A paper entitled “Should the Mantel test
be used in spatial analysis?” written by Pierre Legendre, Marie-Josée Fortin
and Daniel Borcard was published recently in Methods in
Ecology and Evolution (in press version here). It may be necessary to remind you that Mantel test has been a trend in
several publications of ecology and genetics, and specifically in microbial
ecology, is my main interest.
Most publications use the Mantel
and partial Mantel tests to detect spatial structure in communities and to
control spatial correlation between two or three data sets. However, as the
authors reported, “this is an incorrect use of that test”. When I read this sentence (in the first topic of
abstract) I thought, “Oh no! That is exactly what I did in my dissertation (to
acquire my master’s degree)”. However, I was not alone in this mistake. I read
several papers during my masters which used the Mantel test with same propose
(Figure 1).
 |
Figure 1. Comparative
analysis between a pair-wise community dissimilarity matrix and pair-wise
spatial, temporal or environmental distances. Mantel test has been used with
these types of data.
|
What is exactly problem of using Mantel test with such intent?
Mantel test was designed to relate spatial and temporal
distance matrices (Mantel, 1967). After that, the test was adapted to be
used as a nonparametric analysis between two dissimilarity matrices and with
time, after many steps, as a spatial analysis in ecology and genetics (for more details see the Introduction of Legendre et
al., 2015). The big
problem is that the Mantel test should be use in questions involving
dissimilarity matrices, and not questions that input the data as a “raw data
table” (e.g., geographic coordinates).
When I finished reading the papers, decided do a
little analysis in microbial ecology literature about that. I did a research on Google Scholar for papers
published since 2014 using "microbial ecology" AND "mantel"
as keywords in any part of paper. I found 487 papers. To refine more my search,
I did the same search in PubMed database and I found 10 papers.
I analyzed these 10 papers and found the following results.
Eight papers used the Mantel test to evaluate the correlation between
ecological dissimilarity matrix (e.g.,
Bray-Curtis dissimilarity calculated by an OTU data table) and geographic
matrix or environmental data (e.g.,
pH, temperature, vegetation types, etc.). This approach is incorrect because they
used the R2M of Mantel test as R2 obtained by
Pearson correlation. Legendre and co-authors devoted a section of their paper
to explain why these two metrics differ, which is mainly by your assumption of
what is a null hypothesis. As you can read in this citation:
“The Mantel test H0
is the absence of relationship between values in two dissimilarity matrices,
not the independence between two random variables or data tables.”
Legendre et al., (2015) explained several other
problems in use Mantel test with this type of data, but I will not give you
spoilers of the paper. They also propose that studies describing spatial
structure should use the distance-based Moran’s eigenvector map (dbMEM, Borcard & Legendre, 2002). This approach has been used
extensively in metacommunity (Heino et al., 2015) studies and we, microbial
ecologists, must begin focus on this method in our next studies.
For other opinions read the
post of Rob Denton in the collaborative blog “The Molecular Ecologist”.
References:
Borcard, D., & P. Legendre, 2002. All-scale spatial analysis of
ecological data by means of principal coordinates of neighbour matrices.
Ecological Modelling 153: 51–68.
Heino, J., A. S. Melo, T. Siqueira, J. Soininen, S. Valanko,
& L. M. Bini, 2015. Metacommunity organisation, spatial extent and
dispersal in aquatic systems: patterns, processes and prospects. Freshwater
Biology 60: 845–869, http://doi.wiley.com/10.1111/fwb.12533.
Legendre, P., M.-J. Fortin, & D. Borcard, 2015. Should
the Mantel test be used in spatial analysis?. Methods in Ecology and Evolution
n/a – n/a, http://doi.wiley.com/10.1111/2041-210X.12425.
Mantel, N., 1967. The detection of disease clustering and a
generalized regression approach. Cancer research 27: 209–220,
http://www.ncbi.nlm.nih.gov/pubmed/6018555.
