Detecting co-selection through excess linkage disequilibrium in bacterial genomes

Abstract

Population genomics has revolutionized our ability to study bacterial evolution by enabling data-driven discovery of the genetic architecture of trait variation. Genome-wide association studies (GWAS) have more recently become accompanied by genome-wide epistasis and co-selection (GWES) analysis, which offers a phenotype-free approach to generating hypotheses about selective processes that simultaneously impact multiple loci across the genome. However, existing GWES methods only consider associations between distant pairs of loci within the genome due to the strong impact of linkage-disequilibrium (LD) over short distances. Based on the general functional organisation of genomes it is nevertheless expected that majority of co-selection and epistasis will act within relatively short genomic proximity, on co-variation occurring within genes and their promoter regions, and within operons. Here, we introduce LDWeaver, which enables an exhaustive GWES across both short- and long-range LD, to disentangle likely neutral co-variation from selection. We demonstrate the ability of LDWeaver to efficiently generate hypotheses about co-selection using large genomic surveys of multiple major human bacterial pathogen species and validate several findings using functional annotation and phenotypic measurements. Our approach will facilitate the study of bacterial evolution in the light of rapidly expanding population genomic data.

Full text

NAR Genomics and Bioinformatics , 2024, 6 , lqae061
https://doi.org/10.1093/nargab/lqae061
Advance access publication date: 6 June 2024
Methods Article
Detecting co-selection through excess linkage
disequilibrium in bacterial genomes
Sudar aka Malla w aar ac hc hi
1 ,
* , Gerry Tonkin-Hill
1
, Anna K. Pöntinen
1 , 2
, Jessica K. Calland
3
,
Rebecca A. Gladstone
1
, Sergio Arredondo-Alonso
1
, Neil MacAlasdair
1
, Harry A. Thorpe
1
,
Janetta To p
4
, Samuel K. Sheppar d
5
, Da vid Balding
6
, Nic holas J. Crouc her
7 , 8 ,† and
Jukka Corander
1 , 9 , 10 ,
*
,†
1
Department of Biostatistics, University of Oslo, Oslo, Norway
2
Norwegian National Advisory Unit on Detection of Antimicrobial Resistance, Department of Microbiology and Infection Control, University
Hospital of North Norway, Tromsø, Norway
3
Oslo Centre for Biostatistics and Epidemiology, Oslo University Hospital, Oslo, Norway
4
Department of Medical Microbiology, UMC Utrecht, Utrecht, The Netherlands
5
Ineos Oxford Institute of Antimicrobial Research, Department of Biology, University of Oxford, Oxford, United Kingdom
6
Melbourne Integrative Genomics, School of BioSciences and School of Mathematics & Statistics, University of Melbourne, Parkville,
Victoria, Australia
7
Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, United Kingdom
8
MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, United Kingdom
9
Parasites and Microbes, Wellcome Sanger Institute, Cambridge, UK
10
Helsinki Institute of Information Technology, Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
*
To whom correspondence should be addressed. Email: smallawaarahchi@gmail.com
Correspondence may also be addressed to Jukka Corander. Tel: +47 22 84 53 00; Fax: +47 22 84 53 01; Email: jukka.corander@medisin.uio.no
†
The last two authors should be regarded as Joint Last Authors.
Abstract
Population genomics has re v olutioniz ed our ability to study bacterial e v olution b y enabling data-driv en disco v ery of the genetic architecture of
trait variation. Genome-wide association studies (GWAS) ha v e more recently become accompanied by genome-wide epistasis and co-selection
(GWES) analysis, which offers a phenotype-free approach to generating hypotheses about selective processes that simultaneously impact
multiple loci across the genome. Ho w e v er, e xisting GWES methods only consider associations between distant pairs of loci within the genome
due to the strong impact of linkage-disequilibrium (LD) o v er short distances. Based on the general functional organisation of genomes it is
ne v ertheless e xpected that majorit y of co-selection and epist asis will act within relatively short genomic pro ximity, on co-v ariation occurring
within genes and their promoter regions, and within operons. Here, we introduce LDWeaver, which enables an exhaustive GWES across both
short- and long-range LD, to disentangle likely neutral co-variation from selection. We demonstrate the ability of LD Wea v er to efciently generate
hypotheses about co-selection using large genomic surv e y s of multiple major human bacterial pathogen species and v alidate se v eral ndings
using functional annotation and phenotypic measurements. Our approach will facilitate the study of bacterial e v olution in the light of rapidly
expanding population genomic data.
Introduction
The rapid rate of evolution of bacterial genomes has made
them a popular target of studying selection in both exper-
imental and natural populations. The emergence of afford-
able high-resolution population genomics a decade ago ush-
ered us into a new era with improved possibilities to inves-
tigate both microscopic and macroscopic evolution of bac-
terial genomes, including for example codon bias ( 1 ), inter-
genic selection ( 2 ) and variation in gene content ( 3 ). Despite
steady progress in genome-wide association study (GWAS)
methodologies specically designed for bacterial populations
( 4 ,5 ), the difculty of measuring quantitative phenotypic vari-
ation in large numbers of isolates has restricted the use of
GWAS mostly to the study of antibiotic resistance, with a
few exceptions covering for example duration of coloniza-
tion ( 6 ), genome-wide transcriptomics ( 7 ) and virulence ( 8 ).
Traits such as reproductive rate, survival and transmissibil-
ity are of key interest in bacteria but remain difcult to mea-
sure in sufcient numbers in natural populations. Motivated
by this obstacle, phenotype-free approaches to uncovering sig-
nals of selection have been introduced ( 9–12 ), based on the
rationale that positively selected variation in complex traits
would likely be caused by synchronized changes in multiple
genes and / or regulatory elements that are detectable from ex-
cess linkage disequilibrium (LD) between distant sites across
a sample of genomes. This provides a methodological toolkit
complementary to GWAS enabling analyses termed genome-
wide epistasis and co-selection studies (GWES), which has
been recently used to unravel signals of selection due to epista-
sis for a wide diversity of bacteria ( 13–16 ). Arnold et al., using
positive, negative and sign epistasis models, demonstrated that
under selection, even relatively weak epistasis is sufcient for
Received: February 11, 2024. Revised: April 15, 2024. Editorial Decision: May 13, 2024. Accepted: May 14, 2024
©The Author(s) 2024. Published by Oxford University Press on behalf of NAR Genomics and Bioinformatics.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https: // creativecommons.org / licenses / by / 4.0 / ),
which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
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2 NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2
driving adaptation in moderately to highly recombinogenic
bacteria, which provides a more theoretical justication for
GWES analysis ( 17 ), see also the recent work on the possi-
bly saltational role of epistasis in highly recombining bacterial
species ( 18 ).
Existing GWES approaches are limited to discovering links
between distant loci within the region where LD asymptotes
towards its lower bound. However, many co-evolving loci are
organized into clusters of genes (e.g. co-transcribed in oper-
ons). Therefore, studying only long-range links ignores most
of the allelic co-variation occurring in genomes. A ne-scale
haplotype structure analysis of Neisseria gonorrhoeae indeed
revealed numerous likely examples of positive co-selection in
different regions of the chromosome of this highly recom-
binant species, and extensive population genetic simulations
suggested that such LD patterns could be explained by either
directional selection on horizontally acquired alleles, or bal-
ancing selection maintaining the diversity ( 19 ). Motivated by
these insights, we aimed at developing a scalable statistical
approach that disentangles neutral LD from co-selection and
epistasis at any genomic distance. Apart from co-selection and
epistasis, LD can also be inuenced by various other factors,
including population structure, population expansion, muta-
tion and admixture. While disentangling neutral LD remains
a valuable approach for identifying co-selection and epistasis,
sole reliance on it cannot distinguish between underlying evo-
lutionary factors. Since wet-lab-based validation would typ-
ically be necessary to resolve causal factors underlying ob-
served deviations from a baseline neutral LD, this serves as a
useful starting point towards identifying important molecular
drivers of success in bacterial populations.
