Plasmid transfer rates differ depending on plasmid size and function

To investigate how plasmids move between S. sonnei lineages, we reconstructed the joint evolutionary history of S. sonnei chromosomal DNA and four plasmids (pINV, spA, spB & spC) (Figs 2 and S1). We further considered two additional alignments of the spA plasmid to explore the potential use of this new method in reconstructing the movement of specific mobile AMR elements within populations. This small plasmid contains up to four AMR genes that include strA & B, sul2, and sometimes tet(A) that were established to move between lineages. For spA, the number of reconstructed transfer events strongly depends on which part of the spA plasmid is used for the analyses (S2 Fig). For the first analyses (entire spA), we used the entire spA plasmid for isolates that had ≥70% coverage of the spA plasmid, regardless of AMR profile, with a focus on tracking the plasmid. In a second set of analyses, we used an alignment of the four AMR genes strA & B, sul2 and tet(A), that included the region between strB and tetA, which also encoded a transposase and tetR (AMR genes only dataset) (see Methods). Finally, we considered only the genes coding for strA & B and sul2 and the flanking region of ∼100 bases of strB (strA & B + sul + flanking dataset) as these three genes are known to frequently move together. S3 Fig shows the location of these genes on the spA plasmid, and it highlights the regions of the spA plasmid used. We also performed long-read sequencing using ONT platforms of selected isolates (see Methods) that are members of the clade highlighted in red in S4 Fig to determine the location of AMR genes in genomes with different coverage of the spA reference genome (S3 Fig). We made this distinction in part due to evidence that the AMR genes carried on the spA plasmid had integrated into the chromosome for some isolates for which we had lower coverage of the spA plasmid. This lower coverage suggested that these AMR genes were not being carried on the spA plasmid in these genomes (S3 Fig).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Co-divergence of the core chromosome and plasmids in Shigella sonnei.

A Proportion of lineages carrying a plasmid between 2000 and 2020. The inner shaded areas denote the 50% HPD, and the outer area is the 95% highest posterior density (HPD). The dotted lines denote the proportion of samples with a plasmid. B Here, we show the maximum clade credibility (MCC) network of Shigella sonnei inferred using the chromosomal DNA, the virulence plasmid pINV, and the small plasmids spA, spB, and spC. The MCC network is the network in the posterior distribution that maximizes the sum of clade credibility of the chromosome and plasmid trees. Vertical lines are used to denote plasmid transfer events, where the circles denote the branch to which a plasmid was transferred. The color of the circle denotes either spA, spB, or spC, having jumped between bacterial lineages. The dashed lines correspond to branches from which plasmids branch off. The tip labels in blue, green, and red denote whether a plasmid was detected in a leaf. The black dots denote the presence of antimicrobial resistance determinants to the different drug classes.

https://doi.org/10.1371/journal.ppat.1013621.g002

To illustrate the differences, we reconstructed a tanglegram from chromosomal and spA timed plasmid trees inferred using IQ-TREE 2 and TreeTime [28–30]. As shown in S4 Fig, there is evidence for multiple rearrangements between the chromosome and plasmid trees, indicating plasmids are moving. The 70% coverage cutoff used for the entire spA tree removes a group of isolates highlighted in red in S4 Fig, suggesting either that the genes present on spA changed or that the AMR genes integrated into a different plasmid or the chromosome (S3 Fig).

We next tested whether there is evidence for the different parts of spA to code for different evolutionary histories, or whether they mostly differ by their amount of genomic information. To do so, we analysed isolates that reached the coverage thresholds for all three parts of the spA plasmid as described above. We then treated them each as a separate segment in a phylogenetic network analysis and reconstructed the joint reticulation network describing the shared evolutionary history of the three parts of spA, not finding evidence for the different parts of spA to code for different evolutionary histories (see S5 Fig)

We then reconstructed the movement of the plasmids between bacterial lineages using CoalPT in three different analyses using the different spA alignments. From the overall S. sonnei dataset, we subsampled 400 isolates. For the subsampling, we used the number of available plasmid sequences per isolate as the weights in the subsampling, but did not perform any additional subsampling to have even sample numbers over time. This strategy is enriching for isolates that have more plasmids present.

