I would not say that PCoA is the preferred ordination technique in microbial ecology. nMDS is also widely use and I would think the ratio is in favour of nMDS, and as you said there is other methods used sometimes with different name but doing the same thing.

 But I agree that PCoA increased in popularity over the last few years. In my point of view, the main reasons why the use of PCoA is increasing, mainly for OTU for next generation sequencing, is because of 2 reasons:

- QIIME use PCoA and made it available to people working on OTU

- couple big research group (subsequently influential !?) in microbial ecology started to use routinely PCoA in their articles, making PCoA more "fashionable".

Saying that, you could prefer PCoA than other methods for good reason, such as similar concept than statistical analysis you perform in parallel. But I think if you could map who use what, we will see that some country, labs, or univ are more incline to use specific tools than others not necessarily based on objective reasons, but more historical/culture in the univ, and also program related. And this last point come back to the first reason I mentioned, the software you use, or have access to, or know how to use may explain a good part of PCoA extension.

I am sure other people will have a different point of view, but this is what I think. Hope this will start the debate.

Besides the QIIME which is very popular in studies of microbial ecology, another extremely popular tool for those working with metagenome is the mg-rast which also uses PCoA.

Thanks for the thoughts!

So far I have gathered that:

1. NMDS is widely used in microbial ecology, like it is in plant ecology

2. The popularity of PCoA is partly driven by familiarity, partly by inclusion in widely used tools such as QIIME and mg-rast, and partly by what famous labs are doing.

3. PCoA might be the right tool for the job

I have noticed the "culture effect" too, where one set of tools is standard in one institution or region but not in others. This seems to be driven by strong personalities, or historical precedence.

I guess what I really want to know, perhaps from someone that prefers using PCoA over NMDS is what exactly do you prefer? Since the answer always depends on the data, I'll supply a hypothetical scenario: I collect soil from 50 sites on a complex environmental gradient, used high throughput sequencing to obtain abundance data on all OTUs present. Now I want to link distance in the community matrix back to environmental gradients. I imagine there would be 1000's of OTUs in the community matrix.

Context: I teach NMDS in a data analysis graduate course designed for ecologists. I currently do not cover PCoA, due to lack of familiarity (and worries about horseshoe effects), but would like to figure out if it is something that I should make time to cover. If PCoA is going to persist in ecology for good reason, that would be something I should cover to stay current.

Thanks!

In your example I would go for nMDS because I consider that it is better than PCoA to show gradients in data. But I will probably try multiple methods to visualise my data if I consider the visualisation not good. Sometimes, trying different methods that you think might work is useful, because you do not know your results in advance, “only” the design of your experiment and measurement you did. So sometimes you may think one method will work, but because of the nature of your results (often, or most of the times in ecology (?) you will not fully expect the outcome of your results), another will be better.

nMDS and PCoA both work with any type of distance (not like PCA), so PCoA is not affected by the presence of zero. However, both method work differently, and PCoA try to explain most of the variance of your data and use linear mapping (like PCA), while nMDS use ranks distance and a non-linear mapping approach.

I think it is worth teaching to your student both because they behave in a different way and both are likely to be useful in different situation. And as a conclusion, I always insist on the fact those methods are plots of your samples, and even if they give information on your results, you lose information with the mapping and only visualise in 2D, you need to couple those methods with statistical analysis…

Finally, I think there is all the information you need about PCoA, nMDS and other methods in the article from Ramette (2007). In a way, it is also a time capsule this article because it dates from 2007, and quantify the use of the different methods and show how PCA was the main method (for bad reason as it do not take into consideration the presence of zero).

A. Ramette (2007) Multivariate analyses in microbial ecology, FEMS Microbiology Ecology, 62, 142-160

What if the stress level of nMDS exceeds 0.2？Is that when we should call PCoA? Besides nMDS and PCoA, I also like DCA. 

If the stress value is above 0.2, it means that your data are not well explained in 2D. The 3D view would decrease the 2D stress, indicating that you have complex results (not just explain in 2D). And if the 3D do not show a substantial decrease in the stress value, trying another method is a good option. Your logic is good.

I really appreciate this discussion on NMDS and PCoA. I think Aimeric Blaud gave already a couple of good arguments to the topic. So as a conclusion I would state: always use several ordination metrics or visualization tools on your data, always look on variances explained in PCoA and stress values in NMDS, evaluate your data not only in a 2D, but also 3D ordination and finally support your interpretations with additional statistics...

Jumping in on the conversation quite late - I've been working on Next Generation Sequencing data on the bacterial microbiome of plants. My first dataset came from one plant species and the second from two different plant species. In the first dataset NMDS worked very well however I could not get a clean NMDS plot which was giving me stress values of nearly zero. I do, however, get a clean PCoA plot from the second data set. From reading the discussion it sounds like this discrepancy is potentially due to the second data set having a higher beta diversity and/or the presence of 0 distances. Do you think that this is the most likely reason for not being able to get an NMDS plot from my second dataset?