GWES methods generally exploit the decay of LD as a func-
tion of genomic distance to label SNP pairs as ‘outliers’ with
respect to the background distribution of LD estimated from
population data. The intuition here, for example in the con-
text of synergistic epistasis, is that when the combined effect
on selection of two or more polymorphic loci is greater than
the sum of their individual effects, this allele combination will
be maintained in association in the population, giving rise to
discernable patterns of LD. Similar to Arnold et al. ( 19 ), it is
possible to extend the notion of ‘outlier’ LD level to SNPs in
close proximity to each other by simulating the distribution of
LD strength as a function of base pair distance using a neutral
Wright-Fisher model. These simulations approximate the pop-
ulation level co-variation of alleles expected under neutrality
and can be used to screen pairs of loci for outliers that may be
due to co-selection. We show that this approach works well
and maintains a low false positive rate. However, as tting
of the neutral model parameters and forward simulation of
the tted model in a sufciently large number of replicates is
computationally costly, we developed an empirical model-free
approximation that is scalable to large population genomic
datasets. The model-free method is motivated by the common
assumption that a majority of the observed LD within a bacte-
rial population reects near-neutrality ( 20–23 ), which implies
that a majority of observations are not strongly inuenced by
selection. As a result, it is possible to analyse and interpret LD
patterns without relying on additional assumptions about un-
derlying genetic models or selection pressures. By extension,
it then becomes feasible to use the empirical LD decay distri-
bution to call outliers. Moreover, the approach accounts for
heterogeneity in evolutionary rates, such as mutation and re-
combination hotspots.
The model-free algorithm is implemented
as an open-source R package ‘LDweaver’
( https:// github.com/ Sudaraka88/ LD W eaver ), which can
be used to perform a comprehensive GWES in large-scale
bacterial datasets. LD W eaver incorporates the functionality
of the popular GWES package Spydrpick for long-range LD
outlier detection ( 12 ) and extends this by allowing analysis of
LD at any genomic distance. LD W eaver provides automated
functional annotations on all putative co-selected SNPs
and generates an array of visualizations to allow users to
efciently explore the results. We use published population
genomic data for the major human pathogens Streptococcus
pneumoniae ( 24 ,25 ), Campylobacter jejuni ( 26 ), Esc heric hia
coli ( 27 ) and Enterococcus faecalis ( 28 ) to identify both
known and novel signals of co-selection linked to the molec-
ular basis of pathogenicity, survival and other key bacterial
phenotypes.
Materials and methods
Measuring LD
By default, LD W eaver removes sites with MAF < 0.01 and gap
frequency > 0.15. Sites with ‘gap’ as the second most common
allele are also discarded from the analysis by default, but LD-
Weaver has a ltering option called ‘relaxed’ that retains these
sites in the analysis. This option could be particularly useful
for alignments with a limited number of SNPs, as gaps can
reect insertions or deletions with functional effects ( 80 ).
Following SpydrPick ( 12 ), we use MI to measure LD. The
pairwise MI between two sites (modelled as discrete random
variables) is given by:
MI
(
X, Y
)
=

x ∈ X

y ∈ Y
p
(
x, y
)
log p
(
x, y
)
p
(
x
)
p
(
y
)
(1)
Where X and Y denote two sites with alleles x ∈ X
and y ∈ Y, respectively. For SNP data, the alphabet com-
prises nucleotides A, C, G, T and the gap character N. Here
p( x, y ) denotes the joint probability of x = X and y = Y
and p (x ) , p (y ) are the corresponding marginal probabilities
which are estimated from count data ( 12 ).
Let n
s denote the number of sequences in the alignment,
then:
ˆ
p
(
x, y
)
=
n
(
x, y
)
+ 0 . 5
n
s
+ r
x
r
Y ×0 . 5
(2)
where n ( x, y ) = | S
xy
| is the number of sequences with X = x
and Y = y , r
X = | X| and r
Y = | Y | .
Strong population structure in bacteria presents a prob-
lem for analysis ( 80 ). We adopt a widely-used sequence-
reweighting approach ( 10–12 , 81 , 82 ). The weight w
i
∈
[ 1 /n, 1 ] for sequence i is computed as the reciprocal of
the number of sequences with mean per-site Hamming dis-
tance < t , where t is a dataset-dependent threshold that
typically satises t ∈ ( 0 . 1 , 0 . 25 ) . This population structure
correction is applied to the LD structure estimation by sub-
stituting effective counts in Eq. ( 2 ) given by n
s
=
n

i =1
w
i and
n ( x, y ) = 
i ∈ S
xy
w
i
.
In practice, the MI computation process is optimised using a
sparse matrix representation and performed in blocks of SNPs
( 83 ), which can be feasible even in systems with relatively low
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NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2 3
memory. LD W eaver requires genome-wide short-range links
to be retained in memory (see below), but most long-range
links with low MI values are discarded after processing each
SNP block. The user species an approximate number of long-
range links to be retained for downstream analysis.
Modelling short-range links.
By default, SpydrPick ( 12 ) uses S = 10 kb as the threshold
for dening a short-range link, but in LD W eaver we chose
S = 20 kb as the default threshold to better capture the re-
gion of rapid LD decay. The user can adjust this parameter as
required.
Additionally, LD W eaver accounts for genome-wide varia-
tion in local LD patterns, which can arise due to varying mu-
tation and / or recombination rates, by introducing a clustering
and segregation step. First, for each coding sequence (CDS)
segment in the annotations le, the per-site number of mis-
matches between the CDS and its reference sequence (i.e. the
per-site Hamming distance) is computed. Next, the CDS are
clustered using the k -means algorithm ( 84 ). Due to the chal-
lenges in accounting for heterogeneity stemming from popula-
tion structure ( 80 ), LD W eaver avoids estimating this parame-
ter and the choice of the number of clusters is a user modiable
(default k = 3 ). A user can avoid clustering by setting the
k = 1 . Generally, the LD W eaver output with CDS diversity
and clustering (similar to Figure 1 B) can be useful to deter-
mine k . In Supplementary Figures S2 , S3 , S6 , S8 and S9 , for
each dataset analysed, we show our choice of k and the out-
put CDS diversity and clustering plot. Generally, increasing
k beyond a sensible value will have a limited impact on nal
analysis, provided that enough CDS remain in all clusters to
approximately estimate the decay of background LD.
Since CDS regions exclude intergenic regions, each inter-
genic SNP is manually merged into the cluster closest to its
genomic location.
We used the C. jejuni dataset to compare the modelling of
short-range rapid LD decay between ( 1 ) the LD W eaver model-
free approach and ( 2 ) computationally demanding neutral
simulations. For each cluster, we used mcorr ( 85 ) to estimate
the parameter triplet: mutation rate, recombination rate and
the recombination tract length. For each parameter triplet,
100 neutral replicates were generated using bacmeta ( 86 ). In
each simulation 20 subpopulations of bacteria, each compris-
ing 1000 individuals with a 200 kb gen-me were included to
generate a sufciently large and diverse alignment. Migration
rate probability was set at the default 0.01. Each simulation
was performed for 20 000 generations to ensure convergence
and then 1000 individuals were sampled. The mean LD decay
was directly estimated from this neutral data as a function of
bp-sep (base-pair separation).
