Understanding drivers of phylogenetic clustering and terminal branch lengths distribution in epidemics of Mycobacterium tuberculosis
Abstract
Detecting factors associated with transmission is important to understand disease epidemics, and to design effective public health measures. Clustering and terminal branch lengths (TBL) analyses are commonly applied to genomic data sets of Mycobacterium tuberculosis (MTB) to identify subpopulations with increased transmission. Here, I used a simulationbased approach to investigate what epidemiological processes influence the results of clustering and TBL analyses, and whether differences in transmission can be detected with these methods. I simulated MTB epidemics with different dynamics (latency, infectious period, transmission rate, basic reproductive number R0, sampling proportion, sampling period, and molecular clock), and found that all considered factors, except for the length of the infectious period, affect the results of clustering and TBL distributions. I show that standard interpretations of this type of analyses ignore two main caveats: (1) clustering results and TBL depend on many factors that have nothing to do with transmission, (2) clustering results and TBL do not tell anything about whether the epidemic is stable, growing, or shrinking, unless all the additional parameters that influence these metrics are known, or assumed identical between subpopulations. An important consequence is that the optimal SNP threshold for clustering depends on the epidemiological conditions, and that subpopulations with different epidemiological characteristics should not be analyzed with the same threshold. Finally, these results suggest that different clustering rates and TBL distributions, that are found consistently between different MTB lineages, are probably due to intrinsic bacterial factors, and do not indicate necessarily differences in transmission or evolutionary success.
Editor's evaluation
Grouping pathogen genomes into clusters is a key tool in genomic epidemiology. In this paper, the author takes a simulationbased approach to investigate the epidemiological processes that influence clustering in tuberculosis genomic epidemiology. The simulations explore whether differences in transmission can be detected with clusteringbased analysis. This work finds that clustering can be impacted by sampling strategy as well as by changes in transmission and population dynamics, and draws out some interpretations of these results for users of clustering in this field.
https://doi.org/10.7554/eLife.76780.sa0Introduction
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 nonclustered 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 subpopulations, such as different age groups, HIVpositive patients, bacterial lineages and others (GuerraAssunção 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 subpopulation. Further studies used clustering rates (the percentage of clustered strains), to characterize the extent of transmission in bacterial subpopulations (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 subpopulations associated with clustering and shorter terminal branches are necessarily transmitting more.
Results
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 birthdeath 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 selfcure, 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.
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).
Clock rate, sampling proportion, and sampling period
First, I tested whether the clock rate, sampling proportion, and sampling period affect clustering rates and TBL. The details of these analyses are available as Appendix. I considered three different clock rates (4 × 10^{–8}, 8 × 10^{–8}, and 1.2 × 10^{–7} nucleotide changes per site per year), four sampling proportions (25%, 50%, 75%, and 100% of cases sampled), and three sampling periods (5, 10, and 20 years). For each scenario, I performed 1000 simulations and compared clustering rates and TBL. I found that: (1) higher clock rates led to lower clustering rates and longer TBL (Appendix 1), (2) lower sampling proportions resulted in lower clustering rates and longer TBL (Appendix 2), and (3) shorter sampling periods resulted in lower clustering rates and longer terminal branches (Appendix 3). Finally, I also tested whether different sample sizes could have an influence on the results of these analyses, and found that TBL and median clustering rates did not change when using a lower threshold on the minimum number of tips in the simulated tree (Appendix 4).
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 subclinical 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.
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).
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).
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.
Discussion
The interpretation of clustering rates and TBL
Especially in lowincidence regions, clustering has proved to be useful to rapidly identify outbreaks and recent transmission (see Walker et al., 2018 for an example). However, the use of clustering analyses and their interpretation has evolved with time, and went beyond the identification of linked bacterial strains. Researchers often look for association with clusters, or differences in clustering rates, to characterize the extent of transmission in different subpopulations coexisting in highincidence areas. Recently, the distribution of TBL has been used in a similar fashion.
