In the last decade well beyond half a million bacterial genomes have been sequenced worldwide, about 7% of these from Mycobacterium tuberculosis (MTB) strains (Blackwell et al., 2021). One of the reasons behind these extensive sequencing efforts is the use of whole genome sequencing in molecular epidemiology. Molecular epidemiology studies of MTB (and of other pathogens) use microbial genome sequences sampled from different patients to investigate epidemiological dynamics such as transmission, relapses, and the acquisition and spread of antibiotic resistance (Hatherell et al., 2016; Guthrie and Gardy, 2017; Nikolayevskyy et al., 2019). One of the most popular approaches to analyze this data is to cluster strains in groups based on their genetic distance. The identification of clustered MTB strains is commonly interpreted as evidence for recent local transmission, while patients infected with non-clustered strains (singletons) are thought to be novel introductions (i.e. patients that got infected somewhere else). Similarly, when studying the epidemiology of antibiotic resistance, clustered strains are considered as cases of transmission of resistance, while singletons are thought to be more likely to represent instances of resistance acquisition (Hatherell et al., 2016).

In MTB studies, clusters are often defined based on a single nucleotide polymorphism (SNP) threshold: strains with fewer SNPs than a given threshold are grouped together in the same cluster. However, this has been criticized, because it is not clear which value should be used (Stimson et al., 2019). A review of more than 30 publications concluded that a threshold of six SNPs could be used to identify cases of direct transmission (Nikolayevskyy et al., 2019), but other studies proposed different thresholds for different settings (see Table 1 in Hatherell et al., 2016 for some examples). Alternative approaches have been proposed to overcome the limits of SNP thresholds. For example, the method proposed by Stimson et al., 2019 groups strains based on a probabilistic model that takes into account the clock rate and the time of sampling. Other studies sidestepped the choice of one specific value by performing clustering multiple times with different thresholds, and comparing the results (Holt et al., 2018; Meehan et al., 2018; Yang et al., 2018; López et al., 2020; Shuaib et al., 2020; Cox et al., 2021, Liu et al., 2021; Walter et al., 2022; Yang et al., 2022). Despite their limitations, clustering methods are considered useful to study transmission dynamics in MTB. Many studies tested the association of clustered strains with host and bacterial sub-populations, such as different age groups, HIV-positive patients, bacterial lineages and others (Guerra-Assunção et al., 2015; Asare et al., 2020; Sobkowiak et al., 2020; Cox et al., 2021, Gygli et al., 2021; Merker et al., 2021; Yang et al., 2022). In these analyses, a positive association is interpreted as evidence for increased transmission of a certain sub-population. Further studies used clustering rates (the percentage of clustered strains), to characterize the extent of transmission in bacterial sub-populations (Holt et al., 2018; Shuaib et al., 2020). For example, Holt et al., 2018 found that in Vietnam, MTB Lineage 2 (L2) had higher clustering rates compared to MTB Lineage 4 (L4) and MTB Lineage 1 (L1), and interpreted these results as evidence for more frequent transmission of L2 strains, compared to L4 and L1 strains. Finally, in recent studies the distribution of terminal branch lengths (TBL) was used as a proxy for transmissibility in different MTB lineages (Holt et al., 2018; Freschi et al., 2021; Walter et al., 2022), partially complementing classical clustering analyses. All these approaches are based on the assumption that increased transmission results in increased clustering rates and shorter terminal branches. However, it is known that other factors could influence the results of clustering, for example it was posited that higher rates of molecular evolution, and low sampling rates should lead to lower clustering rates (Stimson et al., 2019, Menardo et al., 2019).

There is a consensus that epidemiological dynamics have an influence on the shape of MTB phylogenies, and therefore on clustering and TBL, though how they do so was never explored with quantitative studies. Here, I used simulations to explore what factors influence clustering results and TBL in MTB epidemics. I simulated the molecular evolution of MTB strains under different epidemiological conditions. I then inferred phylogenetic trees and computed clustering rates and TBL from the simulated data. With this approach I investigated the molecular clock rate, sampling proportion, sampling period, transmission rate, basic reproductive number (R0), length of the latency period, and length of the infectious period. I found that all these factors affect the results of clustering and TBL, except for the length of the infectious period. These results are in contradiction with the standard interpretation of MTB epidemiological studies, namely that sub-populations associated with clustering and shorter terminal branches are necessarily transmitting more.

To investigate the expected patterns of genetic diversity under different epidemiological conditions, I assembled a pipeline to simulate the evolution of MTB genomes in different epidemiological settings (Figure 1). The details are reported in the Materials and methods section. Briefly, the pipeline simulates a transmission tree using a birth-death model in which transmission events occur at rate λ and originate in the infectious compartment I, leading to a new exposed individual in compartment E. Exposed individuals become infectious at rate ψ, by moving from compartment E to compartment I. The time spent in the compartment E represents the latency period. Individuals are removed from compartment I by death or self-cure, occurring at rate σ, or sampling, occurring at rate ε. The sampling rate ε corresponds to the rate at which infectious individuals are diagnosed and treated. With the onset of treatment, it is assumed that patients stop being infectious immediately. The time spent in compartment I represents the infectious period.

