NetCoMi (Network Construction and Comparison for Microbiome Data) provides functionality for constructing, analyzing, and comparing networks suitable for the application on microbial compositional data. The R package implements the workflow proposed in
Stefanie Peschel, Christian L Müller, Erika von Mutius, Anne-Laure Boulesteix, Martin Depner (2020). NetCoMi: network construction and comparison for microbiome data in R. Briefings in Bioinformatics, bbaa290. https://doi.org/10.1093/bib/bbaa290.
NetCoMi allows its users to construct, analyze, and compare microbial association or dissimilarity networks in a fast and reproducible manner. Starting with a read count matrix originating from a sequencing process, the pipeline includes a wide range of existing methods for treating zeros in the data, normalization, computing microbial associations or dissimilarities, and sparsifying the resulting association/ dissimilarity matrix. These methods can be combined in a modular fashion to generate microbial networks. NetCoMi can either be used for constructing, analyzing and visualizing a single network, or for comparing two networks in a graphical as well as a quantitative manner, including statistical tests. The package furthermore offers functionality for constructing differential networks, where only differentially associated taxa are connected.
Exemplary network comparison using soil microbiome data (‘soilrep’ data from phyloseq package). Microbial associations are compared between the two experimantal settings ‘warming’ and ‘non-warming’ using the same layout in both groups.
Here is an overview of methods available for network construction, together with some information on their implementation in R:
Association measures:
- Pearson coefficient
(
cor()fromstatspackage) - Spearman coefficient
(
cor()fromstatspackage) - Biweight Midcorrelation
bicor()fromWGCNApackage - SparCC
(
sparcc()fromSpiecEasipackage) - CCLasso (R code on GitHub)
- CCREPE
(
ccrepepackage) - SpiecEasi (
SpiecEasipackage) - SPRING (
SPRINGpackage) - gCoda (R code on GitHub)
- propr
(
proprpackage)
Dissimilarity measures:
- Euclidean distance
(
vegdist()fromveganpackage) - Bray-Curtis dissimilarity
(
vegdist()fromveganpackage) - Kullback-Leibler divergence (KLD)
(
KLD()fromLaplacesDemonpackage) - Jeffrey divergence (own code using
KLD()fromLaplacesDemonpackage) - Jensen-Shannon divergence (own code using
KLD()fromLaplacesDemonpackage) - Compositional KLD (own implementation following [Martín-Fernández et al., 1999])
- Aitchison distance
(
vegdist()andclr()fromSpiecEasipackage)
Methods for zero replacement:
- Adding a predefined pseudo count
- Multiplicative replacement
(
multReplfromzCompositionspackage) - Modified EM alr-algorithm
(
lrEMfromzCompositionspackage) - Bayesian-multiplicative replacement
(
cmultReplfromzCompositionspackage)
Normalization methods:
- Total Sum Scaling (TSS) (own implementation)
- Cumulative Sum Scaling (CSS) (
cumNormMatfrommetagenomeSeqpackage) - Common Sum Scaling (COM) (own implementation)
- Rarefying (
rrarefyfromveganpackage) - Variance Stabilizing Transformation (VST)
(
varianceStabilizingTransformationfromDESeq2package) - Centered log-ratio (clr) transformation
(
clr()fromSpiecEasipackage))
TSS, CSS, COM, VST, and the clr transformation are described in [Badri et al., 2020].
# Required packages
install.packages("devtools")
install.packages("BiocManager")
# Install NetCoMi
devtools::install_github("stefpeschel/NetCoMi",
dependencies = c("Depends", "Imports", "LinkingTo"),
repos = c("https://cloud.r-project.org/",
BiocManager::repositories()))If there are any errors during installation, please install the missing dependencies manually.
In particular the automatic installation of
SPRING and
SpiecEasi (only available on
GitHub) does sometimes not work. These packages can be installed as
follows:
devtools::install_github("GraceYoon/SPRING")
devtools::install_github("zdk123/SpiecEasi")Packages that are optionally required in certain settings are not installed together with NetCoMi. These can be installed automatically using:
installNetCoMiPacks()
# Please check:
?installNetCoMiPacks()If not installed via installNetCoMiPacks(), the required package is
installed by the respective NetCoMi function when needed.
Thanks to @daydream-boost, NetCoMi can also be installed from conda bioconda channel with
# You can install an individual environment firstly with
# conda create -n NetCoMi
# conda activate NetCoMi
conda install -c bioconda -c conda-forge r-netcomiEveryone who wants to use new features not included in any releases is invited to install NetCoMi’s development version:
devtools::install_github("stefpeschel/NetCoMi",
ref = "develop",
dependencies = c("Depends", "Imports", "LinkingTo"),
repos = c("https://cloud.r-project.org/",
BiocManager::repositories()))Please check the NEWS document for features implemented on develop branch.
We use the American Gut data from
SpiecEasi package to look at
some examples of how NetCoMi is applied. NetCoMi’s main functions are
netConstruct() for network construction, netAnalyze() for network
analysis, and netCompare() for network comparison. As you will see in
the following, these three functions must be executed in the
aforementioned order. A further function is diffnet() for constructing
a differential association network. diffnet() must be applied to the
object returned by netConstruct().
First of all, we load NetCoMi and the data from American Gut Project
(provided by SpiecEasi, which
is automatically loaded together with NetCoMi).
library(NetCoMi)
data("amgut1.filt")
data("amgut2.filt.phy")Network construction and analysis
We firstly construct a single association network using SPRING for estimating associations (conditional dependence) between OTUs.