Since CoalPT assumes that there is no inter-lineage recombination within chromosomes or plasmids, we masked sections with evidence of recombination in the chromosome but assumed that there is no intralineage recombination on the plasmid alignments (see Methods). We used a separate strict molecular clock and HKY+ [31] substitution model for the chromosome and for each plasmid. We additionally assume a constant-size coalescent process and infer the effective population size and the rate of plasmid transfer, allowing each plasmid to have a different transfer rate.

Modelling changing effective population sizes over time may put a change in the relative weight on longer or shorter networks, which can then lead to slightly different plasmid transfer rate estimates. However, this bias is expected to be small for cases with well-informed rates of evolution, such as provided by the chromosomal sequences here [32], and the rates across the different plasmids will be affected to a similar degree. Further, any bias is likely to be in the same direction for all plasmids. The prevalence of the smaller plasmids was relatively constant over the sampling period (S1C Fig), with spA and spC being frequently detected in different lineages and genotypes of S. sonnei (S3 and S6 Figs). In contrast, the spB plasmid was predominantly found in S. sonnei isolates belonging to genotypes that are part of global lineage III, although it was detected in six isolates in lineage 2 (S1 Table). We found little to no support for the virulence plasmid, pINV, having been transferred between different bacterial lineages, suggesting co-divergence of the chromosome and pINV (S7 Fig). This finding is consistent with the known evolution of Shigella species.

Importantly, the spA plasmid was inferred to have the highest transfer rate between bacterial lineages of S. sonnei. The spA plasmid is the only small plasmid that carries AMR determinants (S8 Fig). The other two small plasmids, spB and spC, displayed lower rates of plasmid transfer (S8 Fig). These two plasmids were inferred to have high copy numbers based on relative read depth to the chromosome from Oxford Nanopore Technologies (ONT) data and were not characterized to have any direct ability to mobilize. The number of inferred plasmid transfer events was the highest when using entire spA plasmids and the lowest when only using AMR genes. The same patterns hold when looking at the rate at which plasmids are transferred (S8 and S9 Figs), with the entire spA showing the highest transfer rate.

We next computed the rate at which plasmids are being lost in S. sonnei. We first calculated the number of times a plasmid has been lost as the number of child edges (i.e., branches) in a network for which the parent branch carries a plasmid while the child branch itself does not. We then divide this number by the total length of the plasmid tree to get an estimate of the rate at which the plasmid is lost in units of plasmid loss events per unit time. We restrict this analysis to events in the last 10 years since sample collection. We calculate this heuristic for the posterior distribution of networks to estimate the uncertainty of the heuristic. Importantly, the rate at which plasmids are lost is a heuristic based on the reconstruction networks and not directly a model parameter. In the future, this rate could be explicitly incorporated as a model parameter into CoalPT.

The virulence plasmid, which in S. sonnei is known to be often lost in culture [14,33], but it forms part of the core genome of all Shigella species, had the highest rate of being lost (S9 Fig). This was expected, given the known loss in culture. The smaller plasmids were all lost at a lower rate relative to the pINV plasmid of S. sonnei (S10 Fig). These patterns may, at least in part, be driven by the plasmids not being detected or being lost in culture, but may also reflect that these smaller plasmids have limited fitness costs and, as such, are more readily maintained. To further test this point, we performed an analysis where we modeled the presence and absence of pINV, spA, spB, and spC as a continuous-time Markov chain evolving on the chromosome [34]. We compare the rate at which plasmids are gained and lost between the true, observed data, and when we randomly permutate the tip to presence-absence mapping. We find that the rate of gain/loss for pINV is equal between the true and the permuted presence absence (see S11 Fig), indicating that the plasmid is randomly lost during the sampling process, while the three small plasmids show strong differences between the true presence absence and the permuted assignments. We also estimated the individual rates of gain and loss using this approach (see S12 Fig). While this does not fully model the ancestral history of each plasmid, we find that the estimates are broadly consistent with both our estimates using the phylogenetic network inference.

