-
MICROBIOME DATA ARE COMPOSITIONAL
Adam R. Rivers, Ph.D.September 2019 https://tinyecology.com
What this means and how to deal with it
Agricultural Research Service
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SEQUENCING IS A SAMPLING PROCESS• Sequencing samples n DNA
molecules
from a pool of n molecules. n
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EVERY TAXA(GENE) AFFECTS ALL OTHERS
• In quantitative metagenomics reads are assigned to taxa (or
genes).
• The total number of taxa and the reads assigned to each taxa
affect all other taxa.
Gloor et al. Microbiome Datasets Are Compositional
which must be filled. Returning to our tiger and ladybuganalogy,
the migration of ladybugs into an area containinga fixed number of
slots that are already filled must displaceeither tigers or
ladybugs from the occupied slots. This analogyextents, without
restriction, to any number of taxa, and to anyfixed capacity
instrument (Aitchison, 1986; Lovell et al., 2011;Friedman and Alm,
2012; Fernandes et al., 2013, 2014; Lovellet al., 2015; Mandal et
al., 2015; Gloor et al., 2016a,b; Gloor andReid, 2016; Tsilimigras
and Fodor, 2016). Thus, the total readcount observed in a HTS run
is a fixed-size, random sampleof the relative abundance of the
molecules in the underlyingecosystem. Moreover, the count can not
be related to the absolutenumber of molecules in the input sample
as shown in Figure 1.This is implicitly acknowledged when
microbiome datasets areconverted to relative abundance values, or
normalized counts,or are rarefied (McMurdie and Holmes, 2014; Weiss
et al., 2017)prior to analysis. Thus the number of reads obtained
is irrelevant,and contains only information on the precision of the
estimate(Fernandes et al., 2013). Data that are naturally described
asproportions or probabilities, or with a constant or
irrelevantsum, are referred to as compositional data. Compositional
datacontains information about the relationships between the
parts(Aitchison, 1986; Pawlowsky-Glahn et al., 2015).
Data about a microbiome collected by high throughputsequencing
are often examined under the assumption thatsequencing is, in some
way, counting the number of moleculesassociated with the bacteria
in the population, as illustrated bythe top barplot in Figure 1B.
We can see the difference betweencounts and compositions by
comparing the data for the actualcounts for three samples in the
top barplot with their proportionsin the bottom barplot. Note, that
samples 2 and 3 in Figure 1Bhave the same proportional abundances
even though they havedifferent absolute counts prior to sequencing.
The difference inapparent direction of change is shown in Figure 1C
and we canobserve that the relationship between absolute abundance
in theenvironment and the relative abundance after sequencing is
notpredictable.
2. PROBLEMS WITH CURRENT METHODSOF ANALYSIS
We will briefly outline the problems that arise
whencompositional data are examined using a
non-compositionalparadigm, stepping through the usual stages of
analysis shownin Figure 2. All these issues have been extensively
reviewedand debated in both the older and the more recent
literature infields as diverse as economics, geology and ecology.
Thus, ratherthan present an exhaustive explanation of the problems,
we willoutline the major issue and cite a few useful resources.
It is very difficult to collect exactly the same numberof
sequence reads for each sample. This can be because ofdifferences
in platform (e.g., MiSeq vs. HiSeq) or because oftechnical
difficulties in loading the same molar amounts of thesequencing
libraries on the instrument, or because of randomvariation. The
total number of counts observed (often referred toas read depth) is
a major confounder for distance or dissimilarity
FIGURE 1 | High-throughput sequencing data are compositional.
(A)
illustrates that the data observed after sequencing a set of
nucleic acids from a
bacterial population cannot inform on the absolute abundance of
molecules.
The number of counts in a high throughput sequencing (HTS)
dataset reflect
the proportion of counts per feature (OTU, gene, etc.) per
sample, multiplied by
the sequencing depth. Therefore, only the relative abundances
are available.
