if Arrow 1 is X big then WL is significant or something. These ordination techniques don't quite work like that. They provide a gradient not a categorical value. From your output, you can see that increases in WL are associated with increases in CEC, % Clay, and  Olsen P, while FO is (potentially) inversely associated pH and TOC; GR is (of the variables measured) most closely associated with C:N. So, variation in your samples is associated with those variables. Ordination techniques are great for helping us understand and visualize relationships and associations for confounding or related variables on specific species, but they don't tell you WL is significantly different than GR, or that XX increases in %clay will result in XX increase in WL. You can use things like general linear models or multiple regression to test for things like that, and use ordination techniques to better understand what's driving the relationships you've found. That's an answer that'll probably drive statisticians bananas, but hopefully it'll helps you better understand what you've got.

CA is a method, where you try to simplify the Distribution data of the community(e.g. species)  you sampled. As mentioned before, unimodal distributions are assumed for the species. CA does not include Information on environonmental factors. If you want to include environonmental factors, you can use CCA. This Analysis produces 2 sets of axes: one for your species - still assuming unimodal distribution and a second for environmental factors, assuming linear relationships. In CCA both set of axes are optimized, so that the environmental axes explain the species axes. The biplots shown with CCA superimpose environmental and species axes. If a species (in your case ist genes, but that does not matter) is Close to a (set of) environmental factors in the biplot, it is likely to be affected by These environmental factors (or something correlated with them). ANother interesting Features of the axes: the first is always the most important one, the second somewhat less important, etc, e.g. in your case pH, TOC and C:N are more important for the genes than  for example sand or TN, TP.

The arch effect is seen, for example, when  species are not arranged "in a cloud, but in an arch. This indicates, that there are non-linear Relations between the axis, e.g. one assumption of Ordination is violated. This is also a concern in other analyis (PCA).

Kind regards Irene

Ordination can help to find structure in complicated data sets. By using various mathematical calculations, ordination techniques will identify similarity between species and samples. Results are then projected onto two dimensions in such a way that species and samples most similar to one another will be close together, and species and samples most dissimilar from one another will appear farther apart :)

Thanks all of you for this. Irene Zweimüller, this is really helpful.