The data are filtered within netConstruct() as follows:
- Only samples with a total number of reads of at least 1000 are
included (argument
filtSamp). - Only the 50 taxa with highest frequency are included (argument
filtTax).
measure defines the association or dissimilarity measure, which is
"spring" in our case. Additional arguments are passed to SPRING()
via measurePar. nlambda and rep.num are set to 10 for a decreased
execution time, but should be higher for real data.
Normalization as well as zero handling is performed internally in
SPRING(). Hence, we set normMethod and zeroMethod to "none".
We furthermore set sparsMethod to "none" because SPRING returns a
sparse network where no additional sparsification step is necessary.
We use the “signed” method for transforming associations into
dissimilarities (argument dissFunc). In doing so, strongly negatively
associated taxa have a high dissimilarity and, in turn, a low
similarity, which corresponds to edge weights in the network plot.
The verbose argument is set to 3 so that all messages generated by
netConstruct() as well as messages of external functions are printed.
net_single <- netConstruct(amgut1.filt,
filtTax = "highestFreq",
filtTaxPar = list(highestFreq = 50),
filtSamp = "totalReads",
filtSampPar = list(totalReads = 1000),
measure = "spring",
measurePar = list(nlambda=10,
rep.num=10),
normMethod = "none",
zeroMethod = "none",
sparsMethod = "none",
dissFunc = "signed",
verbose = 3,
seed = 123456)Note: The fast version of latent correlation computation (for which
SPRING uses the mixedCCA
package) is available again, but so far only on GitHub. To use the
multilinear approximation method already, please install mixedCCA from
GitHub (devtools::install_github("irinagain/mixedCCA")) and set the
SPRING argument Rmethod to “approx”:
measurePar = list(Rmethod = "approx", ...). Note that netConstruct()
will throw a warning in the current NetCoMi version. Using the
multilinear approximation considerably decreases execution time.
Analyzing the constructed network
NetCoMi’s netAnalyze() function is used for analyzing the constructed
network(s).
Here, centrLCC is set to TRUE meaning that centralities are
calculated only for nodes in the largest connected component (LCC).
Clusters are identified using greedy modularity optimization (by
cluster_fast_greedy() from igraph package).
Hubs are nodes with an eigenvector centrality value above the empirical
95% quantile of all eigenvector centralities in the network (argument
hubPar).
weightDeg and normDeg are set to FALSE so that the degree of a
node is simply defined as number of nodes that are adjacent to the node.
props_single <- netAnalyze(net_single,
centrLCC = TRUE,
clustMethod = "cluster_fast_greedy",
hubPar = "eigenvector",
weightDeg = FALSE, normDeg = FALSE)
#?summary.microNetProps
summary(props_single, numbNodes = 5L)##
## Component sizes
## ```````````````
## size: 48 1
## #: 1 2
## ______________________________
## Global network properties
## `````````````````````````
## Largest connected component (LCC):
##
## Relative LCC size 0.96000
## Clustering coefficient 0.33595
## Modularity 0.53407
## Positive edge percentage 88.34951
## Edge density 0.09131
## Natural connectivity 0.02856
## Vertex connectivity 1.00000
## Edge connectivity 1.00000
## Average dissimilarity* 0.97035
## Average path length** 2.36877
##
## Whole network:
##
## Number of components 3.00000
## Clustering coefficient 0.33595
## Modularity 0.53407
## Positive edge percentage 88.34951
## Edge density 0.08408
## Natural connectivity 0.02714
##
## *Dissimilarity = 1 - edge weight
## **Path length: Units with average dissimilarity
##
## ______________________________
## Clusters
## - In the whole network
## - Algorithm: cluster_fast_greedy
## ````````````````````````````````
##
## name: 0 1 2 3 4 5
## #: 2 12 17 10 5 4
##
## ______________________________
## Hubs
## - In alphabetical/numerical order
## - Based on empirical quantiles of centralities
## ```````````````````````````````````````````````
## 190597
## 288134
## 311477
##
## ______________________________
## Centrality measures
## - In decreasing order
## - Centrality of disconnected components is zero
## ````````````````````````````````````````````````
## Degree (unnormalized):
##
## 288134 10
## 190597 9
## 311477 9
## 188236 8
## 199487 8
##
## Betweenness centrality (normalized):
##
## 302160 0.31360
## 268332 0.24144
## 259569 0.23404
## 470973 0.21462
## 119010 0.19704
##
## Closeness centrality (normalized):
##
## 288134 0.68431
## 311477 0.68417
## 199487 0.68108
## 302160 0.67528
## 188236 0.66867
##
## Eigenvector centrality (normalized):
##
## 288134 1.00000
## 311477 0.94406
## 190597 0.90806
## 199487 0.85436
## 188236 0.72730
Visualizing the network
We use the determined clusters as node colors and scale the node sizes according to the node’s eigenvector centrality.
# help page
?plot.microNetPropsp <- plot(props_single,
nodeColor = "cluster",
nodeSize = "eigenvector",
title1 = "Network on OTU level with SPRING associations",
showTitle = TRUE,
cexTitle = 2.3)
legend(0.7, 1.1, cex = 2.2, title = "estimated association:",
legend = c("+","-"), lty = 1, lwd = 3, col = c("#009900","red"),
bty = "n", horiz = TRUE)
Note that edge weights are (non-negative) similarities, however, the
edges belonging to negative estimated associations are colored in red by
default (negDiffCol = TRUE).