Figure 1

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A similar epidemiological model was used previously in a phylodynamic analysis of two MTB outbreaks (Kühnert et al., 2016; Kühnert et al., 2018). In a second step, the pipeline simulates the evolution of genome sequences along the tree given a clock rate π, and it computes the clustering rates under different SNP thresholds, and the terminal branch lengths. This pipeline allows to test how clustering rates and TBL distributions change under different sampling proportions, sampling periods, molecular clock rates, transmission rates, basic reproductive numbers (R0 = λ/(σ+ε)), lengths of the latency period (determined by ψ), and lengths of the infectious period (determined by σ+ε). Moreover, with this approach it is possible to investigate how the different factors impact the choice of a sensible SNP threshold. To do this, I defined the ‘95% sensitivity SNP threshold’ as the minimum threshold for which at least 95% of strains are clustered in at least 95% of the simulations. A lower SNP threshold would lead to lower sensitivity (i.e. simulated samples, which are the result of recent transmission, would not be clustered), while a larger threshold would lead to low specificity, although this cannot be quantified with this analysis (see Materials and methods for additional information).

Latency

Next, I tested whether differences in the duration of the latent period could result in different clustering rates and TBL. Here, latency is defined as the period in which an individual is infected but not yet infectious. Typically, the shift to infectiousness in TB patients is considered to occur with the onset of symptoms. However, in recent years, the importance of sub-clinical TB has been reconsidered. It is possible that a considerable part of TB transmission occurs from asymptomatic patients, although this has not been yet quantified (Kendall et al., 2021). Given the uncertainty about the length of the latent period I tested three different rates of progression to infectiousness ψ=0.5, 1, 2, corresponding to a median latent period of ~16.6, 8.3, and 4.2 months, respectively. These values represent the range of duration of asymptomatic infection estimated in different countries (Ku et al., 2021). All other parameters were constant in all simulations (π=8 × 10^–8; σ = ε=0.5; λ=1, sampling period = 10 years). I found that longer latency resulted in lower clustering rates and longer TBL (Figure 2, Table 1). Correspondingly, the 95% sensitivity threshold was 10, 6, and 5 SNPs, and the mean of the TBL distribution was 0.87, 0.56, and 0.41, respectively for long, mid, and short latency.

Figure 2

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Table 1

Scenario	λ	ε	R0	σ	ψ	π	95% SNP threshold	100% SNP threshold	95% CI TBL	MeanTBL
Short latency	1	0.5	1	0.5	2	8 × 10–8	5	15	0–2	0.41
Mid latency	1	0.5	1	0.5	1	8 × 10–8	6	17	0–3	0.56
Long latency	1	0.5	1	0.5	0.5	8 × 10–8	10	20	0–5	0.87

Transmission, infectious period, and R0

I tested how different transmission and sampling rates impact the results of clustering and the TBL distributions. In these analyses, I set the death rate σ to zero, so that all individuals are sampled, and the length of the infectious period is therefore determined by the sampling rate ε. I found that clustering results and TBL depend on the transmission rate, with higher values leading to higher clustering rates and shorter TBL. Conversely, the sampling rate had no major effect (Appendix 5). I tested whether the threshold on the minimum tree size could bias these analyses (the difference from Appendix 4 is that R0 can be different from one). I found that different thresholds on the minimum number of tips sampled in the simulated tree can influence clustering and TBL, but for the settings used in this study this effect was negligible, and the results were robust to different thresholds (Appendix 5).

Sampling and transmission rates are particularly interesting parameters because together they determine R0, and whether the epidemic will grow or shrink. R0 is the ratio between the rate at which infectious individuals are created (numerator) and the rate at which infectious individuals are removed (denominator). If the numerator is larger than the denominator the epidemic will grow (R0 >1). Conversely, if the denominator is larger than the numerator the epidemic will shrink (R0 <1). Specifically, with the epidemiological model used in this study the numerator is the transmission rate (λ), while the denominator is determined by the sum of the sampling and death rates (σ+ε), so that R0 = λ / (σ +ε). Because only the numerator affects the results of clustering rates and TBL, changes in these two metrics will correlate with R0 only when the denominator (σ +ε) is fixed. To show this I tested three different sampling rates: ε=0.5, 1, and 2, corresponding to a median infectious period of ~16.6, 8.3, and 4.2 months, respectively. These values cover well the possible length of the symptomatic period estimated in different countries (Ku et al., 2021). For each value of ε, I considered three different transmission rates leading to three scenarios: a shrinking epidemic with R0=0.9, a stable epidemic with R0=1, and a growing epidemic with R0=1.1. All other parameters were constant in all simulations (Table 2). When considering scenarios with different sampling rates, and therefore infectious periods, I found no correlation between R0 and clustering rates, nor between R0 and TBL distributions. However, when the duration of the infection period, and all other parameters (except the transmission rate) were fixed, larger values of R0 correlated with higher clustering rates and shorter TBL (Table 2, Figure 3).