The results presented above demonstrate that these approaches suffer from two major limitations: (1) the transmission rate (per unit of time) does correlate positively with clustering rates, and negatively with TBL. However, it is not the only factor doing so. The lengths of the latency period, the molecular clock rate, the sampling period, and the sampling proportion all influence clustering and TBL. Therefore, differences between subpopulations might have nothing to do with differences in transmission. In other words, increased clustering might be due to shorter latency, lower clock rates, longer sampling periods, or higher sampling proportion, and not to increased transmission. (2) The transmission rate expressed per unit of time does not determine the dynamic of an epidemic. Whether an epidemic, or a subpopulation is growing or not, depends on the ratio between the transmission rate (λ) and the rate at which infectious individuals stop being infectious (ε+σ). This ratio (R0) represents the average number of transmission events during an individual infectious period (transmission per generation). Unless all other parameters are held fixed, R0 does not correlate with clustering rates or TBL. Consequently, TBL and clustering rates can be used to estimate whether a subpopulation is stable, shrinking, or growing (in relative terms compared to another subpopulation), only by assuming that the clock rate, the latency and infectious periods, the sampling period, and the sampling proportion are identical in the two subpopulations. Moreover, the simple comparison of clustering rates and TBL distributions without formal statistical inference disregards stochastic effects. The same epidemiological process can generate different clustering rates and TBL. Statistical inference is necessary to test whether the observed differences are significant. Altogether, these results resonate with the findings of Poon, 2016, who reported that clustering methods used to study the epidemiology of HIV were biased towards detecting different sampling rates among subpopulations, and not variation in transmission rates.
In addition to clustering rates and TBL, researchers can use complementary data to understand the epidemiological dynamics. For example, the change through time in the proportion of cases belonging to a certain type can be used as a proxy for the relative reproductive number (i.e. if a type is increasing in proportion within a population, it should have a larger R0 compared to other types). Similarly, if the absolute number of cases is increasing, R0 should be greater than one. However, there can be confounding factors, such as the migration of strains from other regions. Finally, the length of the infectious and latent period can be estimated (with some assumptions) from prevalence surveys and notification data (Ku et al., 2021). Usually this is done at the population level, the same analysis on individual lineages, or clones, could provide useful insights on the heterogeneity of MTB populations.
Is there an optimal SNP threshold?
The optimal SNP threshold is the one that maximizes sensitivity and specificity. Here 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 (Materials and methods). In other words, this is the threshold that maximizes specificity at a 95% sensitivity level. One important result is that this threshold depends strongly on the epidemiological conditions and on the sample size: across all scenarios simulated for this study the 95% sensitivity threshold ranged between 3 and 11 SNPs, and more extreme values are not impossible. Ideally, molecular epidemiological studies should use larger thresholds for settings characterized by longer latency, lower transmission rates, shorter sampling periods, and/or lower sampling proportions. However, if a MTB population is not uniform, but consists of subpopulations with different epidemiological characteristics, or molecular clock rates, using a single SNP threshold will lead to biased results.
Biology and epidemiology of MTB lineages
The issues discussed above are most relevant when comparing different bacterial subpopulations, such as the MTB lineages. Different MTB lineages have different clustering rates and distributions of TBL, independently from the region of sampling. For example, compared to other lineages, L2 was consistently found to have shorter TBL and higher clustering rates virtually everywhere, including in Vietnam (Holt et al., 2018, Hang et al., 2019), Malawi (GuerraAssunção et al., 2015; Sobkowiak et al., 2020), Uzbekistan (Merker et al., 2018), South Africa (Cox et al., 2021), Georgia (Gygli et al., 2021), Iran (Vaziri et al., 2019), as well as globally (Freschi et al., 2021). At the opposite end of the spectrum, L1 was repeatedly found to have longer terminal branches, and lower clustering rates, compared to other lineages (GuerraAssunção et al., 2015; Holt et al., 2018, Hang et al., 2019, Sobkowiak et al., 2020; Freschi et al., 2021). This repeated pattern is probably due to intrinsic bacterial factors, which affect clustering and TBL in all epidemiological settings. Different sampling proportions and sampling periods among lineages are unlikely to be responsible for this widespread pattern. The three remaining factors that could explain the global differences between L2 and L1 are: (1) clock rates, (2) latency, and (3) transmission rates per unit of time.
A faster molecular clock for L1 would explain the lower clustering rates and longer terminal branches. However, the little evidence that is available does not support this hypothesis. L1 and L2 were found to have similar clock rates when analyzed with the same set of methods, although the uncertainty of the estimates was very large (Menardo et al., 2019). Among other studies that inferred the clock rate for L2, most confirmed a moderately high rate (~1 × 10^{–7}, Merker et al., 2018; Rutaihwa et al., 2019; Torres Ortiz et al., 2021), while one estimated a higher rate of evolution (~3 × 10^{–7}, Eldholm et al., 2016). The only additional study to attempt the estimation of the clock rate of L1 found a lack of a temporal signal (Menardo et al., 2021). Altogether the available evidence is limited, and more precise estimates are needed to understand whether the rate of molecular evolution contributes to the different clustering rates and TBL for L1 and L2.