By default, a different transparency value is added to edges with an
absolute weight below and above the cut value (arguments
edgeTranspLow and edgeTranspHigh). The determined cut value can be
read out as follows:
p$q1$Arguments$cut## 75%
## 0.3367287
Let’s construct another network using Pearson’s correlation coefficient
as association measure. The input is now a phyloseq object.
Since Pearson correlations may lead to compositional effects when applied to sequencing data, we use the clr transformation as normalization method. Zero treatment is necessary in this case.
A threshold of 0.3 is used as sparsification method, so that only OTUs with an absolute correlation greater than or equal to 0.3 are connected.
net_single2 <- netConstruct(amgut2.filt.phy,
measure = "pearson",
normMethod = "clr",
zeroMethod = "multRepl",
sparsMethod = "threshold",
thresh = 0.3,
verbose = 3)## 2 rows with zero sum removed.
## 138 taxa and 294 samples remaining.
##
## Zero treatment:
## Execute multRepl() ...
## Warning in (function (X, label = NULL, dl = NULL, frac = 0.65, imp.missing = FALSE, : Row(s) containing more than 80% zeros/unobserved values were found (check it out using zPatterns).
## (You can use the z.warning argument to modify the warning threshold).
## Done.
##
## Normalization:
## Execute clr(){SpiecEasi} ... Done.
##
## Calculate 'pearson' associations ... Done.
##
## Sparsify associations via 'threshold' ... Done.
Network analysis and plotting:
props_single2 <- netAnalyze(net_single2, clustMethod = "cluster_fast_greedy")
plot(props_single2,
nodeColor = "cluster",
nodeSize = "eigenvector",
title1 = "Network on OTU level with Pearson correlations",
showTitle = TRUE,
cexTitle = 2.3)
legend(0.7, 1.1, cex = 2.2, title = "estimated correlation:",
legend = c("+","-"), lty = 1, lwd = 3, col = c("#009900","red"),
bty = "n", horiz = TRUE)
Let’s improve the visualization by changing the following arguments:
repulsion = 0.8: Place the nodes further apartrmSingles = TRUE: Single nodes are removedlabelScale = FALSEandcexLabels = 1.6: All labels have equal size and are enlarged to improve readability of small node’s labelsnodeSizeSpread = 3(default is 4): Node sizes are more similar if the value is decreased. This argument (in combination withcexNodes) is useful to enlarge small nodes while keeping the size of big nodes.
plot(props_single2,
nodeColor = "cluster",
nodeSize = "eigenvector",
repulsion = 0.8,
rmSingles = TRUE,
labelScale = FALSE,
cexLabels = 1.6,
nodeSizeSpread = 3,
cexNodes = 2,
title1 = "Network on OTU level with Pearson correlations",
showTitle = TRUE,
cexTitle = 2.3)
legend(0.7, 1.1, cex = 2.2, title = "estimated correlation:",
legend = c("+","-"), lty = 1, lwd = 3, col = c("#009900","red"),
bty = "n", horiz = TRUE)
We now construct a further network, where OTUs are agglomerated to genera.
# Agglomerate to genus level
amgut_genus <- phyloseq::tax_glom(amgut2.filt.phy, taxrank = "Rank6")
taxtab <- amgut_genus@tax_table@.Data
# Find undefined taxa (in this data set, unknowns occur only up to Rank5)
miss_f <- which(taxtab[, "Rank5"] == "f__")
miss_g <- which(taxtab[, "Rank6"] == "g__")
# Number unspecified genera
taxtab[miss_f, "Rank5"] <- paste0("f__", 1:length(miss_f))
taxtab[miss_g, "Rank6"] <- paste0("g__", 1:length(miss_g))
# Find duplicate genera
dupl_g <- which(duplicated(taxtab[, "Rank6"]) |
duplicated(taxtab[, "Rank6"], fromLast = TRUE))
for(i in seq_along(taxtab)){
# The next higher non-missing rank is assigned to unspecified genera
if(i %in% miss_f && i %in% miss_g){
taxtab[i, "Rank6"] <- paste0(taxtab[i, "Rank6"], "(", taxtab[i, "Rank4"], ")")
} else if(i %in% miss_g){
taxtab[i, "Rank6"] <- paste0(taxtab[i, "Rank6"], "(", taxtab[i, "Rank5"], ")")
}
# Family names are added to duplicate genera
if(i %in% dupl_g){
taxtab[i, "Rank6"] <- paste0(taxtab[i, "Rank6"], "(", taxtab[i, "Rank5"], ")")
}
}
amgut_genus@tax_table@.Data <- taxtab
rownames(amgut_genus@otu_table@.Data) <- taxtab[, "Rank6"]
# Network construction and analysis
net_single3 <- netConstruct(amgut_genus,
measure = "pearson",
zeroMethod = "multRepl",
normMethod = "clr",
sparsMethod = "threshold",
thresh = 0.3,
verbose = 3)## 2 rows with zero sum removed.
## 43 taxa and 294 samples remaining.
##
## Zero treatment:
## Execute multRepl() ...
## Warning in (function (X, label = NULL, dl = NULL, frac = 0.65, imp.missing = FALSE, : Row(s) containing more than 80% zeros/unobserved values were found (check it out using zPatterns).