Accounting for the co-divergence of chromosomes and plasmids is essential to estimating rates of evolution in plasmids

The evolution of the genome of bacterial species occurs, in part, as a result of selective pressures on the core and accessory genomes. The core will likely be under strong selective constraints, while the accessory may be subject to weaker selection. Indeed, we find that plasmids tend to have higher molecular evolutionary clock rates than those of the chromosome (Figs 3 and S13). SNPs within the bacterial chromosome have been the focus of bacterial phylodynamics to date due to enough temporal signal in the sequence data to model the population dynamics, facilitated by the bacterial chromosome being orders of magnitude larger than some plasmids. In the case of S. sonnei, the chromosome has approximately 22 times more nucleotides than the virulence plasmid, pINV, and between ∼570 to ∼2300 times more than spA–spC. In spite of the higher rates of evolution in plasmids, compared to the chromosome, we would still expect an alignment of SNPs in the core chromosome to have a larger number of SNPs due to its sheer size. As such, plasmids are less likely to contain as much information as the chromosome and thus are less likely to behave as measurably evolving populations [35,36]. That is the measurable accumulation of genomic change over the time window of sampling. However, modelling the joint evolution of chromosomes, which are measurably evolving, and plasmids changes this. The timing of past coalescent events where chromosomal and plasmid co-diverged is potentially well informed by the chromosomal DNA, which is measurably evolving. These ’co-divergence’ events of chromosomes and plasmids can then act as calibration points to infer the rates of evolution of plasmids.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Rates of evolution for plasmids and core chromosome in Shigella sonnei.

Here, we compare estimates inferred by assuming an individual rate of evolution in units of substitutions per site per year for the chromosome and plasmids (in green) to those where we explicitly model the joint evolutionary history of these lineages as a phylogenetic network (in orange). The posterior estimates of the evolutionary rate of the chromosomal and plasmid DNA of S. sonnei sequences isolated in Melbourne, Australia, over several years. The numbers denote the mean posterior, and values in brackets are the 95% highest posterior densities (HPD).

https://doi.org/10.1371/journal.ppat.1013621.g003

To illustrate how modeling the co-divergence of the chromosomal and plasmid DNA impacts inferences of the evolutionary rate, we reconstructed the phylogenetic trees of the chromosomes, virulence (pINV), spA, spB, and spC plasmids individually (Fig 3). For the chromosome and the pINV, we used SNP alignments, which only contain the SNPs, in order to reduce the size of the dataset. For spA–spC, we used the full alignments (with gaps, Ns, and both variant and invariant sites) obtained from alignment to the reference genomes (see Methods). We used the same priors and evolutionary models (strict clock model and HKY+) as for the network inference described above and a constant coalescent population model. We then inferred the phylogenetic trees, evolutionary rates, and other parameters. For the network inference, we inferred a separate evolutionary rate for the chromosome and each plasmid. To calculate from the SNP alignment to the whole genome rate of evolution of the chromosome and the virulence plasmid, we multiply the rate estimate based on the SNP alignment by the ratio of SNP sites (11kb) over the whole genome length (4.8Mb).

As shown in S13A Fig, we found the chromosome to evolve at a rate with mean subs/site/year (95% highest posterior density, HPD ), and the virulence plasmid to evolve at a rate with mean subs/site/year (95% HPD ). The small plasmids spA–spC all evolve at substantially higher rates, with means of between and subs/site/year. Importantly, inferring these rates of evolution would be impossible using the plasmid alignments alone and thus requires information about the co-divergence of the plasmids and the chromosome.

To further explore the impact of our approach on estimates of evolutionary rates, we compared the inferred rates for plasmids using the coalescent with plasmid transfer and individual tree inference using simulations. As shown in S14 Fig, using tree inference only to retrieve rates of evolution will return the prior on the evolutionary rate, even for cases with relatively many SNPs, implying that the data are not sufficiently informative to drive the estimate of this parameter. The reason is that even in cases with many SNPs in total, the number of SNPs per time that one expects to occur over the sampling period of five years is only subs/site/year  = 0.5 SNPs for the largest plasmid. The network approach, on the other hand, is able to infer the rates of evolution of plasmids even when only a few SNPs occur (S13B Fig) because the chromosome data act as a form of molecular clock calibration and thus there is more data available for inference. Lastly, we tested whether the strict clock assumption we used for the chromosomal data was valid. We find some evidence for a higher coefficient of variation describing rate heterogeneity across lineages in the true data compared to simulated data under a strict clock, but the confidence intervals overlap (see S15 Fig). This indicates that there may be a slight variation in evolutionary rates among lineages that is not fully accounted for using the strict clock model.