The bar plots in (B) show the difference between the count of
molecules and
the proportion of molecules for two features, A (red) and B
(gray) in three
samples. The top bar graphs show the total counts for three
samples, and the
height of the color illustrates the total count of the feature.
When the three
samples are sequenced we lose the absolute count information and
only have
relative abundances, proportions, or “normalized counts” as
shown in the
bottom bar graph. Note that features A and B in samples 2 and 3
appear with
the same relative abundances, even though the counts in the
environment are
different. The table below in (C) shows real and perceived
changes for each
sample if we transition from one sample to another.
calculations for multivariate ordinations derived from
thesedistances (McMurdie and Holmes, 2014). Initial attempts in
themicrobiome field used “rarefaction” or subsampling of the
readcounts of each sample to a common read depth to attempt
tocorrect this problem (Lozupone et al., 2011; Wong et al.,
2016).The use of subsampling has been questioned since it results
ina loss of information and precision (McMurdie and Holmes,2014),
and the practice of count normalization from the RNA-seq field has
been advocated instead. There are a number ofcount normalization
methods used and two, the trimmed meanof M values (TMM) (Robinson
and Oshlack, 2010), and themedian method (Anders and Huber, 2010)
are similar to a log-ratio transformations, but are less suitable
in highly asymmetricalor sparse datasets (Fernandes et al., 2013;
Gloor et al., 2016a).These transformations are further undesirable
since the numberof counts observed by the instrument, by design,
can not containany information on the actual number of molecules in
theenvironment, and because the investigator naturally
interpretsthe results as counts instead of log-ratios.
One of the first analysis steps in a traditional
analysis,following rarefaction or count normalization, is the
calculation ofa distance or dissimilarity (DD) matrix from the data
that is used
Frontiers in Microbiology | www.frontiersin.org 2 November 2017
| Volume 8 | Article 2224
Gloor et al. 2017
Example 1
-
EVERY TAXA(GENE) AFFECTS ALL OTHERS
• In quantitative metagenomics reads are assigned to taxa (or
genes).
• The total number of taxa and the reads assigned to each taxa
affect all other taxa.
Example 2
Morton et al. 2016
https://doi.org/10.3389/fmicb.2017.02224https://doi.org/10.1128/mSystems.00162-16.
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EARLY WAYS OF DEALING WITH COMPOSITIONS
Method Issues
Rarefaction loss of information and precision
RNASeq TMM and median ratio
Similar to CLR but bad for asymmetrical data and sparse data
RPKM largely abandoned since it corrects for the wrong thing
All the above Give outputs in “counts”, the wrong mindset
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NEGATIVE CORRELATION BIAS• We know that ratio data (including
data
normalized by a sum) suffer from negative correlation bias.
• Because a composition must sum to one, some creations must be
negative and some must be positive even if no such correlation
exists. 490 Prof. Karl Pearson.
exist correlation between u and v. Thus a real danger arises
when a statistical biologist attribntes the correlation between two
functions like uand vto organic relationship. The particular case
that iflikely to occur is when uand v are indices with the same
denominator for the correlation of indices seems at first sight a
very plausible measure of organic correlation.
The difficulty and dang’er which arise from the use of indices
was brought home to me recently in an endeavour to deal with a
consider able series of personal equation data. In this case it was
convenient to divide the errors made by three observers in
estimating a variable quantity by the actual value of the quantity.
As a result there appeared a high degree of correlation between
three series of abso lutely independent judgments. It was some time
before I realised that this correlation had nothing to do with the
manner of judging, but was a special case of the above principle
due to the use of indices.
A further illustration is of the following kind. Select three
num bers within certain ranges at random, say x, y, z, these will
be pair and pair uncorrelated. Form the proper fractions xjy and
zjy for each triplet, and correlation will be found between these
indices.