LD W eaver directly models the LD-decay using the genomic
alignment, separately for each cluster. At each discrete bp-sep,
the 95th percentile ( q
95
) MI value is extracted from the ge-
nomic data. Here, q
95 was chosen intuitively as a reasonable
choice to model the background LD ( 87 ). Next, the linear
model: log ( q
95
) ∼log ( bp _ sep ) is tted and the exponent
of the tted values of this model (i.e. ˆ
q
95 ) is chosen as the
bp-sep dependent short-range background-LD threshold. The
95th percentile is chosen to be modelled because it is close to
the upper tail of the distribution, which is the region of inter-
est, but little affected by large outliers so that the tted curve
is reasonably smooth.
Outlier calling and link ranking.
Outlier calling is performed at each discrete bp-sep value. Let
d ∈ [ 1 , S ] denote the bp-sep of interest, let L (d) denote
all the links that are d bp-sep apart and let L
∗(d) de-
note the subset with MI ( L ( d) ) ≥ˆ
q
95
(d) . First, the model:
MI ( L ( d) ) −ˆ
q
95
(d) ∼Beta ( α, β) is tted ( 88 ) in order to
compute an approximate, ∀ L
∗(d) , a short-range p-value (re-
ferred to as ‘srp’ in LD W eaver to denote short-range p-value).
Links with MI < ˆ
q
95
(d) are always discarded and the user
can choose a srp cut-off value (default p = 1 e −3 ) to further
reduce the set of links retained.
Although a model-free, permutation analysis is available to
compute the srp, it would greatly add to the computational
burden for large bacterial genomic datasets and is not re-
quired because the Beta distribution provides a good approxi-
mation. We conrmed this empirically by performing multiple
trials comparing permutation-based and beta-approximation
p-values using the descdist() function available in the R pack-
age, tdistrplus ( 88 ).
The ˆ
q
95 values are modelled separately for each genome
cluster. The srp for links between sites from the same cluster is
computed using the LD-decay model tted to data from that
cluster. When a link spans two clusters, the maximum of the
two srp values is used.
Filtering indirect links
Because of its success in inferring gene expression networks
( 89 ) and its utility in SpydrPick, we added ARACNE as a l-
tering step to the LD W eaver pipeline to overcome the inability
of pairwise methods to distinguish ‘direct’ associations. For
a dataset with 100 000 SNPs, MI values will be computed
for approximately 5 billion unique links. When performing
GWES, the interest is typically focussed on links with high MI
values (i.e. with larger than normal linkage). However, many
of these links will be driven by the same underlying associa-
tion. Identifying the causal link is extremely challenging, es-
pecially for bacterial data due to factors such as clonality and
genome plasticity ( 80 ).
Given multiple links that can be explained by the same un-
derlying causal effect, we use ARACNE to retain only the link
with the strongest signal (called a ‘direct’ link). This can re-
duce the number of links retained by several orders of mag-
nitude, greatly reducing the manual curation task. ARACNE
scans the entire LD landscape and a link ( X, Y ) is consid-
ered to be indirect if MI ( X, Y ) ≤[ MI ( X, Z ) , MI ( Z, Y ) ] for
any SNP Z. A detailed explanation of the ARACNE algorithm
and this specic ltering step is available in ( 12 ).
Detecting outliers in long-range links
Long-range (bp-sep > S ) background LD varies little with
bp-sep, so the genome clustering step that was used to model
short-range links is not required. To determine a background-
LD threshold ( 12 ), we adopt an approach similar to that of
SpydrPick in which LD W eaver computes the Tukey ( 90 ) out-
lier threshold: T
1
= Q
1
+ 1 . 5 ×I QR , where I QR = Q
1
−
Q
3 and Q
1 and Q
3 are the rst and third quartiles, respec-
tively. Links with MI > T
1 are directly ranked based on the
MI value. In cases where < 5000 links surpass T
1
, LD W eaver
retains the top 5000 (default) links based on MI value.
The Tukey outlier detection approach is simple, but we
prefer it to a permutation approach for two reasons. Firstly,
this threshold has limited impact on the long-range GWES
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4 NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2
analysis itself. While an outlier is dened based on whether
its MI value passes this threshold, it has no bearing on link
ranking itself. Downstream analysis and the eventual manual
curation can be performed on the highest-ranked subset of
ARACNE direct links without requiring a threshold. Secondly,
due to the high degree of LD observed in bacteria, the back-
ground MI values computed from the observed MSA could be
larger than the null MI values computed from a label-shufed
model. Therefore, the computed permutation threshold could
potentially be too conservative.
While LD W eaver can perform GWES analysis on both
short- and long-range links, it is fully compatible with the
SpydrPick output for long-range link analysis. For a dataset
that has already been analysed using SpydrPick, users have
the option to rst perform only the short-range analysis in
LD W eaver, then present the SpydrPick output as input to LD-
Weaver to perform the downstream analyses of long-range
links.
Downstream analyses and visualizing putative links
and sites.
We have integrated several powerful R visualization tools into
LD W eaver ( 91 ,92 ). To prioritize and perform wet-lab based
modelling and validation, it is helpful to understand the func-
tional annotations of the SNPs involved in high-MI links.
Therefore, functional annotations are added to all such SNPs
using SnpEff ( 29 ). Additionally, LD W eaver classies each SNP
as non-synonymous, synonymous, or intergenic. The non-
synonymous versus synonymous distinction is based on the
most common allele at multi-allelic sites. Based on this clas-
sication, LD W eaver generates an additional output compris-
ing, by default, a set of 250 top ranked links excluding links
between two synonymous sites.
GWES Manhattan plots were introduced to visualize the
distribution of MI as a function of bp-sep ( 12 ). LD W eaver
generates the long-range GWES plot introduced in SpydrPick,
along with two plots for short-range links. The rst short-
range plot is similar to the long-range GWES plot but with
points shaded according to the srp value. The second plot
shows the segregation of links into genomic clusters. While
these plots are less informative compared to Manhattan plots
in genome-wide association studies (GWAS) due to the lack of
genomic positions, they can be useful to assess the LD-decay
t between ˆ
q
95
and the genomic data.
LD W eaver also generates a linear tanglegram using the R
package ChromoMap ( 93 ) to indicate the genomic positions
of top ranked links in the short range. These tanglegrams span
the whole genome and are broken down into segments for im-
proved utility . Additionally , LD W eaver generates a gure de-
picting a genome-wide overview of the LD structure in the
dataset. First, a sparse, SNP-level LD matrix is created using
the MI values of the saved link data. Then, an averaging kernel
is applied to reduce the dimensions of the matrix to approxi-
mately 1000 ×1000 ( 94 ). The resulting matrix is plotted in
the form of a heatmap with SNP positions as x and y labels
( 95 ). This bird’s-eye view can be useful in some analyses to
quickly identify high-LD regions and blocks.
Additionally, LD W eaver generates a network plot for top
ranked links using the R package ggraph ( 96 ). The gene-level
regions of each site are extracted from the annotations le
and the links between these regions are coerced into a net-
work ( 97 ). To reduce clutter in the network plot, edges with
only 1 link between nodes are removed. Afterwards, any nodes
with no edges between them are also dropped from the plot.
The edges are coloured to depict the number of links between
genes. Furthermore, the edge width and transparency are also
moderated to reect the MI value of the highest ranked link
between the two regions. Furthermore, LD W eaver provides
the option to generate a similar gene network for any chosen
gene. The user can decide whether to use short-range, long-
range or both link lists to generate this plot.
Using a user-provided phylogeny, LD W eaver can generate
a tree-plot of user-determined putative sites and phenotypes.
This type of plot is inspired by some of the visualization op-
tions available in Microreact ( 98 ) and has also been widely
used in the previous GWES literature ( 11 ,15 ). The phylogeny
will be midpoint rooted by default ( 99 ,100 ) and the SNP data,
user provided phenotypes are sorted in the same order as the
phylogeny . Finally , the plot is generated using the R package
ggtree ( 101 ).