Longer latency would cause low clustering rates and long terminal branches in L1. Here, latency is defined as the period between being infected and becoming infectious, and it is typically thought to correspond to the period of asymptomatic infection. Although, presymptomatic transmission could be more important than previously thought (Kendall et al., 2021). There is some indirect evidence for a longer asymptomatic period in L1: a recent study estimated that asymptomatic infection is longer in TB patients in Southeast Asian countries such as Lao, Cambodia, and the Philippines (Ku et al., 2021), where L1 is responsible for more than half of TB cases (Schopfer et al., 2015; Chen et al., 2017; Somphavong, 2018; Netikul et al., 2021). In these countries, latency was found to be up to three times longer compared to Pakistan, Ethiopia and Zambia, where L1 is rare (Mulenga et al., 2010; Firdessa et al., 2013; Chihota et al., 2018; Tulu and Ameni, 2018; Wiens et al., 2018; Ali et al., 2019). Moreover, it is well documented that L2 is the most virulent MTB lineage (Hanekom et al., 2011; Peters et al., 2020), while L1 is less virulent compared to L2, L3, and L4 (Bottai et al., 2020). Virulence is often measured as bacterial growth rate in animal models or in human cell lines, and it seems quite natural that an infection of faster growing bacteria would have a shorter latency period.
A higher transmission rate per unit of time would also cause higher clustering rates and lower terminal branches in L2. This is how the results of these analyses are typically interpreted. Some partial evidence for this comes from a study in The Gambia, that found that household contacts of patients infected with L2 strains were more likely to develop disease within two years, compared to contacts of patients infected with other strains (de Jong et al., 2008). This could be the result of shorter latency, or higher transmission rates for L2. If L2 has a constitutively higher transmission rate, its proportion in a MTB population is expected to be stable only if the infectious period is shorter compared to other lineages. For example, in Malawi L2 was found to have higher clustering rates compared to L1, however the proportion of cases caused by the two lineages did not change over 20 years of monitoring (Sobkowiak et al., 2020). Assuming higher transmission rates for L2, these results can only be explained with a shorter infectious period of L2 compared to L1. Similarly to latency, the period between onset of symptoms and diagnosis was estimated to be longer in Southeast Asian countries where the MTB populations are dominated by L1 (Ku et al., 2021). This trend was not as strong as in the case of latency, but this is not surprising, as the delay in seeking care and receiving treatment does not depend only on bacterial and host factors, but also on the public health system and other social conditions. As for latency, higher virulence could explain the higher transmission rate and shorter infectious period for L2 compared to L1.
To summarize, different clustering results and TBL between L1 and L2 are likely caused by differences in latency and/or transmission rate per unit of time. However, the analysis of TBL distribution and clusters cannot tease these two factors apart. In this discussion I focused on L1 and L2, as these two lineages represent the extremes in terms of clustering and TBL. For all other lineages the same logic applies, differences in latency, transmission, and clock rates influence the tree topology in different combinations, resulting in intermediate TBL and clustering rates. Importantly, the effects of all these factors are additive. For example, in a lineage with longer latency and lower clock rate, the longer latency would result in lower clustering rates and longer TBL, while the lower clock rate has the opposite effect. The outcome will be determined by the magnitude of the changes: if the variation in clock rates is large enough to compensate for the longer latency, clustering rates will be larger and TBL shorter, otherwise clustering rates will be lower, and TBL longer.
Conclusions
The take home message of this study is that clustering analyses and TBL can tell us only so much about the dynamics of MTB epidemics. While clustering will continue to be useful to detect linked strains, conclusions about differences in transmission among subpopulations are at best a simplification that conflates many different factors, at worst outright wrong. Phylodynamic methods that estimate the parameters of an epidemiological model from genomic data are becoming available (Kühnert et al., 2016; Didelot et al., 2017; Volz and Siveroni, 2018). However, these analyses have limits that cannot be overcome exclusively with phylogenetic data (Louca et al., 2021), and in any case they are challenging with current MTB data sets (Kühnert et al., 2018; Walter et al., 2022). Methodological advances, the integration of different types of data, and more complete and longer sampling series of MTB epidemics will allow to study epidemiological dynamics more accurately in the future. In the meantime, the results of clustering and TBL analyses should not be overinterpreted.
Materials and methods
Simulation pipeline
MTB epidemics were simulated using an ExposedInfectious epidemiological model. The model has two compartments, one for infectious individuals (I) and one for exposed individuals (E), the latter contains individuals that have been infected but are not yet infectious. Individuals in compartment I generate new infections adding new exposed individuals in compartment E with rate λ. Exposed individuals become infectious moving from compartment E to compartment I with rate ψ. Individuals are removed from compartment I either by death (or selfcure), occurring at rate σ or sampling, occurring at rate ε. Under this model the reproductive number R0 corresponds to λ/(σ+ε).