The application of this idea to biology seems of considerable
importance. For example, a quantity of bones are taken from an
ossuarium, and are put together in groups, which are asserted to be
those of individual skeletons. To test this a biologist takes the
triplet femur, tibia, humerus, and seeks the correlation between
the indices femur / humerus and tibia / humerus. He might
reasonably conclude that this correlation marked organic
relationship, and believe that the bones had really been put
together substantially in their individual grouping. As a matter of
fact, since the coefficients of variation for femur, tibia, and
humerus are approximately equal, there would be, as we shall see
later, a correlation of about 0'4 to 0'*> between these indices
had the bones been sorted absolutely at random. I term this a
spurious organic correlation, or simply a spurious correlation. I
understand by this phrase the amount of correlation which would
still exist between the indices, were the absolute lengths on which
they depend disti’ibuted at random.
It has hitherto been usual to measure the organic correlation of
the organs of shrimps, prawns, crabs, Ac., by the correlation of
indices in which the denominator represents the total body length
or total cara pace length. Now suppose a table formed of the
absolute lengths and the indices of, say, some thousand
individuals. Let an “ imp ” (allied to the Maxwellian demon)
redistribute the indices at random, they would then exhibit no
correlation; if the corresponding absolute lengths followed along
with the indices in the redistribution, they also would exhibit no
correlation. Now let us suppose the indices not to have been
calculated, but the imp to redistribute the abso-
Pearson, 1896
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CORRELATION EXAMPLE
Bacteria195011
Bacteria1B
879362
Bacteria2
62763
Bacteria3
236274
Bacteria4
1219595
Unidentified
1205361373771166881655192528910
19747965891046217575115306759020020110291602928417
7517998807477188167542191681212124802802416994
5420456493956034465749962164249099898595114189388
302106681620188674392966865704480262980378119099
20845431983084106192945143280248776245182224279220214416412829
Correlated 0.998Randomly sampled from log normal distribution
logmean = 10 (13 for unidentified) log SD=1
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CORRELATION EXAMPLECorrelated 0.998
Randomly sampled from log normal distribution logmean = 10 (13
for unidentified) log SD=1
Divide each sample by the sumBacteria10.00418
Bacteria1B
0.17
Bacteria2
0.00857
Bacteria3
0.00756
Bacteria4
0.182
Unidentified
0.01360.0420.02870.0570.0494
0.008690.1870.01430.005630.1720.008540.06120.02720.05520.0555
0.03310.01910.01020.006020.01120.02160.03710.006110.09660.0332
0.02380.1090.1310.01430.07440.01850.2780.2430.03930.0183
0.01330.1290.2760.02380.1440.06420.02450.007340.0130.0373
0.9170.3840.5610.9430.4170.8740.5570.6880.7390.806
-
CORRELATION EXAMPLE
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Bacteria1
Bacteria1B
Bacteria2
Bacteria3
Bacteria4
Unidentified
0.99
−0.04
0.04
0.28
−0.78
−0.03
0.1
0.28
−0.82
−0.18
−0.37
0.14
0.04
−0.52 −0.58
All samples Drop Unidentified
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Bacteria1
Bacteria1B
Bacteria2
Bacteria3
Bacteria4
0.95
−0.12
−0.53
−0.3
−0.05
−0.46
−0.42
−0.3
−0.27 −0.41
-
CORRELATION EXAMPLECorrelation of Aitchison composition Drop
Unidentified
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Bacteria1