Finally, LD W eaver generates the output required to
dynamically visualize links using the R package GWE-
SExplorer ( https:// github.com/ jurikuronen/ GWES-Explorer ).
This Node.js based shiny app can be used to generate the
GWES Manhattan plot, circular tanglegram and the tree-plot
for an arbitrarily chosen subset of putative links.
Runtime
A complete LD W eaver analysis with default parameters on a
dataset comprising 2000 sequences with 80 000 SNPs on av-
erage requires 4756 s ( ∼80 min) on a computer with 32GB of
ram and 10 parallel CPU cores running R version 4.2.2 with
openBLAS v0.3.21 support.
Results
Overview of LDWeaver
Performing GWES analysis using LD W eaver requires two in-
puts, a multiple sequence alignment (MSA) and the annotation
le of the reference in Genbank or Gff3 format. Initially, LD-
Weaver lters out sites with low minor allele frequency (de-
fault: 0.01) and high gap frequency (default: 0.15), with an
option for a ‘relaxed’ lter to retain sites with gap (N) as
the second most common allele. Following SpydrPick ( 12 ),
LD between each SNP pair is measured using mutual infor-
mation (MI). To address population structure, a sequence-
reweighting approach is applied, where the weight for each
sequence is computed as the reciprocal of the number of se-
quences with a mean per-site Hamming distance below a user
denable threshold (default: 0.1).
Generally, SNPs in genomic proximity tend to have very
high LD, but LD levels rapidly decline with base-pair distance
to a constant value for all long-range SNP pairs (see Figure
1 A). First, LD W eaver uses a user-denable genomic distance
threshold to classify short range links (default: links between
sites < 20 kb apart are considered short range). To determine
a threshold for outlier calling, it is necessary to model the de-
cay in LD with genomic distance and the shape of this decay
is determined by many factors. These may include the type of
species, population structure, local mutation and recombina-
tion rates, variation in gene content and selection pressures. To
account for this heterogeneity, LD W eaver measures the per-
site mean Hamming distance within coding regions around
the chromosome and clusters them using k -means based on
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NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2 5
Figure 1.
Ov ervie w of the LD Wea v er pipeline. ( A ) Genome-wide linkage disequilibrium (LD) f or 1480 Camp ylobacter jejuni isolates ( 26 ). LD is measured
using mutual information (MI) and a weighting strategy is emplo y ed to account for population str uct ure. T he ax es correspond to genomic positions in the
NCTC 1 1 1 68 reference genome, and the colour intensity reects the strength of LD . Blue triangles outline regions of long-range LD , while the
short-range high-LD region is outlined in red. ( B ) Genomic diversity (measured using Hamming distance compared to the reference) within each coding
region (CDS) is used to account for local variation in short-range background LD. Each point corresponds to a CDS, and the vertical axis shows the
a v erage number of sites that differ from the reference. K-means clustering is used to divide the CDS into three clusters (see legend). Sites from
intergenic regions are allocated to the nearest cluster. ( C–F ) GWES Manhattan plots show the distribution of LD measured using weighted MI ( y -axis) at
varying genomic distances ( x -axis). Fo r better visualisation in this overview gure, numeric values are removed from the y -axis. All links (between
synon ymous, non-synon ymous and intergenic sites) are included in these plots. Plots are sho wn f or short-range links in the three clusters (C–E) and
long-range links (F). Modelled background LD is shown respectively using red, green, blue, and black dashed lines, respectively. The colour shading of
each point indicates the ranking given to outlier links (see the colour bar in the rightmost panel - numeric values removed to reduce clutter). The topmost
(bright red) colour signies rank 1, highlighting the most extreme outlier. Decreasing ranks follow the colour bar from top-bottom. Fo r short- and long-
range analyses, link ranking is based on the estimated short-range P -value and the measured MI, respectively (see Materials and methods). Links that
are either inferred as indirect or with MI below the background LD are shown in grey and not ranked. In (F) the background LD is invariant to genomic
distance and computed using the Tuk e y criteria (dashed black line). ( G ) The LDWeaver network plot generated for metE summarises all the outlier links
in v olving a site in the gene. Here, the edges are coloured based on the number of links between linked genomic region nodes (see Campylobacter
results section). ( H ) In v estigating the allele distribution within the linked region (alleles panel) shows that several deletions and mutations observed
within se v eral clonal comple x es are driving the high LD signal pick ed up b y LD Wea v er. T his and the subsequent ph ylogenetic trees sho wn in this
manuscript were generated using FastTree 2 ( 10 2 ).
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6 NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2
the estimated local diversity (see Figure 1 B). Based on the out-
put in Figure 1 B (generated by LD W eaver), the user has the
option to select the most appropriate number of clusters for
the dataset (default: 3).
Background decay in LD is modelled separately for each
cluster. Here, a linear model is tted to log transformed 95th
percentile MI values and the corresponding base pair separa-
tion. Afterwards, the exponent of tted values is used as the
base pair separation dependent background LD (see Figure
1 C–E). Since long-range background LD is uniform (see Fig-
ure 1 F), the Tukey outlier approach in SpydrPick can be used
to estimate the background LD.
After calling outliers based on the estimated background
LD, LD W eaver provides a list of locus pairs ranked in or-
der of strength of evidence for co-selection. This ranking is
based on the outlier short-range P -value (see Materials and
Methods). LD W eaver includes several options to ease the task
of generating a list of potential epistatic SNP-pairs for ex-
pert manual curation and wet lab validation. First, all out-
lier links are annotated using SnpEff ( 29 ) and links that in-
clude a non-synonymous substitution are given a higher pri-
ority. Afterwards, this SNP classication is leveraged to gen-
erate an additional output comprising a set of (default: 250)
top-ranked links after discarding links between two synony-
mous sites. All short-range results presented in this manuscript
using real data are based on analysing these top 250 most sig-
nicant links. Furthermore, LD W eaver summarizes links into
networks (see Figure 1 G), which helps to prioritize the most
promising genome regions. Finally, LD W eaver can be used to
visualize the allele distributions within these networks (see
Figure 1 H).
LDWeaver detects co-selection signals in simulated
genomes.
With the detection of long-range links validated previously
( 12 ), the primary objective here is to detect links short-range
under epistasis by looking for signs of co-selection between
SNPs. We validated LDWeaver using Wright-Fisher models
representing several evolutionary scenarios that were simu-
lated using SLiM version 4 ( 30 ). Although the original de-
sign of SLiM does not support simulating bacterial evolu-
tion, recent advances ( 31 ) now enable considering circular
genomes, horizontal gene transfer, and bacterial recombina-
tion. Notably, SLiM is one of the only available options with
the ability to simulate epistasis in bacterial populations and
generate full genome alignments as output, which is necessary
for LD W eaver analysis.
To make the simulations as realistic as possible, we chose
the rst 200 kb from the ATCC 700669 ( S. pneumoniae ) refer-
ence genome as the ancestral sequence. Each simulation com-
prised 10 000 isolates, equally distributed across 10 subpop-
ulations. Recombination tract lengths were drawn from a ge-
ometric distribution with a mean of 500 bp, while mutation
and recombination rates were xed at 2e-7 (per bp, per gen-
eration) and 8e-7 (per bp, per generation), respectively. The
simulations allowed migration between all 10 subpopulations
at a rate of 5e-2 (per bp, per generation).
Introducing positive or negative synergistic epistasis alone
led to a loss of genetic diversity through xations after several
generations, which stands in contrast with observations in real
bacterial populations ( 32 ). While such epistatic interactions
are undoubtedly present in bacterial populations, these simu-
lations lack the complexity needed to model the processes that
continuously shape the LD within populations. To address this
and to maintain more realistic levels of genetic diversity, we
opted to simulate a balancing selection scenario employing a
version of negative multiplicative (synergistic) epistasis.