## (You can use the z.warning argument to modify the warning threshold).
## Done.
##
## Normalization:
## Execute clr(){SpiecEasi} ... Done.
##
## Calculate 'pearson' associations ... Done.
##
## Sparsify associations via 'threshold' ... Done.
props_single3 <- netAnalyze(net_single3, clustMethod = "cluster_fast_greedy")Network plots
Modifications:
- Fruchterman-Reingold layout algorithm from
igraphpackage used (passed toplotas matrix) - Shortened labels
- Fixed node sizes, where hubs are enlarged
- Node color is gray for all nodes (transparancy is lower for hub nodes by default)
# Compute layout
graph3 <- igraph::graph_from_adjacency_matrix(net_single3$adjaMat1, weighted = TRUE)
set.seed(123456)
lay_fr <- igraph::layout_with_fr(graph3)
# Row names of the layout matrix must match the node names
rownames(lay_fr) <- rownames(net_single3$adjaMat1)
plot(props_single3,
layout = lay_fr,
shortenLabels = "simple",
labelLength = 10,
nodeSize = "fix",
nodeColor = "gray",
cexNodes = 0.8,
cexHubs = 1.1,
cexLabels = 1.2,
title1 = "Network on genus level with Pearson correlations",
showTitle = TRUE,
cexTitle = 2.3)
legend(0.7, 1.1, cex = 2.2, title = "estimated correlation:",
legend = c("+","-"), lty = 1, lwd = 3, col = c("#009900","red"),
bty = "n", horiz = TRUE)
Since the above visualization is obviously not optimal, we make further adjustments:
- This time, the Fruchterman-Reingold layout algorithm is computed within the plot function and thus applied to the “reduced” network without singletons
- Leading patterns “g__” are removed
- Labels are not scaled to node sizes
- Single nodes are removed
- Node sizes are scaled to the column sums of clr-transformed data
- Node colors represent the determined clusters
- Border color of hub nodes is changed from black to darkgray
- Label size of hubs is enlarged
set.seed(123456)
graph3 <- igraph::graph_from_adjacency_matrix(net_single3$adjaMat1, weighted = TRUE)
lay_fr <- igraph::layout_with_fr(graph3)
rownames(lay_fr) <- rownames(net_single3$adjaMat1)
plot(props_single3,
layout = "layout_with_fr",
shortenLabels = "simple",
labelLength = 10,
charToRm = "g__",
labelScale = FALSE,
rmSingles = TRUE,
nodeSize = "clr",
nodeColor = "cluster",
hubBorderCol = "darkgray",
cexNodes = 2,
cexLabels = 1.5,
cexHubLabels = 2,
title1 = "Network on genus level with Pearson correlations",
showTitle = TRUE,
cexTitle = 2.3)
legend(0.7, 1.1, cex = 2.2, title = "estimated correlation:",
legend = c("+","-"), lty = 1, lwd = 3, col = c("#009900","red"),
bty = "n", horiz = TRUE)
Let’s check whether the largest nodes are actually those with highest
column sums in the matrix with normalized counts returned by
netConstruct().
sort(colSums(net_single3$normCounts1), decreasing = TRUE)[1:10]## g__Bacteroides g__Klebsiella
## 1200.7971 1137.4928
## g__Faecalibacterium g__5(o__Clostridiales)
## 708.0877 549.2647
## g__2(f__Ruminococcaceae) g__3(f__Lachnospiraceae)
## 502.1889 493.7558
## g__6(f__Enterobacteriaceae) g__Roseburia
## 363.3841 333.8737
## g__Parabacteroides g__Coprococcus
## 328.0495 274.4082
In order to further improve our plot, we use the following modifications:
- This time, we choose the “spring” layout as part of
qgraph()(the function is generally used for network plotting in NetCoMi) - A repulsion value below 1 places the nodes further apart
- Labels are not shortened anymore
- Nodes (bacteria on genus level) are colored according to the respective phylum
- Edges representing positive associations are colored in blue, negative ones in orange (just to give an example for alternative edge coloring)
- Transparency is increased for edges with high weight to improve the readability of node labels
# Get phyla names from the taxonomic table created before
phyla <- as.factor(gsub("p__", "", taxtab[, "Rank2"]))
names(phyla) <- taxtab[, "Rank6"]
#table(phyla)
# Define phylum colors
phylcol <- c("cyan", "blue3", "red", "lawngreen", "yellow", "deeppink")
plot(props_single3,
layout = "spring",
repulsion = 0.84,
shortenLabels = "none",
charToRm = "g__",
labelScale = FALSE,
rmSingles = TRUE,
nodeSize = "clr",
nodeSizeSpread = 4,
nodeColor = "feature",
featVecCol = phyla,
colorVec = phylcol,
posCol = "darkturquoise",
negCol = "orange",
edgeTranspLow = 0,
edgeTranspHigh = 40,
cexNodes = 2,
cexLabels = 2,
cexHubLabels = 2.5,
title1 = "Network on genus level with Pearson correlations",
showTitle = TRUE,
cexTitle = 2.3)
# Colors used in the legend should be equally transparent as in the plot
phylcol_transp <- NetCoMi:::colToTransp(phylcol, 60)
legend(-1.2, 1.2, cex = 2, pt.cex = 2.5, title = "Phylum:",
legend=levels(phyla), col = phylcol_transp, bty = "n", pch = 16)
legend(0.7, 1.1, cex = 2.2, title = "estimated correlation:",
legend = c("+","-"), lty = 1, lwd = 3, col = c("darkturquoise","orange"),
bty = "n", horiz = TRUE)
Now let’s look how two networks are compared using NetCoMi.
Network construction
The covariate "SEASONAL_ALLERGIES” is used for splitting the data set
into two groups. The metagMisc
package offers a function for splitting phyloseq objects according to a
variable. The two resulting phyloseq objects (we ignore the group
‘None’) can directly be passed to NetCoMi.
