The are a number (actually not a number but infinity, according to the concept of True Diversity, see below) of diversity indexes. The most basic is the richness, which correspond to the total number of OTUs on each sample in your case. For that index of course you don't need to normalize, because the count of each OTU for each sample is not taken into account. But other diversity metrics normally considers the eveness for the categories (OTUs in your case) and that will be affected if a proper normalization is not applied. Diversity indexes in this line are Shannon or Simpson indexes, although all these can be seen as particular cases of the True Diversity. See this article if you are interested:

"Tuomisto, Hanna. "A consistent terminology for quantifying species diversity? Yes, it does exist." Oecologia 164.4 (2010): 853-860."

Anyway.. the question is how to normalize. The most basic way is dividing each count for each OTU by the total number of sequences in each sample. However, consider that the 16S gene might have multiple copies on some genomes, and so some authors do a normalization that consider this fact, in order to not count a single species multiple times just because it has multiple 16S gene copies in its genome. This is difficult to accomplish in metagenomics because you don't normally have access to all the genomes present in the environment, so you don't have information for this normalization. In this case, these authors detect the closest sequenced genome sequence by means of a BLAST for example, and then assume that the environmental organisms will share that number of copies of 16S and compute a normalization according to that number. On the other hand, other authors prefer to sequence other genes which have been observed that are always single copy on every sequenced genome so far (typically some ribosomal proteins like L2 if I remember well). 

But you already have 16S sequences, and they are probably environmental, so I recommend you to normalize just by the number of total sequences on each sample, as a first approach, but be aware of that issue of the multiple copies, and other possible issues like the heteroscedasticity of the data.

EDITED: please take a look at the entire discussion here, which has been interesting thanks to all that answered. 

I hope that helps. Best regards.

Article A consistent terminology for quantifying species diversity? ...

You could created a PCA using the OTU counts per sample and plot all the different axis against the sampling depth (thus total sequences per samples). If you find a significant correlation, sampling depth will affect your conclusions to some degree. The analysis will tell you how much. If the effect is strong, you might want to consider one of the many methods to correct for unequal sampling depth.

I don't actually agree that it would be such a good idea to just divide your OTU counts by number of sequences as suggested by Salvador. There is some more reasoning about this approach written down by McMurdie in his Waste Not Want Not article (he supports it). However this all kind of assumes that the reads are at least somewhat homogeneously spread, which is most often not the case and as you have said it's not the case for you. 

Samples that have a very low coverage will get multiplied by significantly larger coefficient (assuming you'd be dividing by sequence count and multiplying by mean sequence count which is along the lines of what McMurdie suggests). This will definitely influence any richness measure (especially Chao or similar ones who count singletons - your singletons will be inflated by that coefficient) and I think that also Shannon will be influenced since you're working with smaller number of representatives in that set due to it being under sampled (unless your community is super simple and you know you've definitely sampled it well even in your low coverage samples, but I'll take a wild guess that it's not the case).

It also makes NMDS and probably all other ordinations behave really oddly. That's just something I've tried. I don't know why.

From my experience I cannot recommend any such procedure. I find a good old sub-setting to even depth and eventually kicking out samples that really didn't work well much more consistent and overall very understandable in it's effect.

Adam, although you are right in many things you said, you are not providing any solution to the proposed problem, because it's normal to have different sample sizes in these procedures -- you might end up kicking out all of your samples from the analysis. I started by recognizing that normalization is not that simple as dividing the OTUs numbers by the total sample size for some reasons -- you are giving yet another ones. Also, although I would not recommend to use the Chao1 index for richness, this is calculated as follows:

Chao1 = observed_richness + singletons2/( 2 * multitons)

where:

observed_richness: total number of different OTUs, singletons: number of OTUs with a single representative (or sequence in this case), multitons: number of OTUs with two or more representatives.

As can be seen, the singletons have, in effect, a quadratic effect here, but singletons will probably occur only when some sample sizes would be really small compared to the others, but this is not normally the case when sequencing with the same technology. It should be rare the case that for example one sample has an order of magnitude size higher than other (assuming same sequencing technology).

I really recommend to check the true diversity concept (see my first message) here instead, because in that concept there exists a parameter to control what the diversity will be oriented to, whether to the more abundant OTUs or to the more rare ones, and this can be helpful to control the behaviour of the index when in a different sample size scenario. 

Anyway, dividing by the total sample size is far from a perfect normalization, but it's clearly the most simple and with less assumptions. One should really start from there and then explore possibilities based on these first exploratory results.

Best regards.