Bacteria1B
Bacteria2
Bacteria3
Bacteria4
Unidentified
0.99
−0.04
0.04
0.28
−0.78
−0.03
0.1
0.28
−0.82
−0.18
−0.37
0.14
0.04
−0.52 −0.58−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Bacteria1
Bacteria1B
Bacteria2
Bacteria3
Bacteria4
0.99
−0.04
0.04
0.28
−0.03
0.1
0.28
−0.18
−0.37 0.04
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DISTANCE AND DISSIMILARITY METRICSTypical metrics• Unifrac•
Bray-Curtis• Jensen-Shannon
Bray-Curtis Aitchison (Correct metric)
Better metrics• Unifrac -> PhILR• Others -> Aitchison
Bacteria3
Bacteria1B
Bacteria1
Bacteria4
Unidentified
Bacteria2
Bacteria3
Bacteria1B
Bacteria1
Bacteria4
Unidentified
Bacteria2
Unidentified
Bacteria2
Bacteria3
Bacteria4
Bacteria1
Bacteria1B
Unidentified
Bacteria2
Bacteria3
Bacteria4
Bacteria1
Bacteria1B
https://doi.org/10.7554/eLife.21887
-
PCA ORDINATION ISSUES
−0.6 −0.4 −0.2 0.0 0.2 0.4
−0.6
−0.4
−0.2
0.0
0.2
0.4
Comp.1
Com
p.2
1
2
3
4
5
6
78
9
10
−0.6 −0.4 −0.2 0.0 0.2 0.4
−0.6
−0.4
−0.2
0.0
0.2
0.4
Bacteria1Bacteria1B
Bacteria2
Bacteria3
Bacteria4
Unidentified
−0.6 −0.4 −0.2 0.0 0.2 0.4
−0.6
−0.4
−0.2
0.0
0.2
0.4
Comp.1
Com
p.2
1
2
3
4
5
6
78
9
10
−3 −2 −1 0 1 2
−3−2
−10
12
Bacteria1Bacteria1B
Bacteria2
Bacteria3
Bacteria4
Unidentified
Untransformed Transformed
-
UNDERSTANDING COMPOSITIONS
-
SIMPLEX AS A NUMBER SPACE• The sum does not matter
• The components are a proportion of some whole
• The number space is Simplex
• Examples:• Composition of soil [silt, sand, clay]• NGS
Sequencing data• Time use surveys
Ternary soil plot
-
THE SIMPLEX NUMBER SPACE
Key arithmetic operations can be defined:• Closure
• Perturbation
• Powering
Key requirements for simplex operations• Sub-compositionally
coherent• Order invariant• Scale invariant
-
TRANSFORMATIONS FROM SIMPLEXThe simplex can be transformed into
real space using Log ratio transformations
Additive Log Ratio (ALR)
Centered Log ratio (CLR)
Isometric Log Ratio (ILR)
Where geometric mean is
Working in transformed space allows us to use many
existing statistical tools
-
ISOMETRIC LOG RATIOUseful because its isometric
or
DC to Tel Aviv is always 6400 km
log-ratio analysis algebraic-geometric structure C-coordinates
balances
circles and ellipses
-2
-1
0
1
2
3
4
-2 -1 0 1 2 3
in S3 coordinate representation
log-ratio analysis algebraic-geometric structure C-coordinates
balances
parallel lines
x2
x1
x3
n
-4
-2
0
2
4
-4 -2 0 2 4
in S3 coordinate representation
Useful because points are now independent
-
ISOMETRIC LOG RATIO
So what is Phi?Binary partitionsCLR X
-
ISOMETRIC LOG RATIO
So what is Phi?Binary partitions1 -1CLR X
-
ISOMETRIC LOG RATIO
So what is Phi?Binary partitions1 -1
1 -1
CLR X
-
ISOMETRIC LOG RATIO
So what is Phi?Binary partitions1 -1
1 -1
CLR X
-
ISOMETRIC LOG RATIO
So what is Phi?Binary partitions1 -1
1 -1
CLR X
Dot Product
ILR
-
ISOMETRIC LOG RATIO
20
40
60
80
100
20
40
60
80
100
20 40 60 80 100
Bacteria1BBacteria1
Bacteria2
Bacteria1B
Bacteria1 Bacteria2
-
GENERAL CODA SOFTWARE
Microbiome specific software covered later
CoDaPack• From the “Official”
CoDa group in Girona
• Compositions• Compositional• zCompositions• coda.base
Scikit bio • skbio.stats.composition
-
A COMPOSITIONAL WORKFLOW FOR METAGENOMICS
-
Normalization Distance Ordination Multivariate comparison
CorrelationDifferential abundance
Old Rarefaction DESeqBray-Curtis
UnifracPcoA
(abundance)perMANOVA
ANOSIMPearson
SpearmanEDGER DESeq
CompositionalCLR ALR ILR
Aitchisonphilr PCA (variance)
perMANOVA ANOSIM
SparCCSpiecEasi