We select the 50 nodes with highest variance to get smaller networks.
# devtools::install_github("vmikk/metagMisc")
# Split the phyloseq object into two groups
amgut_split <- metagMisc::phyloseq_sep_variable(amgut2.filt.phy,
"SEASONAL_ALLERGIES")# Network construction
net_season <- netConstruct(data = amgut_split$no,
data2 = amgut_split$yes,
filtTax = "highestVar",
filtTaxPar = list(highestVar = 50),
measure = "spring",
measurePar = list(nlambda=10,
rep.num=10),
normMethod = "none",
zeroMethod = "none",
sparsMethod = "none",
dissFunc = "signed",
verbose = 3,
seed = 123456)Alternatively, a group vector could be passed to group, according to
which the data set is split into two groups:
# netConstruct() expects samples in rows
countMat <- t(amgut2.filt.phy@otu_table@.Data)
group_vec <- phyloseq::get_variable(amgut2.filt.phy, "SEASONAL_ALLERGIES")
# Select the two groups of interest (level "none" is excluded)
sel <- which(group_vec %in% c("no", "yes"))
group_vec <- group_vec[sel]
countMat <- countMat[sel, ]
net_season <- netConstruct(countMat,
group = group_vec,
filtTax = "highestVar",
filtTaxPar = list(highestVar = 50),
measure = "spring",
measurePar = list(nlambda=10,
rep.num=10),
normMethod = "none",
zeroMethod = "none",
sparsMethod = "none",
dissFunc = "signed",
verbose = 3,
seed = 123456)Network analysis
The object returned by netConstruct() containing both networks is
again passed to netAnalyze(). Network properties are computed for both
networks simultaneously.
To demonstrate further functionalities of netAnalyze(), we play around
with the available arguments, even if the chosen setting might not be
optimal.
centrLCC = FALSE: Centralities are calculated for all nodes (not only for the largest connected component).avDissIgnoreInf = TRUE: Nodes with an infinite dissimilarity are ignored when calculating the average dissimilarity.sPathNorm = FALSE: Shortest paths are not normalized by average dissimilarity.hubPar = c("degree", "between", "closeness"): Hubs are nodes with highest degree, betweenness, and closeness centrality at the same time.lnormFit = TRUEandhubQuant = 0.9: A log-normal distribution is fitted to the centrality values to identify nodes with “highest” centrality values. Here, a node is identified as hub if for each of the three centrality measures, the node’s centrality value is above the 90% quantile of the fitted log-normal distribution.- The non-normalized centralities are used for all four measures.
Note! The arguments must be set carefully, depending on the research questions. NetCoMi’s default values are not generally preferable in all practical cases!
props_season <- netAnalyze(net_season,
centrLCC = FALSE,
avDissIgnoreInf = TRUE,
sPathNorm = FALSE,
clustMethod = "cluster_fast_greedy",
hubPar = c("degree", "between", "closeness"),
hubQuant = 0.9,
lnormFit = TRUE,
normDeg = FALSE,
normBetw = FALSE,
normClose = FALSE,
normEigen = FALSE)
summary(props_season)##
## Component sizes
## ```````````````
## Group 1:
## size: 31 8 1
## #: 1 1 4
##
## Group 2:
## size: 41 1
## #: 1 2
## ______________________________
## Global network properties
## `````````````````````````
## Largest connected component (LCC):
## group '1' group '2'
## Relative LCC size 0.72093 0.95349
## Clustering coefficient 0.27184 0.29563
## Modularity 0.51794 0.54832
## Positive edge percentage 100.00000 100.00000
## Edge density 0.11183 0.09512
## Natural connectivity 0.04296 0.03257
## Vertex connectivity 1.00000 1.00000
## Edge connectivity 1.00000 1.00000
## Average dissimilarity* 0.68093 0.67856
## Average path length** 2.23420 2.49366
##
## Whole network:
## group '1' group '2'
## Number of components 6.00000 3.00000
## Clustering coefficient 0.31801 0.29563
## Modularity 0.62749 0.54832
## Positive edge percentage 100.00000 100.00000
## Edge density 0.06977 0.08638
## Natural connectivity 0.02979 0.03072
##
## *Dissimilarity = 1 - edge weight
## **Path length: Sum of dissimilarities along the path
##
## ______________________________
## Clusters
## - In the whole network
## - Algorithm: cluster_fast_greedy
## ````````````````````````````````
## group '1':
## name: 0 1 2 3 4
## #: 4 10 13 8 8
##
## group '2':
## name: 0 1 2 3 4 5
## #: 2 6 11 8 8 8
##
## ______________________________
## Hubs
## - In alphabetical/numerical order
## - Based on log-normal quantiles of centralities
## ```````````````````````````````````````````````
## group '1' group '2'
## 322235
##
## ______________________________
## Centrality measures
## - In decreasing order
## - Computed for the complete network
## ````````````````````````````````````
## Degree (unnormalized):
## group '1' group '2'
## 322235 7 9
## 364563 7 5
## 259569 7 5
## 184983 6 5
## 9715 5 4
## ______ ______
## 322235 7 9
## 363302 4 9
## 158660 3 6
## 90487 3 5
## 188236 4 5
##
## Betweenness centrality (unnormalized):
## group '1' group '2'
## 364563 148 82
## 188236 144 87
## 259569 122 39
## 331820 115 8
## 322235 106 226
## ______ ______
## 158660 0 317
## 470239 5 256
## 10116 0 233
## 322235 106 226
## 326792 0 161
##
## Closeness centrality (unnormalized):
## group '1' group '2'
## 364563 22.67435 25.8268
## 259569 22.19566 23.95331
## 322235 22.16201 30.01882
## 188236 21.1072 26.37219
## 184983 20.05729 22.58749
## ______ ______
## 322235 22.16201 30.01882
## 158660 17.64517 27.65208
## 363302 17.27045 27.60924
## 326792 17.95217 26.47107
## 188236 21.1072 26.37219
##
## Eigenvector centrality (unnormalized):
## group '1' group '2'
## 364563 0.30443 0.21366
## 184983 0.29043 0.2695
## 188236 0.23918 0.23401
## 516022 0.23486 0.14099
## 190464 0.22311 0.21348
## ______ ______
## 363302 0.21619 0.38174
## 322235 0.14534 0.29655
## 194648 0.17437 0.28065
## 184983 0.29043 0.2695
## 188236 0.23918 0.23401
In the above setting, only one hub node (in the “Seasonal allergies” network) has been identified.