Hi Salvator, 

Please do read my answer properly as you will find out that I have indeed offered a solution. That is sunsetting to even depth (also known as retraction). It's a conservative approach, but it's very robust in my experience. 

Also, in my experience, and the may vary from yours, singletons and very rare OTUs actually constitute a significant proportion of any sample, not just the low coverage ones. After all vast number of bacterial communities display a log decay curve of ranked abundance. Therefore singletons are playing a major role in most communities. 

And yes, alas order of magnitude difference in coverage is actually plausible. It's not a good result, but I've worked with multiple datasets where that was the case. Then of course one needs to consider removing the worst samples if possible, but that's up to one's consideration. 

I agree with you that it's a good idea to try different approaches, but it's essential to really scrutinize the results. And I'm speaking from my own experience because I've started with the McMurdie's method and it took me quite a long time to realise that it introduced a major bias to my analysis. 

Best regards,

Adam

I guess you mean by "subsetting to even depth" to randomly re-sampling your samples to the size of the smallest sample, right? I have seen this method applied in some works, however, this can produce even more singletons (when using the chao1 index) in the re-sampled samples that were reduced in size because of the re-sampling process... (see above) 

Again, before doing any of these aproaches you first want to quantify how large the problem is. We have no idea about what environment and how diverse the samples are. Perhaps they are very simple systems. Thus, "measure twice, cut once". 

Only then you should look into methods. to fix the problem.

Hi!, Thanks for the answers and discussion. Maybe some information will be useful.

My samples are coming from saline lakes. I take five sediments and try to compare diversity among a gradient. There is a big difference between the number of reads (5.000 to 170.000). I calculated diversity indexes with crude data and it shows no big difference in Shannon and Simpson indexes. Furthermore, the MDS shows a very coherent distribution. If I cut, resample or normalize it varies a lot. So, what do you think, would be a good method?

Thanks again.

Hey Alex,

I agree with Adam that rarefying is conservative but robust. The thing you need to pay attention is when you use this method, you need to get rid of the low depth samples, which means you need to abandon some of the samples if your sample sizes varied significantly. What I suggest you to do is to draw a rarefaction curve (richness vs. sequence number) to see at which depth your samples reach maximum richness that is your sample size using to rarefy. For example, if most samples reach maximum at 8,000, then you need to abandon all the samples under 8,000 sequences.

On the other hand, if you will lose lots of samples. Then you need to consider the newest methods, such as DESeq2 and MetagenomeSeq, which can be done in either QIIME or R. I suggest you to read this paper. Waste not, want not: why rarefying microbiome data is inadmissible.

Best,

Haito

I can't understand why people here is recommending rarefying while at the same time suggesting an article that state in its very title that that procedure is inadmissible. That article in fact was referenced previously here by Adam Šťovíček in his first answer. The complete reference is:

McMurdie, Paul J., and Susan Holmes. "Waste not, want not: why rarefying microbiome data is inadmissible." PLoS computational biology 10.4 (2014): e1003531.

And indeed it's a must-read for everyone working in microbial ecology. Here the authors, demonstrate that rarefying (subsetting samples to even size, as previously called here) is the worst option (they regard it as 'inadmissible'!) since it requires loss of potentially valuable information in the analyses (loss of statistical power). However, normalization by sample size (use of proportions), only has the drawback of not addressing heteroscedasticity, which is the differential dispersion or variance that the counted features (e.g. species) may display across the samples. This condition is normally found in RNA-seq data, because gene expression is a highly dynamical process -- way more than the dynamics of microbial communities, and some genes can vary a lot their expression patterns while others can simply not. Thus, it is unclear that the presence of species can have such characteristic in every experiment. So, for starting with something simple, or exploratory, I still recommend proportions (dividing counts by sample size) rather than rarefied counts (one may ask why the authors rather did not entitle the article ...normalize by sample size is inadmissible). Then, of course, if one suspects the data may have the heteroscedasticity problem, the statistical solutions given in that article must be considered.

EDITED: so much controversy still exists for this normalization process... a more recent article lend support to rarefying in some cases, and I am updating this here because I've being suggesting naive proportions instead. The article also suggests another method called ANCOM. In summary, it does not exists a single best normalization method, and exploring all the possibilities is currently the best way to go.

Weiss, Sophie, et al. "Normalization and microbial differential abundance strategies depend upon data characteristics." Microbiome 5.1 (2017): 27.

Article Waste Not, Want Not: Why Rarefying Microbiome Data Is Inadmissible

Article Normalization and microbial differential abundance strategie...