Each of these events is modeled as a Poisson process, so that the probability of the event to occur through time is exponentially distributed. The mean and median of the exponential distribution are calculated respectively as 1/rate and ln(2)/rate. For example, with ψ=1, the average and median latency periods are 1 and ~0.69 years, respectively.
The BEAST v2.6.6 (Bouckaert et al., 2019) package MASTER v6.1.2 (Vaughan and Drummond, 2013) was used to simulate phylogenetic trees under the parameters of the epidemiological model. Simulations were stopped after 30 years, or before in case the simulated lineage went extinct.
A postsimulation condition was implemented by specifying the minimum and maximum number of tips in the phylogenetic tree necessary to accept the simulation. This threshold regard the total number of tips sampled during the simulated period, not the number of lineages existing at the most recent time point. Unless differently specified in the text, the minimum number of tips for the simulated tree was 100, the maximum was 2500. Because different sampling periods can result in different TBL and clustering rates (see Results), for the analysis of transmission rates, infectious period, R0, and for the example, an additional postsimulation condition on the tree height was set: the simulation was accepted only if the tree height was at least 10 years. If the simulation was accepted, the tree was subsampled to the most recent 10 years of sampling, that is, all tips sampled more than 10 years before the most recent tip were discarded. In some analysis, a different sampling period was used, this was specified in the text. After this step, an outgroup was added to the phylogenetic tree, so that the tree could be rooted for downstream analyses.
Seqgen v1.3.4 (Rambaut and Grass, 1997) was used to simulate genome sequences given the phylogenetic trees and a clock rate in expected nucleotide changes per site per year. One chromosome of 4 Mb was simulated for each tip, corresponding to the size of the MTB genome that is usually considered after discarding repetitive regions (Brites et al., 2018). Simulations were run under a HKY+Γ model with transitiontransversion ratio k=2 and shape parameter for the gamma distribution α=1.
Variable sites were extracted from the whole genome alignments with SNPsites v2.5.1 (Page et al., 2016), recording the number of invariant sites. Phylogenetic trees were inferred form the SNP alignment with RAxMLNG v0.9.0 (Kozlov et al., 2019) using a HKY model, and 2 starting trees (1 random, 1 parsimony). The maximum likelihood tree was rooted using the outgroup, and the branch lengths were converted in expected number of SNPs multiplying them by the alignment length (the number of SNPs). Finally, Treecluster v1.0.3 (Balaban et al., 2019) was used to obtain clusters under different SNP thresholds t = (0, 1... 49, 50), so that the maximum pairwise distance between tips in the cluster was at most t (method ‘max’).
1000 simulations were performed for all tested conditions. Clustering rates were computed for each simulation individually, while the TBL distributions were computed merging all simulations with the same set of parameters.
The pipeline is wrapped in a python script, using Biopython v1.78 (Cock et al., 2009) and ETE3 v3.1.2 (HuertaCepas et al., 2016) to handle sequences and trees. Plots were generated with the R package ggplot2 v3.1.1 (Wickham, 2011).
The simulation pipeline, scripts and data to reproduce these results are available at https://github.com/fmenardo/sim_cluster_MTB, (copy archived at swh:1:rev:aa2e0bb7629c46e64a099247d225466615b55b07, Menardo, 2022).
Rationale for the 95% and 100% SNP thresholds
Under the model used in this study all simulated samples are, by definition, part of a single transmission chain. Therefore, the ground truth is assumed to be that all samples should be clustered. Under these conditions, the sensitivity of an SNP threshold can be estimated directly, it is the percentage of samples that are clustered. The specificity, however, cannot be estimated, as it depends on many other factors that are not included in the model (e.g. migration).
The two thresholds that are reported in the results, that is, the minimum SNP threshold at which at least 95% (or 100%) of samples are clustered in 95% of simulations, maximize specificity, at known acceptable sensitivity levels. These two thresholds are useful because they show that the specificity and sensitivity of a threshold depend on the epidemiological conditions and other factors such as clock rates and sampling (see Results).
Appendix 1
Molecular clock rate
It was pointed out previously that faster evolving lineages will accumulate more mutations, and therefore have longer TBL and lower clustering rates (Stimson et al., 2019), although this is often overlooked. I tested three different rates of molecular evolution (4 × 10^{–8}, 8 × 10^{–8} and 1.2 × 10^{–7} nucleotide changes per site per year), roughly corresponding to the range of possible clock rates in MTB (Menardo et al., 2019). All other parameters were identical in all simulations (λ = ψ=1; σ = ε=0.5, sampling time = 10 years). For this analysis, I simulated 1,000 transmission trees, I then simulated the molecular evolution with different clock rates on the same set of trees. As expected, clustering rates were higher with low clock rates (Appendix 1—figure 1), with the 95% sensitivity threshold equal to 4, 6 and 9, respectively for the lowest, mid, and highest clock rate. Also, the TBL distributions were markedly different, with longer terminal branches for faster clock rates (Appendix 1—table 1).