Evidence for cross-species MDR plasmid exchange and steady growth of pKSR100 prevalence

We next investigated the movement of an MDR plasmid that has been previously well-characterized using genomic epidemiological approaches to be moving within and between lineages of two Shigella species, S. sonnei and S. flexneri. To do so, we compiled three alignments. We made an alignment from SNPs in the reference chromosome for both S. sonnei (n = 789 isolates) and S. flexneri (n = 297 isolates) individually (see Methods). For the MDR plasmid (pKSR100) known to circulate in both species, we aligned sequences from both species jointly. All S. sonnei and S. flexneri isolates that had ≥80% coverage of the reference plasmid were included in the alignment and a core SNP alignment with ≥95% conservation of sites (S16 Fig) (see Methods for plasmid threshold selection for alignments). We then randomly sub-sampled 250 isolates equally from S. sonnei and S. flexneri that carried the pKSR100-like plasmids (250 isolates were selected due to computational limitations). The 250 samples were chosen based on computational limitations. The chromosomal DNA of S. sonnei and S. flexneri were assumed to be their individual trees, while all samples of the pKSR100 plasmids were assumed to be from the same trees. We next reconstructed the joint evolutionary history of the core chromosome and the MDR plasmid, assuming a strict molecular clock for both the chromosome and the MDR plasmid and an HKY+ substitution model. In order to improve the computational efficiency, we fixed the rate of evolution of the core chromosomes to be equal to the estimates in S13 Fig, while estimating the rate of evolution of the MDR plasmid.

We found evidence for multiple events where the MDR plasmid jumped between bacterial lineages within species and also between species (Fig 4 and S17 Fig). These jumps between lineages were, in some cases, associated with a rapid expansion of a clade. For example, we found that the S. sonnei clade expanded after the introduction of an MDR plasmid into the bacterial lineage from S. flexneri around 2010. We next sought to distinguish introductions of the MDR plasmid into S. sonnei and S. flexneri clades by whether they likely originated from the other bacterial species or from an unknown species entirely. To do so, we followed the procedure described in Directionality of plasmid transfer. Additionally, we only considered plasmid transfer events that were introduced into S. sonnei or S. flexneri in the last 50 years. There is evidence for multiple introductions of plasmids into both species from each other (Fig 4), but also from unknown bacterial lineages, which could be other Shigella lineages or from other bacterial species in the same ecological niches, as has been previously reported [37]. We next computed the proportion of lineages in the past that carried the plasmid pKSR100. As shown in Fig 5, we find a steady increase in the proportion of bacterial lineages that carry the pKSR100 plasmid. This increase is inferred to start around the year 2010 and to continue relatively steadily until 2020, when we have the most recent samples in the dataset.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. Estimated number of cross-species movements of pKSR100 between S. sonnei and flexneri.

Here, we show the posterior estimates for the number of times where a plasmid moved between S. sonnei and S. flexneri. The assignment of directionality is based on the chromosome. For example, if the parental node at a plasmid transfer event has a chromosome belonging to S. sonnei, the origin is considered S. sonnei.

https://doi.org/10.1371/journal.ppat.1013621.g004

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. Frequency of S. sonnei and S. flexneri clusters with and without pKSR100 plasmid.

A Chromosomal trees of S. sonnei and S. flexneri with the presence or absence of pKSR100 mapped onto the plasmid tree. The width of the branches denotes the log standardized cluster size below a node relative to all other co-existing lineages. B Proportion of lineages with and without pKSR100 since 2020. The inner interval denotes the 50% highest posterior density (HPD) and the outer the 95% computed using the logged trees. C The log standardized cluster sizes below nodes with pKSR100 compared to co-existing lineages without pKSR100.

https://doi.org/10.1371/journal.ppat.1013621.g005

Ethics statement

Data were collected in accordance with the Victorian Public Health and Wellbeing Act 2008. Ethical approval was received from the University of Melbourne Human Research Ethics Committee (study number 1954615.3 and reference number 2024-30320-59894-3).