Visual network comparison
First, the layout is computed separately in both groups (qgraph’s “spring” layout in this case).
Node sizes are scaled according to the mclr-transformed data since
SPRING uses the mclr transformation as normalization method.
Node colors represent clusters. Note that by default, two clusters have
the same color in both groups if they have at least two nodes in common
(sameColThresh = 2). Set sameClustCol to FALSE to get different
cluster colors.
plot(props_season,
sameLayout = FALSE,
nodeColor = "cluster",
nodeSize = "mclr",
labelScale = FALSE,
cexNodes = 1.5,
cexLabels = 2.5,
cexHubLabels = 3,
cexTitle = 3.7,
groupNames = c("No seasonal allergies", "Seasonal allergies"),
hubBorderCol = "gray40")
legend("bottom", title = "estimated association:", legend = c("+","-"),
col = c("#009900","red"), inset = 0.02, cex = 4, lty = 1, lwd = 4,
bty = "n", horiz = TRUE)
Using different layouts leads to a “nice-looking” network plot for each group, however, it is difficult to identify group differences at first glance.
Thus, we now use the same layout in both groups. In the following, the layout is computed for group 1 (the left network) and taken over for group 2.
rmSingles is set to "inboth" because only nodes that are unconnected
in both groups can be removed if the same layout is used.
plot(props_season,
sameLayout = TRUE,
layoutGroup = 1,
rmSingles = "inboth",
nodeSize = "mclr",
labelScale = FALSE,
cexNodes = 1.5,
cexLabels = 2.5,
cexHubLabels = 3,
cexTitle = 3.8,
groupNames = c("No seasonal allergies", "Seasonal allergies"),
hubBorderCol = "gray40")
legend("bottom", title = "estimated association:", legend = c("+","-"),
col = c("#009900","red"), inset = 0.02, cex = 4, lty = 1, lwd = 4,
bty = "n", horiz = TRUE)
In the above plot, we can see clear differences between the groups. The OTU “322235”, for instance, is more strongly connected in the “Seasonal allergies” group than in the group without seasonal allergies, which is why it is a hub on the right, but not on the left.
However, if the layout of one group is simply taken over to the other,
one of the networks (here the “seasonal allergies” group) is usually not
that nice-looking due to the long edges. Therefore, NetCoMi (>= 1.0.2)
offers a further option (layoutGroup = "union"), where a union of the
two layouts is used in both groups. In doing so, the nodes are placed as
optimal as possible equally for both networks.
The idea and R code for this functionality were provided by Christian L. Müller and Alice Sommer
plot(props_season,
sameLayout = TRUE,
layoutGroup = "union",
rmSingles = "inboth",
nodeSize = "mclr",
labelScale = FALSE,
cexNodes = 1.5,
cexLabels = 2.5,
cexHubLabels = 3,
cexTitle = 3.8,
groupNames = c("No seasonal allergies", "Seasonal allergies"),
hubBorderCol = "gray40")
legend("bottom", title = "estimated association:", legend = c("+","-"),
col = c("#009900","red"), inset = 0.02, cex = 4, lty = 1, lwd = 4,
bty = "n", horiz = TRUE)
Quantitative network comparison
Since runtime is considerably increased if permutation tests are
performed, we set the permTest parameter to FALSE. See the
tutorial_createAssoPerm file for a network comparison including
permutation tests.