Appendix 2
Sampling proportion
To test how different sampling proportions affect clustering rates and TBL, I used 4 different combinations of σ and ε (0.75–0.25; 0.5–0.5; 0.25–0.75; 0–1), corresponding to 4 sampling proportions, in which 25%, 50%, 75%, and 100% of all cases are sampled. All other parameters were kept constant (π=8 × 10^{–8}, λ = ψ=1, sampling time = 10 years). Lower sampling proportions resulted in lower clustering rates and longer terminal branch lengths (Appendix 2—figure 1). The 95% sensitivity threshold was equal to 8, 6, 5, 4 for a sampling proportion of 25%, 50–75%, and 100% respectively, while the mean of the TBL distribution was 0.83, 0.56, 0.45, and 0.39 (Appendix 2—table 1).
Appendix 3
Sampling period
To test whether the length of the sampling period could affect clustering rates and TBL I simulated three different scenarios in which the only difference was that the epidemic was sampled for 5, 10, and 20 years, respectively. All other parameters were kept fixed (π=8 × 10^{–8}, λ = ψ = ε=1, σ=0). I found that shorter sampling periods resulted in lower clustering rates and longer terminal branches (Appendix 3—figure 1 and Appendix 3—table 1). This is probably because with shorter sampling periods the proportion of samples at the edges of the sampling window is larger. These samples are less likely to be clustered, as only one side of the transmission chain is present in the sample set.
Appendix 4
Minimum tree size
All results presented so far are based on the same simulation strategy: lineages are evolved for up to 30 years, or until they go extinct, and the last 10 years are sampled (except for the analysis of the sampling period, in which I tested different values, see above). The only condition imposed on a simulation to be accepted is a minimum and maximum number of tips in the transmission tree simulated by MASTER (before subsampling the last 10 years). The maximum tip number was set to 2500, which is seldom reached within 30 years of simulated evolution, while the minimum number of tips was set to 100. I tested whether a smaller minimum number of tips could change the clustering rates and TBL. I used the same settings used in the mid clock rate analysis presented above, the only difference was that the minimum number of tips was set to 25, 50, or 100. The TBL distribution showed only minor differences (Appendix 4—table 1). The median of the clustering rates was also similar for all settings, the only difference was that the distribution of clustering rates was more dispersed with a lower number of tips (Appendix 4—figure 1). This caused the 95% sensitivity thresholds to be different: 11, 8, and 6 SNPs, respectively with 25, 50, and 100 minimum tips. The larger dispersion was caused by the lower sample sizes, indeed the minimum threshold for which 100% of the samples were clustered in at least 95% of the simulations showed no trend (16, 17, and 17 SNPs from the lowest to the highest threshold).
Appendix 5
Transmission and sampling rates
I tested how the transmission and sampling rates affect the results of clustering and the TBL distribution. I used five different values for the transmission rate (λ=0.8, 0.9, 1, 1.1, 1.2), keeping all other parameters constant (π=8 × 10^{–8}, σ=0, ε=1, ψ=1, sampling time = 10 years). For these analyses I excluded all simulations in which the lineage went extinct in the first ten years, so that the sampling period of the different scenarios is similar (see Materials and methods). I found that higher transmission rates resulted in larger clustering rates and shorter TBL (Appendix 5—figure 1, Appendix 5—table 1). The 95% sensitivity threshold ranged from 6 SNPs, for λ=0.8,–4 SNPs for λ=1.2; while the mean of the TBL distribution ranged from 0.43 to 0.34, for λ=0.8 and 1.2, respectively. Next, I considered different lengths of the infectious period, to do this I used a constant transmission rate λ=1, and five different values of the sampling rate (ε=1.25,1.11111, 1, 0.90909, 0.83333), corresponding to different median infectious periods, included in the range between 6.9 and 10.4 months. I found essentially no differences in the clustering rates for different lengths of the infectious period (Appendix 5—figure 2, Appendix 5—table 2). The 95% sensitivity threshold was equal to 6 SNPs for the two shorter infectious periods (i.e. the higher sampling rates), while it was 4 SNPs for the two longer infectious periods, although this was caused by a greater dispersion of clustering rates in the former two, and there were no differences in the median values. Indeed, the minimum threshold for which 100% of the samples were clustered in at least 95% of the simulations showed no trend (14, 15, 16, 15, and 16 SNPs from the shortest to the longest infectious period). Finally, the mean of the TBL distribution was 0.38 or 0.39 for all settings.