We identied the 22 longest coding regions (CDS) from
within the rst 200kb of the ATCC700669 reference genome,
each with length > 1500 bp, as potential ‘target regions’ for
epistatic interactions. The distribution of these 22 regions on
the genome is illustrated in Figure 2 A. Initially, each CDS was
randomly allocated to one of ve groups represented here us-
ing different colours: magenta, green, blue, purple and orange
(see Figure 2 ). Utilizing these groups, we constructed ve sim-
ulation scenarios, denoted as s1 - s5 . In s1 , all 22 CDS from
the ve groups were selected as targets , covering a combined
target region length of 23.8% of the total genome. For s2 ,
four groups were chosen, resulting in 18 target CDS cover-
ing 20.8% of the genome. Similarly, s3 involved three groups
with 14 CDS with 17.5% coverage, s4 involved two groups
with 10 CDS with 13.7% coverage, and s5 involved only one
group with six CDS and 9.5% coverage. This design ensures
that s5 is considerably more challenging than s1 because only
two orange regions near 70 Kb (see Figure 2 A) can contribute
to ‘between target-region’ short-range links. The remaining
target links in s5 are from ‘within target-regions’.
For all simulation scenarios, three types of mutations were
introduced to the population. All regions outside the target
CDS were assigned mutation type m1 , which had a slightly
deleterious selection coefcient of −0.00001, reecting the as-
sumed near-neutrality in bacterial genomes. The target CDS
were randomly allocated either mutation type m2 or m3 , both
were benecial with an additive selection coefcient of 0.001.
Since both mutation types had the same effect, in the ab-
sence of epistasis, they would x after several generations. An
epistatic interaction was introduced between m2 and m3 ; car-
rying both will result in a 5% reduction in tness.
The simulation was continued for 20000 generations and
1000 genotypes were sampled at the end. Each scenario ( s1–
s5 ) was replicated 100 times, totalling 500 simulations. At the
end of each replicate, the extracted genome alignment was
used for LD W eaver analysis. Importantly, since this simulation
does not account for the complexities of amino acid modi-
cations, SnpEff annotations were avoided, and no distinc-
tions were made between synonymous and non-synonymous
mutations.
In s1 , only 2.4% of examined links were true target links
(i.e. a link from within or between two target CDS regions),
which reduced to 1.3% for s5 (see Supplementary Ta bl e S1 ).
Since LD W eaver is primarily a link ranking algorithm, its per-
formance was evaluated based on its ability to include target
links in the top subset of ranked links. This best aligns with
the analysis method used for real biological data presented in
the manuscript.
For scenarios s1– s5 , 70.4%, 62.6%, 61.8%, 52.4% and
49.8% of top 5 ranked links were target links, respectively.
Next, examining the top 20 ranked links revealed that at least
one target link appeared in all 400 replicates for s1– s4 , and in
97 of 100 s5 replicates (see Figure 2 B). Furthermore, compar-
ing the top 25 link ranking to a random allocation revealed
that LD W eaver performs approx. 30 times better across all
scenarios (see Supplementary Figure S1 ).
Finally, to assess the possibility of a target link being tagged
by an alternative site in genomic proximity due to LD, we cal-
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NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2 7
Figure 2. Validation of LD Wea v er using bacterial population simulations. ( A ) Simulated genomic region (rst 200kb of ATCC700669) showing the target
Coding Sequences (CDS). In each simulation scenario, grouped target CDS (depicted by colours) were chosen for epistatic interactions. In s1 , all 22 CDS
selected and in s5 , only the 6 CDS in the orange group were selected (see main text for a detailed breakdown). ( B ) For each simulation (see legend),
each curve shows the variation between the number of links c hec ked in ranking order ( x -axis) and the probability of detecting a ‘target link’, a link from
within or between two target regions ( y -axis). This reaches 1 when all replicates contain a target link. All replicates from s1–s4 and 97% of replicates
from the most challenging s5 contain a target link within the top 20 ranked . The challenge in s5 is 2-fold: only < 10% of the genome is under epistasis,
and only two orange regions near position 70 Kb (panel a) can contribute to ‘bet ween t arget-region’ short-range links. ( C ) For each simulation scenario
( x -axis), y -axis shows the genomic dist ance between sites in the top 5 ranked links and the closest target region. Most replicates in s1–s5 contain at
least one target link in the top 5 ranked (blue diamond shows median = 0, purple diamond shows mean < 3, which increases from s1 to s5 ). Each
orange dot corresponds to a replicate that does not contain a target link, and the y -axis shows the minimum genomic distance from a target region to a
site. To elaborate, two replicates in s1 do not contain a target region link in the top 5 ranked , and the closest site in each case is approx. 10 0 and 500 bp
to a target region.
culated the genomic distance between all 10 detected sites and
their closest target regions for the top 5 ranked links in each
replicate (see Figure 2 C). In replicates containing a target link
within the top 5 ranked, this distance is 0. For others, it rep-
resents the distance to the nearest target region for the site
that is in the closest genomic proximity to a target region.
The analysis revealed that 94.2% of replicates contain a tar-
get link in the top 5 ranked, as indicated by a median distance
of 0.
LDWeaver detects co-evolutionary links in multiple
pathways in S. pneumoniae.
S. pneumoniae is a naturally transformable nasopharyngeal
commensal and respiratory pathogen. It causes a substantial
global disease burden in humans, representing a major cause
of pneumonia, meningitis, and otitis media. There are > 100
immunologically distinct capsule types, termed serotypes, of
S. pneumoniae . Serotype replacement after the introduction
of pneumococcal conjugate vaccines (PCVs) is a serious con-
cern, particularly given the association of many pneumococcal
genotypes with multidrug resistance ( 33 ).
The LD W eaver analysis of pneumococci focussed on two
populations isolated from carriage in contrasting settings:
Mae La, Thailand and Massachusetts, USA. The Mae La
sample comprised 2663 high quality assemblies (accessions
available in Supplementary information ) ( 32 ) collected from
mother and infant pairs ( 34 ). The Massachusetts sample
( 25 ) comprised 616 draft genomes (accessions available in
Supplementary information ) of similar quality ( 32 ). Both
datasets were aligned to the ATC C 700669 (accession code
FM211187) reference genome ( 35 ), and after ltering out
sites with minor allele frequency (MAF) < 0.01 and gap fre-
quency > 0.15, respectively 88603 and 89386 SNPs were
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8 NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2
retained for analysis (see Supplementary Figures S2 and S3
for LD W eaver plot panels). Analysed and detected link counts
are summarised in Supplementary Table S2 .
Long-range interactions included strong signals of co-
evolution between pbp2b and pbp2x in both populations.
These genes are key in determining resistance to beta lactam
antibiotics and these interactions were reported previously
( 12 ). Another interaction conserved across both populations
was that between three loci encoding immunogenic surface-
exposed degradative enzymes ( 36 ): the beta-galactosidase
BgaA, the immunoglobulin A protease ZmpA, and PabB, en-
coded by a gene directly downstream of that for the ZmpA
paralogue, ZmpB. These co-evolutionary signals may arise
through direct interactions on the surface, or indirect effects
emerging through immune selection for particular combina-
tions of antigens ( 37 ).
The short-range interactions were more similar between
the two populations. Adjacent genes functioning in the
same metabolic pathway included links consistently iden-
tied between the neighbouring coding sequences cdsH
(SPN23F08030) and thiI (SPN23F08040), which are both in-
volved in thiamine biosynthesis ( 38 ). Similarly, the adjacent
genes SPN23F02450 and SPN23F02460 both encode proteins
predicted to function as N-acetyltransferases. Signals were
also identied in both populations between the overlapping
genes SPN23F08250 and SPN23F08260, encoding subunits
of a transporter of unknown function ( 39 ). Hence, LDweaver
can identify signals of proteins likely to be co-evolving as par-
ticipants in the same metabolic pathways.