comp_season <- netCompare(props_season, permTest = FALSE, verbose = FALSE)
summary(comp_season,
groupNames = c("No allergies", "Allergies"),
showCentr = c("degree", "between", "closeness"),
numbNodes = 5)##
## Comparison of Network Properties
## ----------------------------------
## CALL:
## netCompare(x = props_season, permTest = FALSE, verbose = FALSE)
##
## ______________________________
## Global network properties
## `````````````````````````
## Largest connected component (LCC):
## No allergies Allergies difference
## Relative LCC size 0.721 0.953 0.233
## Clustering coefficient 0.272 0.296 0.024
## Moduarity 0.518 0.548 0.030
## Positive edge percentage 100.000 100.000 0.000
## Edge density 0.112 0.095 0.017
## Natural connectivity 0.043 0.033 0.010
## Vertex connectivity 1.000 1.000 0.000
## Edge connectivity 1.000 1.000 0.000
## Average dissimilarity* 0.681 0.679 0.002
## Average path length** 2.234 2.494 0.259
##
## Whole network:
## No allergies Allergies difference
## Number of components 6.000 3.000 3.000
## Clustering coefficient 0.318 0.296 0.022
## Moduarity 0.627 0.548 0.079
## Positive edge percentage 100.000 100.000 0.000
## Edge density 0.070 0.086 0.017
## Natural connectivity 0.030 0.031 0.001
## -----
## *: Dissimilarity = 1 - edge weight
## **Path length: Sum of dissimilarities along the path
##
## ______________________________
## Jaccard index (similarity betw. sets of most central nodes)
## ``````````````````````````````````````````````````````````
## Jacc P(<=Jacc) P(>=Jacc)
## degree 0.286 0.475500 0.738807
## betweenness centr. 0.077 0.038537 * 0.994862
## closeness centr. 0.267 0.404065 0.790760
## eigenvec. centr. 0.667 0.996144 0.018758 *
## hub taxa 0.000 0.666667 1.000000
## -----
## Jaccard index ranges from 0 (compl. different) to 1 (sets equal)
##
## ______________________________
## Adjusted Rand index (similarity betw. clusterings)
## ``````````````````````````````````````````````````
## ARI p-value
## 0.327 0
## -----
## ARI in [-1,1] with ARI=1: perfect agreement betw. clusterings,
## ARI=0: expected for two random clusterings
## p-value: two-tailed test with null hypothesis ARI=0
##
## ______________________________
## Centrality measures
## - In decreasing order
## - Computed for the complete network
## ````````````````````````````````````
## Degree (unnormalized):
## No allergies Allergies abs.diff.
## 363302 4 9 5
## 549871 4 0 4
## 469709 1 4 3
## 158660 3 6 3
## 181016 0 3 3
##
## Betweenness centrality (unnormalized):
## No allergies Allergies abs.diff.
## 158660 0 317 317
## 470239 5 256 251
## 10116 0 233 233
## 326792 0 161 161
## 322235 106 226 120
##
## Closeness centrality (unnormalized):
## No allergies Allergies abs.diff.
## 181016 0.000 22.879 22.879
## 361496 0.000 22.251 22.251
## 549871 19.787 0.000 19.787
## 278234 0.000 15.093 15.093
## 10116 7.039 20.964 13.924
##
## _________________________________________________________
## Significance codes: ***: 0.001, **: 0.01, *: 0.05, .: 0.1
We now build a differential association network, where two nodes are connected if they are differentially associated between the two groups.
Due to its very short execution time, we use Pearson’s correlations for estimating associations between OTUs.
Fisher’s z-test is applied for identifying differentially correlated OTUs. Multiple testing adjustment is done by controlling the local false discovery rate.
Note: sparsMethod is set to "none", just to be able to include all
differential associations in the association network plot (see below).
However, the differential network is always based on the estimated
association matrices before sparsification (the assoEst1 and
assoEst2 matrices returned by netConstruct()).
net_season_pears <- netConstruct(data = amgut_split$no,
data2 = amgut_split$yes,
filtTax = "highestVar",
filtTaxPar = list(highestVar = 50),
measure = "pearson",
normMethod = "clr",
sparsMethod = "none",
thresh = 0.2,
verbose = 3)## Infos about changed arguments:
## Zero replacement needed for clr transformation. 'multRepl' used.
## Data filtering ...
## 95 taxa removed in each data set.
## 1 rows with zero sum removed in group 1.
## 1 rows with zero sum removed in group 2.
## 43 taxa and 162 samples remaining in group 1.
## 43 taxa and 120 samples remaining in group 2.
##
## Zero treatment in group 1:
## Execute multRepl() ...
## Warning in (function (X, label = NULL, dl = NULL, frac = 0.65, imp.missing = FALSE, : Row(s) containing more than 80% zeros/unobserved values were found (check it out using zPatterns).
## (You can use the z.warning argument to modify the warning threshold).
## Done.
##
## Zero treatment in group 2:
## Execute multRepl() ...
## Warning in (function (X, label = NULL, dl = NULL, frac = 0.65, imp.missing = FALSE, : Row(s) containing more than 80% zeros/unobserved values were found (check it out using zPatterns).
## (You can use the z.warning argument to modify the warning threshold).
## Done.
##
## Normalization in group 1:
## Execute clr(){SpiecEasi} ... Done.
##
## Normalization in group 2:
## Execute clr(){SpiecEasi} ... Done.
##
## Calculate 'pearson' associations ... Done.
##
## Calculate associations in group 2 ... Done.
# Differential network construction
diff_season <- diffnet(net_season_pears,
diffMethod = "fisherTest",
adjust = "lfdr")## Adjust for multiple testing using 'lfdr' ...
## Execute fdrtool() ...
## Step 1... determine cutoff point
## Step 2... estimate parameters of null distribution and eta0
## Step 3... compute p-values and estimate empirical PDF/CDF
## Step 4... compute q-values and local fdr
## Done.
# Differential network plot
plot(diff_season,
cexNodes = 0.8,
cexLegend = 3,
cexTitle = 4,
mar = c(2,2,8,5),
legendGroupnames = c("group 'no'", "group 'yes'"),
legendPos = c(0.7,1.6))
In the differential
network shown above, edge colors represent the direction of associations
in the two groups. If, for instance, two OTUs are positively associated
in group 1 and negatively associated in group 2 (such as ‘191541’ and
‘188236’), the respective edge is colored in cyan.