I investigated whether the threshold on the minimum tree size could bias the analyses of scenarios with different R0. In the original analyses I accepted only simulations that resulted in at least 100 tips over the whole simulated period. I repeated these analyses using 200, 50 and 25 as alternative minimum tips thresholds. For both transmission and sampling rates I confirmed the results of the original analysis for all thresholds. Increasing transmission rates (and therefore R0) resulted in larger clustering rates and shorter terminal branches. This trend was clear for all thresholds, and it was monotone over the entire range of R0 values (0.8–1.2). Conversely, the sampling rate did not strongly affect clustering rates and TBL. There might be a weak trend towards lower clustering rates for lower sampling rates, this was similar for all thresholds, and it was mostly visible for R0 values between 0.8 and 1 (Appendix 5—figures 1–8, Appendix 5—Tables 1–8).
To explore the influence of different thresholds more directly, I compared the results obtained with the same settings and different thresholds. To limit the number of supplementary tables and figures I focused on the scenarios with R0=0.8, 1, and 1.2. When I compared the results obtained for R0=0.8, the scenario with potentially the largest bias, I found that the clustering rates and TBL were not identical when using different thresholds on the minimum tree size. There was a weak trend towards lower clustering rates for larger thresholds (on the minimum tree size), although this was not monotone for all SNP thresholds (Appendix 5—figures 9–13, Appendix 5—Tables 9–13). Additionally, for one of the analyses with R0=0.8 (λ=1 and ε=1.25) I found that larger thresholds also resulted in longer terminal branches, although the difference between the mean of the TBL distributions was smaller than 0.01 SNPs (0.3729, 0.3768, 0.3773, and 0.3815 for a threshold of 25, 50, 100, and 200, respectively). These trends were not present for larger values of R0, indicating that they are indeed a bias due to the minimum tree size, which affect scenarios with shrinking populations.
These results suggest that the threshold on the minimum tree size can bias the outcome of some analyses. However, with the settings used in this study this bias was negligible, and the results were robust to different thresholds. For the transmission rate, the trend towards larger clustering rates for higher transmission rates was clear also for scenarios with R0 equal or greater than one, these scenarios are scarcely affected by the bias, further indicating that this is a genuine trend due to the epidemiological process (Appendix 5—figures 1 and 3–5). Conversely, for the sampling rate, the observed trend was evident mostly for scenarios with R0 smaller than one, suggesting that it was caused by the threshold on the tree size (Appendix 5—figures 2 and 6–8). In any case, the differences were rather small, and I conclude that if there is any effect of the sampling rate on clustering and TBL, this is extremely weak.
Data availability
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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Decision letter

Caroline ColijnReviewing Editor; Simon Fraser University, Canada

Eduardo FrancoSenior Editor; McGill University, Canada

Jason AndrewsReviewer; Stanford University, United States

Vegard EldholmReviewer; Norwegian Institute of Public Health, Norway
Our editorial process produces two outputs: i) public reviews designed to be posted alongside the preprint for the benefit of readers; ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.
Decision letter after peer review:
Thank you for submitting your article "Understanding drivers of phylogenetic clustering and terminal branch lengths distribution in epidemics of Mycobacterium tuberculosis" for consideration by eLife. Your article has been reviewed by 2 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The following individuals involved in the review of your submission have agreed to reveal their identity: Jason Andrews (Reviewer #1); Vegard Eldholm (Reviewer #2).
We agree that this paper is interesting, timely and raises important points. As is customary in eLife, the reviewers have discussed their critiques with one another. What follows below is the Reviewing Editor's edited compilation of the essential and ancillary points provided by reviewers in their critiques and in their interaction postreview. Please submit a revised version that addresses these concerns directly. Although we expect that you will address these comments in your response letter, we also need to see the corresponding revision clearly marked in the text of the manuscript. Some of the reviewers' comments may seem to be simple queries or challenges that do not prompt revisions to the text. Please keep in mind, however, that readers may have the same perspective as the reviewers. Therefore, it is essential that you attempt to amend or expand the text to clarify the narrative accordingly.
Essential revisions:
1) Both reviewers had some comments about the simulations for R0 or 1.1 and 0.9 – additional clarity on what impacts R0, and more substantively, can TBL and clustering rate help in estimating R0, if the infectious duration is held fixed? R1 notes "These issues should be addressed and/or the conclusions about lack of ability to infer R0 differences should be tempered a bit".
2) While both reviewers (and I) really like the idea of having an illustrative example showing how this could matter in a scenario with two cocirculating lineages in the same community, the differences seem too pronounced.
3) I have an additional comment (as reviewing editor):
You note that you select simulations with 1002500 tips – how do you initialize the R0 < 1 simulations to end up with at least 100 tips? The tree size will presumably differ with different R0, as will the number of simulations you run that don't meet the size condition.