Table 2

Scenario(Median infectious period (months) - R0)	λ	ε	R0	σ	ψ	π	95% SNP threshold	100% SNP threshold	95% CI TBL	Mean TBL
Long infectious period, shrinking (17–0.9)	0.45	0.5	0.9	0	1	8 × 10–8	7	16	0–3	0.62
Long infectious period, stable (17 - 1)	0.5	0.5	1	0	1	8 × 10–8	6	16	0–3	0.59
Long infectious period, growing (17–1.1)	0.55	0.5	1.1	0	1	8 × 10–8	6	16	0–3	0.57
Medium infectious period, shrinking (8–0.9)	0.9	1	0.9	0	1	8 × 10–8	5	16	0–3	0.41
Medium infectious period, stable (8 - 1)	1	1	1	0	1	8 × 10–8	5	15	0–2	0.38
Medium infectious period, growing (8–1.1)	1.1	1	1.1	0	1	8 × 10–8	4	16	0–2	0.37
Short infectious period, shrinking (4–0.9)	1.8	2	0.9	0	1	8 × 10–8	5	14	0–2	0.31
Short infectious period, stable (4 - 1)	2	2	1	0	1	8 × 10–8	4	15	0–2	0.29
Short infectious period, growing (4–1.1)	2.2	2	1.1	0	1	8 × 10–8	3	17	0–2	0.27

Figure 3

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An example

The results reported above have important implications on the interpretation of molecular epidemiology studies of MTB. To illustrate this in practice let’s consider an example in which two different strains of MTB are causing an epidemic in the same area. The two strains have different epidemiological and biological characteristics. We can think about it like two lineages of MTB, but it could also be two different clones belonging to the same lineage. MTB type 1 is expanding, with a R0 of 1.1, and it is characterized by a slow disease progression, with a median latency period of about one year. Type 1 populations are expected to increase by ~150% every 10 years. Conversely type 2 is shrinking, with a R0 of 0.9, and it is characterized by a shorter median latency period, approximately 5 months. Type 2 populations are expected to shrink by ~50% every 10 years. In addition, type 1 and 2 have moderate differences in their rate of molecular evolution, with a clock rate of respectively 1 × 10^–7 and 7 × 10^–8 nucleotide changes per site per year. In all other aspects the two types are identical. Obviously, under this scenario, type 1 is much more concerning for public health compared to type 2, at least in the long term. I repeated the same analysis presented above for the two types (Table 3).

Table 3

Scenario	λ	ε	R0	σ	ψ	π	95% SNP threshold	100% SNP threshold	95% CI TBL	Mean TBL
Type 1	1.1	0.5	1.1	0.5	0.7	1 × 10–7	8	21	0–4	0.82
Type 2	0.9	0.5	0.9	0.5	1.7	7 × 10–8	5	13	0–2	0.40

Type 2 showed shorter terminal branches: the mean of the TBL distribution was 0.84 and 0.4 SNPs for type 1 and type 2, respectively. Moreover, type 2 had higher clustering rates (Figure 4), and the 95% sensitivity threshold was 8 and 5 SNPs for type 1 and 2, respectively. A typical interpretation of this data would be that type 2 is transmitting more than type 1, because of the shorter terminal branches, and the higher clustering rates. Alternatively, if we picked a specific threshold, we would find that type 2 strains are associated with clustering (for lower thresholds), or that there are no differences in clustering among the two types (for higher thresholds). In any case, a classic molecular epidemiology analysis would conclude that type 2 is transmitting more than type 1, or that there are no differences in transmission between the two types. However, the shorter TBL and larger clustering rates of type 2 are due to its shorter latency and lower clock rate, not to increased transmission. Type 2 has a lower transmission rate compared to type 1, and it is bound to extinction, while type 1 is growing exponentially. This example shows the pitfalls of TBL and clustering analyses to study transmission in MTB epidemics. Admittedly, the simulation parameters for this example were picked to highlight the potential problems. However, the epidemiological characteristics of circulating MTB strains are normally not known, and the differences in latency and clock rates used here are possible. The length of the latent period and the clock rates are well within the range of values estimated with different data sets (Menardo et al., 2019; Ku et al., 2021). Overall, these results show that the standard interpretation of clustering results and TBL distributions can potentially be misleading in some epidemiological settings.

Figure 4

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The current manuscript is a computational study, so no data have been generated for this manuscript. Modelling code and simulation results are available at https://github.com/fmenardo/sim_cluster_MTB, (copy archived at swh:1:rev:aa2e0bb7629c46e64a099247d225466615b55b07).

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Author details

1. Fabrizio Menardo

   Department of Plant and Microbial Biology, University of Zurich, Zurich, Switzerland

   Contribution

   Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Software, Visualization, Writing - original draft, Writing - review and editing

   For correspondence

   fabrizio.menardo@uzh.ch

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7885-4482

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