Coalescent with plasmid transfer

Bacterial lineages can exchange plasmids through different mechanisms. To model this process, we use a coalescent-based model related to the coalescent with re-assortment [26]. In the coalescent with plasmid transfer model, we model a backward-in-time process starting from sampled individuals (Fig 1). We used a separate strict molecular clock and HKY+ [31] substitution model for the chromosome and for each plasmid. The sampled individuals are required to have a chromosome but can have anywhere from 0 to n plasmid sequences. For a given effective population size, N_e, and plasmid transfer rate ρ, we sample the time to the next coalescent event (from present to past) from an exponential distribution with a rate of , where denotes the current number of lineages. The time until the next plasmid transfer event, for each individual plasmid, is drawn from an exponential distribution with mean , with ρ being the plasmid-specific transfer rate and being the number of lineages that have both the chromosome and the plasmid, or more than one plasmid, if the chromosome is absent. Upon a coalescent event, the parental lineage will carry the union of chromosomal and plasmid lineages of the two child lineages. Upon a plasmid transfer event, one plasmid lineage is randomly chosen to branch off into one parental lineage, whereas all other plasmids and the chromosomal lineages will follow the other parental lineage. This is different from how re-assortment is modeled in [26] in that a plasmid transfer occurs relative to the chromosome, and only one plasmid is transferred at a time. In other words, at each plasmid transfer event, we say one plasmid has originated from a different parental lineage than the chromosome. The backwards-in-time rate of a plasmid having originated from a different parental lineage models the forward-in-time process where exactly one plasmid moves from one bacterium to another. The method is agnostic to how a plasmid is transferred, other than the assumption that only one plasmid is transferred at a time. However, we assume that there is no interlineage recombination within the chromosomal or plasmid DNA, although this is an assumption that could potentially be relaxed in the future by employing a similar approach to [27]. Importantly, the resulting phylogenetic network is not constrained to be tree-based (as e.g [48,49]) but allowed to have any possible structure one can simulate under the coalescent with plasmid transfer.

Under a coalescent process, sampling intensity is generally assumed to be low, relative to the effective population size [50]. This assumption applies to the sampling at the level of the isolates in our model. Each isolate is assumed to have at least the chromosomal sequence. In cases where isolates do not have the full set of plasmids, the model currently treats the plasmids as missing data rather than explicitly modelling the loss of plasmids. However, an important distinction is that even when the plasmid transfer and coalescent parameters are correctly estimated, the number of plasmid transfer events inferred refers to those that explain the samples collected, and not necessarily those of the whole population, a situation that is analogous to discrete phylogeographic models [51].

Posterior distribution

In order to perform joint Bayesian inference of phylogenetic networks, the embedding of chromosome and plasmid trees, together with the parameters of the associated models, we use an MCMC algorithm to characterize the joint posterior density. The posterior density is denoted as:

(1)

where denotes the network, μ the parameters of the molecular substitution and clock model, N_e the effective population size and ρ the plasmid transfer rate. The coalescent model N_e can be any model that describes an effective population size over time, meaning it can describe a constant rate coalescent process (constant N_e) or parametric or non-parametric N_e dynamics. The plasmid transfer rate is currently assumed to be constant over time, but can vary between different plasmids. The multiple sequence alignment, that is, the data, is denoted D. denotes the network likelihood, , the network prior and the parameter priors. As is usually done in Bayesian phylogenetics, we assume that .

As is the case in coalescent approaches on trees, we condition on the sampling event, meaning that we assume the sampling events occur at predefined times. As such, the assumptions of the coalescent process apply, such as that a very small fraction of the overall population is sampled. The assumption applies at the isolate level. On the level of plasmids and chromosomes, we assume that for each type of plasmid, we have one sample per isolate. For isolates for which we do not have a specific version of a plasmid, we treat that plasmid as missing information, rather than explicitly modelling its absence. The coalescent events are assumed to happen independently of plasmid transfer events. In particular, this assumes there are no couple of coalescent/plasmid transfer events, which become more likely for very small population sizes [52].

Network likelihood.

As we assume that there is no between-lineage recombination within the chromosomal or plasmid DNA, we can simplify the network likelihood into the tree likelihood of the chromosomal and plasmid DNA. If T_i is the tree of the chromosome or plasmid (with i = 0 being the chromosome tree and i>0 being plasmid trees) and if D_i is either the chromosomal or plasmid alignment, we can write the network likelihood as:

(2)

The tree likelihood calculations use the default implementation of the tree likelihood in BEAST2 [24] and can use beagle [53] to increase the speed of likelihood calculations. Importantly, this approach allows us to use all the default substitution and clock models in BEAST2, including, for example, relaxed clock models discussed here [24].

Network prior.