Given that you also sample in the last 10 years of the simulation. A very different fraction of the process will potentially end up in the last 10 years under the different parameters. Accordingly, the relationship between R0, TBL and clustering will be complex, and the fact that the results don't seem to be informative about R0 may be partly a result of this "simulation bias" and sampling period.
4) R1 notes that more comments on the sources of data that could help to disentangle the impact of differences in latency vs transmission would be helpful. Presumably that's a populationrepresentative sampling that would enable knowing the fraction of cases that are of the two cocirculating types, over time? Or good estimates of the infectious duration? Or either, or both.
5) Please address minor points on clarity and communication raised by the reviewers. In addition, could you comment on the mutation rate during latency, and what might the result be if mutations were not occurring during latency at the rate that they do in active disease?
Reviewer #1 (Recommendations for the authors):
Overall, the manuscript was fairly clear and straightforward to interpret, with a few comments below. The main concern I had was with the overarching conclusion that TBLs are noninformative about R0. The results show that transmission rates are associated with TBL/clustering, but the argument is that R0 is not because it depends on the ratio between the transmission rate and removal rate, each of which can alter those metrics. But it would be reasonable to make assumptions about the infectious duration, for example within a lineage and/or location, enabling comparison between variants within a lineage, within lineage over time or space, etc. Holding infectious duration constant, comparisons of R0 would then be possible through TBL or clustering. Moreover, in some cases, the infectious duration can be directly estimated (i.e. by performing a prevalence study and comparing with notifications), enabling the relation of R0 to TBL/clustering directly through transmission rates. These issues should be addressed and/or the conclusions about lack of ability to infer R0 differences should be tempered a bit. This wouldn't diminish the importance of the study, as explaining the relationship between all of these parameters and these metrics is the valuable task that this article undertakes.
Reviewer #2 (Recommendations for the authors):
First, this is a cool and timely paper, and I really like the approach.
There are however some things I believe could be clarified and perhaps explored a little bit further.
Page 7 "An example": Drawing up an example of how different characteristics of cocirculating TBtypes can result in contraintuitive findings is great. In the example, a less transmissible type nevertheless has an R0 > 1 whereas a more transmissible variant has R0 < 1. Looking at table 2, it seems evident that the more transmissible Type 2 is contracting (R0<1) due to higher cure/death rates and higher sampling compared to the less transmissible Type 1, whereas it exhibits shorter TBLs and higher clustering due to shorter latency and a slower molecular clock compared to Type 1.
I have a few questions/comments which I hope will clear this up a little bit on my part:
 I think the example would be easier to follow if you explained which of the parameters influenced the R0, TBL and clustering rate, as I have tried to do above. If my summary is not correct, I guess that illustrates that this is a bit complex for many readers.
 This is a bit embarrassing, but what specifically should sampling rate be interpreted as here, and throughout the paper? If I get this right, sampling represents both observation and removal (the patient is sampled, and hence also cured and does not transmit further)?
 I think it would also be cool with a little description of the two types in more biological/medical lingo. If I understand correctly, Type 2 is more transmissible, and also characterized by rapid onset of disease (short latency), followed by rapid death, selfcure or healthseeking. This actually makes sense, and the only reason R0 < 1 is that healthseeking, cure and death rates are even more elevated than transmissibility?
Page 3: If I'm not wrong, the model used is a form of birthdeath model? Perhaps this could be spelled out, and if not, explain how it differs from a BD model.
Suppl figures: I believe the numbering of the suppl figures in relation to the text is wrong in quite a few instances
[Editors' note: further revisions were suggested prior to acceptance, as described below.]
Thank you for resubmitting your work entitled "Understanding drivers of phylogenetic clustering and terminal branch lengths distribution in epidemics of Mycobacterium tuberculosis" for further consideration by eLife. Your revised article has been evaluated by a Senior Editor and a Reviewing Editor.
The manuscript has been improved but there are some remaining issues that need to be addressed, as outlined below:
In response to the question about bias induced by having to choose among your simulations, I fear that you have misunderstood the question and therefore haven't addressed it. (The new exploration of the impact of sampling period is nice to have, though). You write: "Regarding the settings: all simulations are initialized as a single individual, simulations that result in less than 100 tips are discarded. For R0 < 1, a larger number of simulations needs to be discarded, as trees are tendentially smaller. "
This is a source of potentially large bias because the tree you obtain is likely not to meaningfully *have* an R0 of 0.9. To grow from 1 to 100, the mean number of offspring that is realised is definitely above 1 for an extended period, even if the parameter you set in the process was such that the *expected* number was less than 1. (I would be curious to see a birthdeath simulation with an R0 of 0.9 that grows from 1 to 100 tips and last over 10 years). The probability of this growth is not zero, but it's small, so the trees you obtain are not at all representative of R0 = 0.9 trees. This means that when the clustering differs or fails to differ, you can't interpret that as being able to identify (or not) trees from R=0.9 vs R=1.1.