We also take a look at the corresponding associations by constructing association networks that include only the differentially associated OTUs.
props_season_pears <- netAnalyze(net_season_pears,
clustMethod = "cluster_fast_greedy",
weightDeg = TRUE,
normDeg = FALSE)
# Identify the differentially associated OTUs
diffmat_sums <- rowSums(diff_season$diffAdjustMat)
diff_asso_names <- names(diffmat_sums[diffmat_sums > 0])
plot(props_season_pears,
nodeFilter = "names",
nodeFilterPar = diff_asso_names,
nodeColor = "gray",
highlightHubs = FALSE,
sameLayout = TRUE,
layoutGroup = "union",
rmSingles = FALSE,
nodeSize = "clr",
edgeTranspHigh = 20,
labelScale = FALSE,
cexNodes = 1.5,
cexLabels = 3,
cexTitle = 3.8,
groupNames = c("No seasonal allergies", "Seasonal allergies"),
hubBorderCol = "gray40")
legend(-0.15,-0.7, title = "estimated correlation:", legend = c("+","-"),
col = c("#009900","red"), inset = 0.05, cex = 4, lty = 1, lwd = 4,
bty = "n", horiz = TRUE)
We can see that the correlation between the aforementioned OTUs ‘191541’ and ‘188236’ is strongly positive in the left group and negative in the right group.
If a dissimilarity measure is used for network construction, nodes are subjects instead of OTUs. The estimated dissimilarities are transformed into similarities, which are used as edge weights so that subjects with a similar microbial composition are placed close together in the network plot.
We construct a single network using Aitchison’s distance being suitable for the application on compositional data.
Since the Aitchison distance is based on the clr-transformation, zeros in the data need to be replaced.
The network is sparsified using the k-nearest neighbor (knn) algorithm.
net_aitchison <- netConstruct(amgut1.filt,
measure = "aitchison",
zeroMethod = "multRepl",
sparsMethod = "knn",
kNeighbor = 3,
verbose = 3)## Infos about changed arguments:
## Counts normalized to fractions for measure 'aitchison'.
## 127 taxa and 289 samples remaining.
##
## Zero treatment:
## Execute multRepl() ...
## Warning in (function (X, label = NULL, dl = NULL, frac = 0.65, imp.missing = FALSE, : Row(s) containing more than 80% zeros/unobserved values were found (check it out using zPatterns).
## (You can use the z.warning argument to modify the warning threshold).
## Done.
##
## Normalization:
## Counts normalized by total sum scaling.
##
## Calculate 'aitchison' dissimilarities ... Done.
##
## Sparsify dissimilarities via 'knn' ... Done.
For cluster detection, we use hierarchical clustering with average
linkage. Internally, k=3 is passed to
cutree()
from stats package so that the tree is cut into 3 clusters.
props_aitchison <- netAnalyze(net_aitchison,
clustMethod = "hierarchical",
clustPar = list(method = "average", k = 3),
hubPar = "eigenvector")
plot(props_aitchison,
nodeColor = "cluster",
nodeSize = "eigenvector",
hubTransp = 40,
edgeTranspLow = 60,
charToRm = "00000",
mar = c(1, 3, 3, 5))
# get green color with 50% transparency
green2 <- colToTransp("#009900", 40)
legend(0.4, 1.1,
cex = 2.2,
legend = c("high similarity (low Aitchison distance)",
"low similarity (high Aitchison distance)"),
lty = 1,
lwd = c(3, 1),
col = c("darkgreen", green2),
bty = "n")
In this dissimilarity-based network, hubs are interpreted as samples with a microbial composition similar to that of many other samples in the data set.
Here is the code for reproducing the network plot shown at the beginning.
data("soilrep")
soil_warm_yes <- phyloseq::subset_samples(soilrep, warmed == "yes")
soil_warm_no <- phyloseq::subset_samples(soilrep, warmed == "no")
net_seas_p <- netConstruct(soil_warm_yes, soil_warm_no,
filtTax = "highestVar",
filtTaxPar = list(highestVar = 500),
zeroMethod = "pseudo",
normMethod = "clr",
measure = "pearson",
verbose = 0)
netprops1 <- netAnalyze(net_seas_p, clustMethod = "cluster_fast_greedy")
nclust <- as.numeric(max(names(table(netprops1$clustering$clust1))))
col <- c(topo.colors(nclust), rainbow(6))
plot(netprops1,
sameLayout = TRUE,
layoutGroup = "union",
colorVec = col,
borderCol = "gray40",
nodeSize = "degree",
cexNodes = 0.9,
nodeSizeSpread = 3,
edgeTranspLow = 80,
edgeTranspHigh = 50,
groupNames = c("Warming", "Non-warming"),
showTitle = TRUE,
cexTitle = 2.8,
mar = c(1,1,3,1),
repulsion = 0.9,
labels = FALSE,
rmSingles = "inboth",
nodeFilter = "clustMin",
nodeFilterPar = 10,
nodeTransp = 50,
hubTransp = 30)[Badri et al., 2020] Michelle Badri, Zachary D. Kurtz, Richard Bonneau, and Christian L. Müller (2020). Shrinkage improves estimation of microbial associations under different normalization methods. NAR Genomics and Bioinformatics, 2(4). doi: 10.1093/NARGAB/LQAA100.
[Martín-Fernández et al., 1999] Josep A Martín-Fernández, Mark J Bren, Carles Barceló-Vidal, and Vera Pawlowsky-Glahn (1999). A measure of difference for compositional data based on measures of divergence. Lippard, Næss, and Sinding-Larsen, 211-216.)