Another regulatory locus involved in short range interac-
tions across both datasets is that encoding the competence reg-
ulator TfoX. Multiple sites were in strong LD in the subset of
isolates encoding this locus, which was absent in a minority of
isolates (see Figure 3 A). Yet these sites are not in the gene itself,
but in the anking intergenic regions, or the adjacent alaDH
pseudogene that encodes an apparently functionally unrelated
alanine dehydrogenase. This suggests that these paired sites do
not interact functionally. A search for the functional sequence
of the alaDH gene identied intact versions in other strepto-
cocci. Further alignments indicated that the tfoX-alaDH pair-
ing was intact in Streptococcus anginosu s. Hence, the vari-
able distribution of this locus in S. pneumoniae is likely the
consequence of one, or more, interspecies transfers through
homologous recombination introducing the gene cassette into
pneumococci, followed by degradation of the alaDH gene into
a non-functional form ( 40 ). Hence the elevated LD identied
in this case may be the consequence of a relatively recent in-
trogression ( 41 ) from another streptococcal species, demon-
strating LD W eaver can identify loci under sufciently strong
selection to drive interspecies transfers ( 40 ).
Another transporter (encoded by SPN23F03500) was
linked to an adjacent pseudogene (SPN23F03510) in both
populations (see Supplementary Figure S4 ). The undisrupted
sequence of SPN23F03510 is predicted to function as a lan-
tibiotic synthesis protein, suggesting the associated trans-
porter is likely to be a self-immunity protein. Hence, this pair-
ing likely represents an example of a non-producing, immune-
only ‘cheater’ bacteriocin phenotype ( 42 ), common in pneu-
mococci ( 43 ). The most variable bacteriocin-encoding locus
in the pneumococcal genome is the blp gene cluster ( 44 ),
in which multiple interactions between genes were detected.
These included interactions between the genes encoding the
BlpRH quorum sensing two component system, and the gene
encoding the cognate peptide pheromone, BlpC ( 45 ), identi-
ed in both populations. Further links were found in the Mas-
sachusetts sample only, which likely represent relationships
between the synthesized bacteriocins and corresponding im-
munity proteins ( 44 ).
In addition to performing biological analyses, we used the
Massachusetts dataset to compare the effect of varying the
CDS clustering parameter ( k ). We repeated the LD W eaver
analysis using k = 1, 3 and 5 and tted the decay model to the
95th percentile of the empirical distribution. Fitted parame-
ters for each case are shown in Supplementary Tab l e S3 . Each
parameter pair corresponds to the slope and intercept of the
tted model (see Materials and methods). Corresponding de-
cay curves are shown in Supplementary Figure S5 a. Next, we
examined the variation between the top 250 ranked links from
each analysis. Links between the same coding regions were
pooled together irrespective of the ranking and the counts are
shown in Supplementary Figure S5 (b). Here, the qualitative
difference between the choice of k = 1 and k = 3 is clear,
however, choosing between k = 3 and k = 5 only results in a
marginal difference.
LDWeaver identies patterns of co-evolution of
cytolethal distending protein toxin subunits in
C. jejuni
C. jejuni is a leading cause of food-borne bacterial gastroen-
teritis worldwide, associated with the consumption of con-
taminated poultry meat. It is well-adapted to colonize the gut
of the majority of mammalian and avian host species and has
been isolated from many environmental sources. The success-
ful colonization of strains is often host-specic for the major-
ity of lineages (specialist clonal complexes) and this is reected
in the population structure during phylogenetic comparison of
genomes. Certain clonal complexes (CCs) are also known to
be host generalists, where the same lineage is well-adapted to
colonize and to survive in multiple different hosts.
The population of C. jejuni is structured by well-dened, ge-
netically similar clusters of isolates (clonal complexes) which
are documented to be maintained over time ( 26 ), despite the
very frequent homologous recombination occurring across
the known lineages ( 26 ,46 ). This high frequency of recom-
bination, which is not limited to any particular region of
the genome, would generally break down the LD observed
in C. jejuni lineages and therefore, potentially disrupt co-
selected / epistatic functional groups of genes throughout the
genome. Despite the high recombination, the population
structure has remained stable over long periods of time ( 26 ),
making C. jejuni an excellent candidate species for the analysis
of short- and long-range epistasis and co-selection links.
A collection of 1480 previously published C. jejuni genomes
( 26 ) consisting of 18 different human, animal, and environ-
mental sources and 37 CCs were selected for LD W eaver analy-
sis (accessions available in Supplementary information ). These
were aligned against the NCTC 11168 reference genome ( 47 )
using snippy. After removing sites with MAF < 0.01 and gap
frequency > 0.15, 102591 SNPs were retained for LD W eaver
analysis (see Supplementary Figure S6 for the LD W eaver plot
panel).
Analysis of short-range interactions identied strong sig-
nals of co-evolution between genes with functions mostly
related to virulence such as: amino acid ABC transporters,
agellar biosynthesis, periplasmic and outer membrane pro-
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NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2 9
Figure 3. Ov ervie w of genomic v ariations of the anking region of the Tf oX competence regulator demonstrated using the Massac huset ts S.
pneumoniae dataset. ( A ) T he ph ylogenetic tree ( n = 616) is coloured according to the serotype shown to the right of the tree. The 4 bars immediately to
the right denote the antimicrobial resistance data for ceftriaxone, erythromycin, benzyl penicillin and trimethoprim, respectively. The key above indicates
the colour shadings for S – sensitive, I – intermediate and R – resistant. Allelic variation in the tfoX locus is shown by the rightmost heatmap and the k e y
abo v e sho ws the colour f or each nucleotide with N indicating an ambiguous base. SNP positions abo v e the heatmap are based on the ATCC 700669
reference. This suggests that the tfoX locus is present in most pneumococci and can be divided into three genotypes: that containing the major alleles
at each polymorphic site; that containing the minor alleles at sites 850664 and 852539, and that containing the minor alleles at these two sites, as well
as sites 851543 and 852789. ( B ) The alignment of representatives of the four observed genotypes in the dataset, demonstrated here using sample data
from selected isolates. Colour shading indicates the identity between regions. In ND6000 (ERR129187) and CH2106 (ERR129095), the anking region is
intact with multiple insertion sequences, two functional genes, a non-coding region and an alaDH pseudogene. The locus is intact, but the insertion
sequences are not observed in BR1 07 6 (ERR129048). In contrast, the entire locus is missing in BR1058 (ERR129043). With reference to the
phylogenetic tree in (A): ND60 0 0 is a serotype 7C isolate between regions 19 F and 11 A , CH2106 is a 19 F isolate, BR1 07 6 is 6C isolate and BR1058 is a
7C isolate. ( C ) Shows the alignment between FM21 1 187 and S. anginosus NCTC10713 genomes. For the region of interest, this is the most similar locus
among streptococcal species. Despite the general divergence between S. pneumoniae and S. anginosus , the tfoX-alaDH gene pair is intact in both
species with high similarity (same k e y as in (B) to show region identity). Ho w e v er, the dissimilarity between the anking regions demonstrates the
typical le v el of div ergence betw een the genomes. Hence, the localiz ed similarity indicates a possible recent introgression into the pneumococcus.
teins, antibiotic efux genes, among others. One of the most
promising ndings was multiple highly signicant links lo-
cated within the cytolethal distending toxin (CDT) genomic
region. The CDT is a protein toxin composed of three sub-
units: CdtA, CdtB and CdtC encoded by a cdtABC operon,
and is considered one of the most important virulence factors
for Campylobacter pathogenesis. CDT acts to halt host cell
division by cell cycle arrest at the G
2 stage occurring before
mitosis ( 48 ). CdtA and CdtC are anchored into the membrane
and act to deliver CdtB to the host cell which arrests the cell
cycle. CdtB has the toxin activity but is reliant on CdtA and
CdtC for its binding and delivery to the host cell ( 49 ).