The network prior is denoted by , which is the probability of observing a network and the embedding of chromosomal and plasmid trees under the coalescent with plasmid transfer model. N_e denotes the effective population size, and ρ the per plasmid transfer rate. The network prior is the equivalent of the tree prior in phylogenetic tree analyses.

We can calculate by expressing it as the product of exponential waiting times between events (i.e., plasmid transfer, coalescent, and sampling events):

(3)

where we define t_i to be the time of the i-th event and L_i to be the coexisting lineages extant immediately prior to this event.

Given that the coalescent process is a constant-size coalescent and given the i-th event is a coalescent event, the event contribution is denoted as:

(4)

If the i-th event is a plasmid transfer event and assuming a constant rate over time, the event contribution is denoted as:

(5)

This event contribution can be generalized to account for different rates of transfer for different plasmids by substituting ρ with the plasmid-specific rate depending on which plasmid was transferred. The interval contribution denotes the probability of not observing any event in a given interval. It can be computed as the product of not observing any coalescence nor any plasmid transfer event in the interval i. We can, therefore, write:

(6)

where denotes the rate of coalescence and can be expressed as:

(7)

and denotes the rate of observing a plasmid transfer event on any co-existing lineage and can be expressed as:

(8)

with n_i being the number of plasmids on and L_i existing in that interval. What the above equation means is that we can observe a plasmid transfer event only on lineages that have either the chromosome or more than one plasmid present, as we can only observe the movement of plasmids relative to other plasmids or the chromosome.

Operator descriptions

Add/remove operator. The add/remove operator adds and removes plasmid transfer events. The add/remove operator on networks is an extension of the subtree prune and regraft move for networks [54]. Similar to [27], we also added an adapted version to sample re-attachment under a coalescent distribution to increase acceptance probabilities. We show an example of such an add/remove step in S19 Fig.

Exchange operator. The exchange operator changes the attachment of edges in the network while keeping the network length constant.

Subnetwork slide operator. The subnetwork slide operator changes the height of nodes, that is, the time from a node relative to the most recent sampled individual, in the network while allowing the change in the topology.

Scale operator. The scale operator scales the heights of the root node or the whole network without changing the network topology.

Gibbs operator. The Gibbs operator samples any part of the network that is older than the root of any segment of the alignment and is thus not informed by any genetic data and is the analog to the Gibbs operator in [26] for re-assortment networks. As a Gibbs operator, this move is always accepted

Empty edge preoperator. The empty edge preoperator augments the network with edges that do not carry any loci for the duration of a move, to allow for larger jumps in network space.

The roots of phylogenetic networks can be much more distant than the roots of the individual plasmid trees. As in [27], we assume the plasmid transfer rate to be reduced prior to the individual plasmid trees having reached their root. As shown in [27], this assumption does not affect parameter inference.

For parameter inference, such as the inference of the N_e and ρ or the evolutionary parameters, we use the operators already implemented in BEAST2

Shigella dataset

S. sonnei (n = 789) and S. flexneri (n = 297) isolates (excluding S. flexneri serotype 6 isolates) received at the Microbiological Diagnostic Unit Public Health Laboratory (MDU PHL, the bacteriology reference laboratory for the state of Victoria, Australia), between January 2016 and December 2020, were included in this study. These isolates were accompanied by the year and month of collection. These isolates undergo routine WGS on Illumina NextSeq platforms using DNA extraction and sequencing protocols previously described [18].

Cluster size comparison

To get a measure of the relative fitness of lineages with and without pKSR100, we compare the number of offspring of lineages with and without the plasmid. To do so, we first map the presence and absence of pKSR100 onto the chromosomal tree. For each lineage, we then count the total number of leaves in the cluster below that node. For each node in the tree, we then compare the number of leaves below that node to the number of leaves below any other co-existing lineage. Next, we log-standardize the cluster sizes across these co-existing lineages and then compare all nodes with and without pKSR100. We do this once for the entire tree and once only for S. sonnei and S. flexneri lineages. We repeat this for all the logged iterations in the posterior distribution to get the 95 % highest posterior density interval across the different iterations.

Visualization

All plots were generated in R using ggplot2 [66], colorblindr [67], and ggpattern [68]. Convergence of MCMC chains was assessed using coda [69]. The networks and tanglegrams are plotted using an adapted version of baltic https://github.com/evogytis/baltic/.