Mantel test

[Laetitia GE Wilkins]

Hi!

I have a very general question. I am wondering how many samples you need to get a reliable Mantel test statistic using the script 'compare_distance_matrices.py'. I have a sample of 10 samples that are in the same geographic region. I wanted to use the Mantel test statistic to investigate if there is an IBD pattern in my data. I fear though that 10 samples are not enough.

Thanks.

Laetitia

[Jai Ram Rideout]

Hi Laetitia,

Unfortunately, I don't have a decisive answer. The number of samples that you'll need depends on the effect size (strength of the relationship) and your significance level (alpha), which varies on a per-study basis.

The Mantel test has been criticized for having low statistical power [1,2], and having a small number of samples may only aggravate this problem (generally, having a smaller number of samples means having lower statistical power). However, I can't really say whether 10 samples will be enough to detect an effect or not for your particular study.

We've been trying out the Mantel test on a couple of microbial ecology datasets [3,4]. In the first study we are looking at soil pH, and in the second study we're analyzing the depth in hypersaline microbial mats. One of the things we've been investigating is the effect that sample size has on the Mantel r statistic and p-value. For these two studies, there is a pretty large effect size (strong positive correlation) between microbial community beta-diversity distances (e.g., UniFrac, Bray-Curtis, etc.) and the variables of interest (pH, mat depth). Even at 10 samples, the Mantel r statistic stays relatively high (e.g., around 0.7-0.8). The p-values are also quite low (p=0.001 at 999 permutations). Thus, it seems that for these two studies, the Mantel test is still detecting the gradients, even when subsampled down to 10 samples.

You might try out the Mantel test, as well as look at your samples in ordination space (e.g., PCoA, coloring them by the variable of interest) to get a better sense of what sort of effect might be there. Additionally, you might consider trying out Procrustes analysis on your data:

http://qiime.org/tutorials/procrustes_analysis.html

Hope this helps,

Jai

1. http://www.webpages.uidaho.edu/~lukeh/pdf/HarmonGlor_2010_Evolution.pdf

2. http://biol09.biol.umontreal.ca/numecol/Reprints/Partial_Mantel_paper.pdf

3. Lauber, Christian L et al. "Pyrosequencing-based assessment of soil pH as a predictor of soil bacterial community structure at the continental scale." Applied and environmental microbiology 75.15 (2009): 5111-5120.

4. Harris, J Kirk et al. "Phylogenetic stratigraphy in the Guerrero Negro hypersaline microbial mat." The ISME journal (2012).

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[Laetitia GE Wilkins]

Dear Jai,

thank you very much. This was what I expected. I am playing around with the Mantel test and PCoA now to get a better feeling for the effect size. I did not fully understand how the Procrustes analysis would be useful to find out more about IBD in my data.

Laetitia

[Jai Ram Rideout]

Hi Laetitia,

Procrustes analysis can be useful when comparing distance matrices, such as a beta diversity distance matrix (e.g., UniFrac distance matrix) to some other distance matrix (e.g., geographic distances). These distance matrices can be run through an ordination method (e.g., PCoA) and then compared using Procrustes analysis.

Procrustes can be useful because it allows you to see whether different types of measurements that are taken from the same set of samples yield similar conclusions. In the Procrustes tutorial I linked to, the distance matrices each come from a different sequencing technology (454 vs Illumina), but you could also compare distance matrices derived using different beta diversity metrics, or even compare 16S to ITS, 16S to metagenomic data, etc.. It may not be a good fit for your particular study, but I thought it was worth mentioning since you're interested in comparing two or more distance matrices (via the Mantel test); Procrustes can also be used to this end.

Hope this helps,

Jai

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