propr ANCOM ALDEx2
THERE IS ANOTHER WAY
From Gloor 2017
-
WORKED EXAMPLEBacteria195011
Bacteria1B
879362
Bacteria2
62763
Bacteria3
236274
Bacteria4
1219595
Unidentified
1205361373771166881655192528910
19747965891046217575115306759020020110291602928417
7517998807477188167542191681212124802802416994
5420456493956034465749962164249099898595114189388
302106681620188674392966865704480262980378119099
20845431983084106192945143280248776245182224279220214416412829
Preprocessing1. Close the dataset (all reads)2. Create a
sub-composition
-
INPUTE ZEROS
So many reasons for a zero…1. Structural zeros, a real zero2.
Missing values3. Below the limit of detection
So many ways to handle zeros…1. pseudo-counts ( add one to
everything)2. Multiplicative replacement3. Mean value replacement4.
Expectation Maximization
It is often helpful to drop components (taxa) that appear in
-
PCA ORDINATION AND DISTANCEQiime 2 package DeicodeDeicode takes
a count matrix with zeros• Calculates CLR on nonzero values•
Calculates Aitchson distance• Performs robust PCA using
Singular
value decomposition
In RWith compositions package computecar using
“clr(acomp())”Distance using “dist, method=“aitchison” function
Compute pca using “pca” function
-
DIVERSITY INDICES AND CURVES
−0.6 −0.4 −0.2 0.0 0.2 0.4
−0.6
−0.4
−0.2
0.0
0.2
0.4
Comp.1
Com
p.2
1
2
3
4
5
6
78
9
10
−0.6 −0.4 −0.2 0.0 0.2 0.4
−0.6
−0.4
−0.2
0.0
0.2
0.4
Bacteria1Bacteria1B
Bacteria2
Bacteria3
Bacteria4
Unidentified
−0.6 −0.4 −0.2 0.0 0.2 0.4
−0.6
−0.4
−0.2
0.0
0.2
0.4
Comp.1
Com
p.2
1
2
3
4
5
6
78
9
10
−3 −2 −1 0 1 2
−3−2
−10
12
Bacteria1Bacteria1B
Bacteria2
Bacteria3
Bacteria4
Unidentified
-
DIVERSITY INDICES AND DISTANCEBray-Curtis Aitchison
Bacteria3
Bacteria1B
Bacteria1
Bacteria4
Unidentified
Bacteria2
Bacteria3
Bacteria1B
Bacteria1
Bacteria4
Unidentified
Bacteria2Unidentified
Bacteria2
Bacteria3
Bacteria4
Bacteria1
Bacteria1B
Unidentified
Bacteria2
Bacteria3
Bacteria4
Bacteria1
Bacteria1B
-
ANCOM (Python)• One of the first• Does pairwise tests in
CLR space• In Qiime 2
STATISTICAL INFERENCE METHODSALDEx2 (R)• Best general use•
Dirichlet used to
model variance • Walsh and KS test• effect sizes &
p-values
MirKat-Coda (R)• Kernel machine
regression• Identifies microbial
subsets that explain multivariate data
MixOmics• A suite of tools • Partial least squares
discriminate analysis
Gneiss• Balance trees
-
ANCOM (Python)• One of the first• Does pairwise tests in
CLR space• In Qiime 2
STATISTICAL INFERENCE METHODSALDEx2 (R)• Best general use•
Dirichlet used to
model variance • Walsh and KS test• effect sizes &
p-values
MirKat-Coda (R)• Kernel machine
regression• Identifies microbial
subsets that explain multivariate data
MixOmics• A suite of tools • Partial least squares
discriminate analysis
Gneiss• Balance trees
DIY!Do your own linear modeling on CLR
data
-
ALDEX2
ALDEx2
ylab="Difference")aldex.plot(x.all, type="MW", test="welch",
xlab="Dispersion",
ylab="Difference")
−2 0 2 4 6 8
05
1015
Log−ratio abundance
Diff
eren
ce
1 2 3 4
05
1015
DispersionD
iffer
ence
Figure 1: MA and Effect plots of ALDEx2 output
The left panel is an Bland-Altman or MA plot that shows the
relationship between abundance and Di�er-
ence. The right panel is an e�ect plot that shows the
relationship between Di�erence and Dispersion. In
both plots features that are not significant are in grey or
black. Features that are statistically significant are
in red. The Log-ratio abundance axis is the clr value for the
feature.