Our results showed that the three subunits were well con-
served throughout the dataset, except for three distinct clus-
ters of isolates identied in wild birds (see Figure 4 ). There
was high variability of the presence / absence and allelic vari-
ation of the three CDT subunits across these three clus-
ters of isolates. For example, all three subunits were ab-
sent from the wild bird-associated ST-1287 CC. Another
wild bird-associated clade, ST-1034 CC (mixed) consisted of
synonymous / non-synonymous nucleotide changes in all sub-
units compared with other sources. Finally, isolates belonging
to the third wild bird-associated clade, ST-1325 CC consisted
of a mix of both the same synonymous / non-synonymous nu-
cleotide changes as seen in ST-1034 CC, some of the isolates
in this cluster also exhibited the same variation as observed in
the other sources and CCs within the dataset, while some iso-
lates had an absence of various CDT subunits (see Figure 4 ).
A recent study comparing the gene sequences of the cdtABC
operon of wild bird, broiler chicken and human sources ( 50 )
conrms the LD W eaver-generated hypothesis of signicant
co-selection occurring within this operon. The study identi-
ed high variability of cdtABC alleles in wild birds with sev-
eral alleles producing no functional CDT. Sequence conser-
vation outside of wild bird sources, such as broiler chickens
and humans, was also observed, suggesting that the variation
of the cdtABC operon may play a role in the host range of
Campylobacter ( 50 ).
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10 NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2
Figure 4. Ov ervie w of allelic v ariation of CDT subunits in the C. jejuni dataset. ( A ) T he ph ylogenetic tree ( n = 1480) is coloured according to the clonal
complex and the key to the left of the tree is labelled according to the corresponding topology of each clonal complex. Allelic variation of the three CDT
subunits (CdtA, CdtB and CdtC ( x axis )) encoded by the cdtABC operon across the tree is represented by the heatmap to the right of the tree. ( B ) The
association of a particular clonal complex with a source is highlighted by the rst panel. The darker the shading (explained by percentage keys at the
bottom of the panel), the higher the percent age of isolates from each source belonging to the particular clonal complex (rows). The rows are ordered by
abundance (column N ) in the C. jejuni dataset. Three panels to the right represent the allelic variation within CdtA (red), CdtB (blue) and CdtC (green)
subunits. The shading represents the percentage of isolates associated with a particular clonal complex / source with either: 1) the unaltered allele; 2) a
nucleotide change (mutated); or, 3) a deletion of the CDT subunit. Shaded k e y s at the bottom of the three panels represent the percentage of isolates.
Potential co-selection was also identied in the gene cluster
containing genes metE and metF (see Figure 1 ). These genes
are located on an operon involved in methionine synthesis
which has been proven to have a vital role in the colonisa-
tion of C. jejuni to the gastrointestinal tract of different hosts
(Kelley et al., 2021). Similar patterns of the presence / absence
and mutated versions of this locus were observed within the
same wild bird clusters as the cdtABC operon (Figures 1 H
and 3 ) while also remaining relatively conserved in the remain-
ing sources and CCs.
In addition to performing biological analyses, in C. jejuni ,
we also explored the impact of the choice of background LD
modelling (LD W eaver approximate vs. using a neutral simu-
lation) on short-range outlier ranking ( Supplementary Figure
S7 ). Link ranking was robust to the modelling choice for gen-
erally high LD links (MI > 0.5) ( Supplementary Figure S7 a),
however, the LD W eaver model allocates systematically higher
ranks to links that are further apart ( Supplementary Figure
S7 b). Given the primary goal of short-range epistasis analysis
is to accurately rank high LD outliers in genomic proximity,
these ndings indicate that the choice of background LD mod-
elling has a minimal impact. Furthermore, both approaches
on average allocate the same score to links between same site
pairs ( Supplementary Figure S7 c).
LDWeaver recapitulates co-evolving links involved
in clade evolution and success of the E. coli
pandemic clone ST131
To investigate epistasis and co-selection in E. coli , we consid-
ered a dataset consisting of 2156 ST131 genome assemblies
(accessions available in Supplementary information ) aligned
against the EC958 reference genome ( 51 ) using Snippy. Loci
with MAF ≥0.01 and gap frequency < 0.15 were included,
leading to 44 092 SNPs (see Supplementary Figure S8 for the
LD W eaver plot panel). It is noted that the E. coli dataset had
the highest amount of LD among all analysed datasets, and
the asymptote of Supplementary Figure S8 b cluster 1 has the
largest intercept among all LD W eaver panel plots.
The E. coli ST131 lineage belongs to the phylogroup B2
that emerged globally around 20 years ago and is associated
with urinary tract (UTI) and bloodstream infections (BSI) ( 52–
54 ). Large epidemiological studies have identied major dif-
ferences in the virulence and antibiotic resistance between the
three main clades of ST131 (A, B and C) ( 55 ). Clade C, which
is associated with uoroquinolone resistance arising from mu-
tations in gyrA and parC has further been split into two sub-
lineages (C1 and C2) with a distinct pattern of mobile ge-
netic elements (MGEs) and associated antimicrobial resistance
(AMR) genes ( 56 ,57 ).
The long-range loci pairs in E. coli ST131 corresponded
to clade C specic SNPs differentiating sub-lineages C1
and C2 ( 58 ). These included links between sites in sbmA
(EC958_0513), a transporter involved in the internalisation
of peptide antibiotics into the cytoplasm ( 59 ) and identied
as a virulence factor in avian extraintestinal E. coli (APEC)
( 60 ), and sites in (i) nikA (EC958_3870), a periplasmic pro-
tein from the ATP-binding cassette type nickel transport sys-
tem acting as the initial receptor of nickel ( 61 ), (ii) acrF
(EC958_4822) encoding an efux pump with homology to
the major pump AcrB ( 62 ), (iii) lepA (EC958_2875) encod-
ing a conserved GTPase with a role in the initiation phase
of translation ( 63 ) and (iv) iscS (EC958_2841) , encoding a
cysteine desulfurase implicated in the activity of a number of
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NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2 11
Fe-S proteins ( 64 ). These clade-specic SNP pairs are spread
across the E. coli chromosome, separated by at least 1 Mbp,
and may have contributed to the recent expansion of the E.
coli sub-lineage C2.
The genome wide distribution of LD estimated from LD-
Weaver revealed multiple interesting patterns (see Figure 5 ).
For example, the short-range co-evolving SNP pairs highly
ranked by LD W eaver correspond to regions involved in
the synthesis of the E. coli capsule polysaccharide ( kpsM
EC958_3343 , kpsC EC958_3337 , kpsS EC958_3338 ) and
type II secretion system located downstream in the chromo-
some ( gspL EC958_3345 , gspM EC958_3344). The observed
tight linkage in the E. coli capsular region might be critical for
having a functional system since the capsule plays an impor-
tant role as a major virulence factor contributing to
the colonization of different eukaryotic host niches, reduc-
ing the efcacy of the immune system by complement inacti-
vation and shaping the horizontal gene transfer mediated by
MGEs ( 65–67 ). These results indicate that the variation within
the capsule region is also
linked to SNPs present in the conserved type II secretion
system. Variation in these regions could thus alter the capsule
expression in E. coli , contributing to a non-capsulated state
that allows the introduction of a new pool of MGEs ( 67 ).