5 Using ALDEx2 modules
The modular approach exposes the underlying intermediate data so
that users can generatetheir own tests. The simple approach
outlined above just calls aldex.clr, aldex.ttest,aldex.effect in
turn and then merges the data into one object. We will show these
modulesin turn, and then examine additional modules.
5.1 The aldex.clr module
The workflow for the modular approach first generates random
instances of the centredlog-ratio transformed values. There are
three inputs: counts table, a vector of conditions, thenumber of
Monte-Carlo instances, a string indicating if iqlr, zero or all
feature are used as thedenominator is required, and level of
verbosity (TRUE or FALSE). We recommend 128 ormore mc.samples for
the t-test, 1000 for a rigorous e�ect size calculation, and at
least 16 forANOVA.
This operation is fast.
x
-
RESOURCESAitchison, J. (John), 2003. A concise guide to
compositional data analysis. Lecture notes. url:
http://www.compositionaldata.com/material/others/Ait2003_A_concise_guide_to_compositional_data_analysis.pdfAitchison,
J. (John), 2003. The statistical analysis of compositional data.
Blackburn Press.Calle, M.L., 2019. Statistical Analysis of
Metagenomics Data. Genomics Inform. 17, e6. doi:10.5808/
GI.2019.17.1.e6Fernandes, A.D., Vu, M.T.H.Q., Edward, L.-M.,
Macklaim, J.M., Gloor, G.B., 2018. A reproducible effect
size is more useful than an irreproducible hypothesis test to
analyze high throughput sequencing datasets.
Gloor, G.B., Macklaim, J.M., Pawlowsky-Glahn, V., Egozcue, J.J.,
2017. Microbiome Datasets Are Compositional: And This Is Not
Optional. Front. Microbiol. 8, 2224.
doi:10.3389/fmicb.2017.02224
Gloor, G.B., Reid, G., 2016. Compositional analysis: a valid
approach to analyze microbiome high-throughput sequencing data.
Can. J. Microbiol. 62, 692–703. doi:10.1139/cjm-2015-0821
Macklaim, J.M., Gloor, G.B., 2018. From RNA-seq to Biological
Inference: Using Compositional Data Analysis in
Meta-Transcriptomics. Humana Press, New York, NY, pp. 193–213.
doi:10.1007/978-1-4939-8728-3_13
Mandal, S., Van Treuren, W., White, R.A., Eggesbø, M., Knight,
R., Peddada, S.D., 2015. Analysis of composition of microbiomes: a
novel method for studying microbial composition. Microb. Ecol.
Health Dis. 26, 27663. doi:10.3402/mehd.v26.27663
Pawlowsky-Glahn, V., Buccianti, A., 2011. Compositional data
analysis : theory and applications. Wiley.Rivera-Pinto, J.,
Egozcue, J.J., Pawlowsky–Glahn, V., Paredes, R., Noguera-Julian,
M., Calle, M.L., 2017.
Balances: a new perspective for microbiome analysis. bioRxiv
219386. doi:10.1101/219386
MINI REVIEWpublished: 15 November 2017
doi: 10.3389/fmicb.2017.02224
Frontiers in Microbiology | www.frontiersin.org 1 November 2017
| Volume 8 | Article 2224
Edited by:
Jessica Galloway-Pena,
University of Texas MD Anderson
Cancer Center, United States
Reviewed by:
Ionas Erb,
Centre for Genomic Regulation, Spain
Jennifer Stearns,
McMaster University, Canada
*Correspondence:
Gregory B. Gloor
[email protected]
Specialty section:
This article was submitted to
Systems Microbiology,
a section of the journal
Frontiers in Microbiology
Received: 10 July 2017
Accepted: 30 October 2017
Published: 15 November 2017
Citation:
Gloor GB, Macklaim JM,
Pawlowsky-Glahn V and Egozcue JJ
(2017) Microbiome Datasets Are
Compositional: And This Is Not
Optional. Front. Microbiol. 8:2224.
doi: 10.3389/fmicb.2017.02224
Microbiome Datasets AreCompositional: And This Is
NotOptionalGregory B. Gloor 1*, Jean M. Macklaim1, Vera
Pawlowsky-Glahn2 and Juan J. Egozcue3
1 Department of Biochemistry, University of Western Ontario,
London, ON, Canada, 2 Departments of Computer Science,
Applied Mathematics, and Statistics, Universitat de Girona,
Girona, Spain, 3 Department of Applied Mathematics, Universitat
Politècnica de Catalunya, Barcelona, Spain
Datasets collected by high-throughput sequencing (HTS) of 16S
rRNA gene amplimers,
metagenomes or metatranscriptomes are commonplace and being used
to study human
disease states, ecological differences between sites, and the
built environment. There is
increasing awareness that microbiome datasets generated by HTS
are compositional
because they have an arbitrary total imposed by the instrument.
However, many
investigators are either unaware of this or assume specific
properties of the compositional
data. The purpose of this review is to alert investigators to
the dangers inherent in
ignoring the compositional nature of the data, and point out
that HTS datasets derived
from microbiome studies can and should be treated as
compositions at all stages of
analysis. We briefly introduce compositional data, illustrate
the pathologies that occur
when compositional data are analyzed inappropriately, and
finally give guidance and point
to resources and examples for the analysis of microbiome
datasets using compositional
data analysis.
Keywords: microbiota, compositional data, high-throughput
sequencing, correlation, Bayesian estimation, count
normalization, relative abundance
1. INTRODUCTION
The collection and analysis of microbiome datasets presents many
challenges in the study design,sample collection, storage, and
sequencing phases, and these have been well reviewed (Robinsonet
al., 2016). Many methods for the analysis of microbiome datasets
assume that sequencingdata are equivalent to ecological data where
the counts of reads assigned to organisms are oftennormalized to a
constant area or volume. Methods applied include count-based
strategies such asBray-Curtis dissimilarity, zero-inflated
Gaussianmodels and negative binomial models (McMurdieand Holmes,
2014; Weiss et al., 2017).
In an ecological study it is possible for many different species
to co-exist, and their absoluteabundance may be important. For
example, in an area containing only tigers, it is importantto know
if the population size is sufficient to maintain needed genetic
diversity for long-termsurvival (Shaffer, 1981). However, the
abundance of one species may not influence the abundanceof another;
the area may contain both tigers and ladybugs, and the migration of
several ladybugsinto the area would not be expected to affect the
number of tigers.
The assumption of true independence can not hold in
high-throughput sequencing (HTS)experiments because the sequencing
instruments can deliver reads only up to the capacity of
theinstrument. Thus, it is proper to think of these instruments as
containing a fixed number of slots
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THANKS
CodaCourse Staff University of Girona (UdG)
Agricultural Research Service