LDWeaver detects novel interactions between sites
associated with virulence in E. faecalis .
E. faecalis represents a classical generalist microorganism,
with little phylogenetic divergence and limited host special-
ization over the population ( 68 ). Few hospital-associated E.
faecalis clusters have been identied, with some overrepre-
sentation of virulence factors and AMR genes ( 28 ,69 ). How-
ever, these lineages as well as the traits potentially underlying
their success predate the modern hospital settings ( 28 ,70 ). The
E. faecalis dataset analysed using LD W eaver comprised 2027
isolates (accessions available in Supplementary information )
aligned against the V583 reference genome ( 71 ) using Snippy.
After ltering out sites with MAF < 0.01 and gap fre-
quency > 0.15, we analysed 85982 SNPs (see Supplementary
Figure S9 for the LD W eaver plot panel).
Inspecting the short-range links within the E. faecalis pop-
ulation revealed multiple top-ranking links in known entero-
coccal virulence genes. Particularly, the elr operon was repre-
sented in several links (see Supplementary Figure S10 ). The
genes in the elr operon code for putative surface proteins and
their overexpression have been associated with increased vir-
ulence and ability to evade host immune defence by resistance
to phagocytosis ( 72 ). Three elr genes, elrB, elrC and elrR , were
linked to each other, and the positive regulator elrE ( 73 ) was
also linked to an ATP-binding cassette transporter.
Another cluster of links involved ace , a widespread viru-
lence gene in E. faecalis , coding for adherence factor ( 74 ,75 ).
In addition to a gene coding for a hypothetical protein, it
was linked to a bacteriocin-encoding entV . This bacteriocin
has been shown to act against fungal Candida albicans co-
infection by the inhibition of biolm formation ( 76 ,77 ) . In-
triguingly, the absence of ace has also been shown to result
in reduced biolm formation in vivo , but despite both ace
and entV being partly involved in biolm-associated entero-
coccal infections ( 78 ), we are not aware of any report of a
direct link between the functions of the two. These ndings
demonstrate the ability of LD W eaver to highlight both known
and putative functional links between enterococcal genes.
Supplementary Figure S10 further illustrates that the minor al-
lele haplotypes at the candidate sites under co-selection are not
enriched in hospital-associated multi-drug resistant lineages.
Given that the ages of these lineages have been estimated as
50–150 years ( 28 ), and that they all share the major alle-
les at these variable sites, the co-selective pressure may have
acted more recently in some other ecological setting outside
hospitals.
Discussion
Bacterial population genomics research is rapidly moving to-
wards an era where hundreds of thousands of whole-genome
sequences will be available for many species. These data repre-
sent an unprecedented opportunity to seek signals of selection
in natural populations and to unravel genomic clues for adap-
tation under changing ecology, which can contribute towards
improved understanding about evolution, dissemination and
maintenance of antibiotic resistance and virulence traits. Ex-
isting GWES methodology has already enabled discoveries of
co-selection affecting polymorphisms across distant genomic
sites in a variety of human pathogens ( 13–15 ). By extending
GWES to joint screening of polymorphisms in close proximity,
we increase the potential of data-driven molecular discovery
for bacterial populations, which are particularly challenging
for GWAS due to the difculty of large-scale measurement of
traits.
Applying our methodology across a diverse spectrum of
bacterial species: S. pneumoniae , C. jejuni , E. coli and E. fae-
calis , has revealed fresh insights into genomic interactions be-
tween proximate variants . Notably, our results were obtained
without use of phenotype data and would not be detected
via conventional genome-wide association (GWAS) methods
as they would typically be discarded due to the inuence of
short-range linkage disequilibrium. Our results included nd-
ings associated with host range, antibiotic resistance, viru-
lence, and immune evasion. Furthermore, our top results of-
ten represented links from genomic islands: tfoX in S. pneu-
moniae , cdtABC in C. jejuni, capsular locus in E. coli and
elr genes in E. faecalis , all of which are self-contained units
that may evolve differently to the rest of the chromosome
due to reduced functional integration. While these novel po-
tential interactions require experimental validation, our ap-
proach drastically reduces the number of pairwise relation-
ships that need to be considered. Recent advances in compu-
tational protein structure prediction could further reduce the
need for time-consuming wet-lab experiments by rapidly con-
sidering the impacts of the identied intragenic interactions
on the resulting protein structure.
A potential target for further development of genome-wide
short-range LD analysis is to consider genomic variation be-
yond reference-based core genome alignments. With the in-
creasing availability of long-read based assemblies of chromo-
somes and plasmids, it would be attractive to consider detec-
tion of co-selection both within plasmids and between plasmid
and host chromosome polymorphisms, to potentially uncover
either compensatory evolution or pre-adaptation to stable car-
riage of particular plasmids ( 79 ).
Furthermore, while wet-lab-based validation will remain
the gold standard to verify combined effects of mutations,
future developments should incorporate information beyond
the DNA sequence, such as gene expression levels, protein
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12 NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2
Figure 5. Genome-wide distribution of e x cess LD in the E. coli ST131 dataset ( n = 2156) measured using LD Wea v er. Appro ximate genomic positions
are marked to the right and bottom of the LD map as per the EC958 reference genome. Brown shading indicates the amount of LD between sites (see
k e y at bottom right for MI values scaled between 0 and 1). Entire genomic regions without excess LD are dropped from the gure to enhance the
visibility of variation within high LD regions and each new region is coloured in an alternating shade of blue and purple in the right panel. Additionally, the
right panel shows genomic regions comprising short-range excess-LD links.
structure alterations and epigenetic variations, which has the
potential to greatly contribute towards improved detection.
Using only DNA sequence information about LD is lim-
iting because, in addition to selection acting on combined
sets of mutations, LD signals can reect evolutionary factors
such as population expansion, elevated mutation rates, and
hitchhiking.
Given its existing and future potential for enabling molec-
ular discoveries, we anticipate that GWES will continue to at-
tract a wide interest from both methodological and applied
perspectives.
Data availability
LD W eaver v. 1 . 5 is available as an R package under a GNU
General Public License (Version 3) on GitHub ( https://github.
com/ Sudaraka88/ LD W eaver ) and the source code is available
on Zenodo ( https:// zenodo.org/ records/ 10016711 ). Genomic
data accessions used in this analysis are available via gshare
( https:// doi.org/ 10.6084/ m9.gshare.24079491 ). An interac-
tive phylogenetic tree (Figure 3 A) clearly marking the detected
isolates can be accessed on microreact ( https://microreact.org/
project/s94ZeKRZUSkz7JZrkwsuFY-spnmschtree ).
Supplementary data
Supplementary Data are available at NARGAB Online.
Funding
J.C. and G.T.H. were funded by NFR [299941]; S.M., N.M.,
S.A.-A., R.A.G. and A.K.P. were funded by the AMR grant
from Trond Mohn Foundation; S.M., N.M. and S.A.-A.
were additionally funded by Marie Skłodowska-Curie Actions
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NAR Genomics and Bioinformatics , 2024, Vol. 6, No. 2 13
[801133]; N.J.C. was supported by a Sir Henry Dale Fel-
lowship, jointly funded by Wellcome and the Royal Society
[104169 / Z / 14 / A; https:// wellcome.org/ ; https:// royalsociety.
org/]. The funders had no role in study design, method de-
velopment and analysis nor interpretation of the results, writ-
ing of the report, and the decision to submit the paper for
publication.
Conict of interest statement
None declared.
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Received: February 11, 2024. Revised: April 15, 2024. Editorial Decision: May 13, 2024. Accepted: May 14, 2024
©The Author(s) 2024. Published by Oxford University Press on behalf of NAR Genomics and Bioinformatics.
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