The tree sizes will be different too, and from coalescent theory, we know that this alone will change the patterns of genetic diversity (and hence the clustering). I would hazard that if you took simulations from identical parameters (birth, death, sampling, etc all the same) but in one set you chose the rejection criterion to have the trees need to grow bigger or last longer than in the other set, you would also find differences in clustering as a sole function of the cutoff criterion. Some portion of what you find is due probably due primarily to size and you could explore this, as well as not so dramatically biasing the trees you analyse by requiring extremely unlikely events before a tree gets into your sample.
Think of it the other way. If you took trees from a simulation with R0> 1 but you *only* looked at trees that went extinct before reaching 10 taxa, and then you did estimation or some other analysis on those trees, they would look very similar to trees with an R0 < 1 because those also die out. By removing the ones that grew you removed the information that R0 was set to be > 1. Conversely, here, by rejecting the vast majority of trees simulated under R0 < 1 that died out, you are removing the information that R0 was ever < 1.
I have asked for a revision because I think this point is not minor, as quite a bit of the paper is focused on clustering and R0 under simulations, and this same issue could impact many of them. It would be interesting to explore a genuinely declining population (rather than one that is declining in expectation because R0 < 1 but growing in its actual realisation because you start with 1 taxon and branch, rejecting those simulations that do not grow). However, initialising that population is challenging because the results would depend on the initial genetic diversity.
As a side note – under point 4 in the response, you note that "At least, in theory, all the parameters of the model can be estimated with phylodynamic analyses." But this paper finds a fundamental unidentifiability that suggests that these parameters are not identifiable: https://academic.oup.com/mbe/article/38/9/4010/6278301. They use likelihoods, not clustering, but since the likelihoods and portion clustered are fundamentally based on the branching times in the phylogenies it seems that their results would probably carry over.
https://doi.org/10.7554/eLife.76780.sa1Author response
Essential revisions:
1) Both reviewers had some comments about the simulations for R0 or 1.1 and 0.9 – additional clarity on what impacts R0, and more substantively, can TBL and clustering rate help in estimating R0, if the infectious duration is held fixed? R1 notes "These issues should be addressed and/or the conclusions about lack of ability to infer R0 differences should be tempered a bit".
Regarding the main point (“can TBL and clustering rate help in estimating R0, if the infectious duration is held fixed?”):
In empirical studies, TBL and clustering rates can be used to estimate R0 only if the clock rate, the sampling proportion, the sampling period, the length of the infectious period, and the length of the latency period are ALL known or held fixed. If the infectious period is fixed, but the other factors are not, R0 would not necessarily correlate with clustering rates and TBL. To show this more clearly, I modified the example (Page 6), which now consists of two MTB “types” with identical sampling and death rates (and therefore identical infectious period), but different latency, transmission and clock rates. One type has R0 = 0.9, and the other has R0 = 1.1 (because of different transmission rates). Again, the shrinking type resulted in larger clustering rates and shorter TBL (because of differences in clock rates and latency). This is described in the response to point (2)
I also expanded the description of what influences R0 (Page 4, Ln 146153):
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 rate and the death rate (σ+ε). R0 = λ / (σ +ε).
In nonmathematical terms R0 is determined by the relation between the transmission rate per unit of time and the average length of the infectious period (which is inversely proportional to the removal rate σ +ε). So that a large transmission rate (per unit of time) can result in a shrinking epidemic if the infectious period is very short. Conversely, a low transmission rate per unit of time can result in a growing epidemic if the infectious period is sufficiently long.
I think some confusion on these issues was generated by the order in which I presented the results. To make these points clearer I modified the structure of the Results section (Pages. 35). I also amended the abstract (Ln 21) and expanded the discussion (Page 7, Ln 234242).
2) While both reviewers (and I) really like the idea of having an illustrative example showing how this could matter in a scenario with two cocirculating lineages in the same community, the differences seem too pronounced.
The main criticism of R1 was that in the example the length of the infectious period was drastically different between the two types, and that there is no direct evidence for differences of this magnitude between strains cocirculating in the same setting. I agree with R1 that the evidence for this is indirect. Therefore, I repeated the analysis assuming identical sampling and death rates for the two types (and therefore the same infectious period), also in this case the shrinking population resulted in higher clustering rates and shorter TBL, which were caused by shorter latency and lower clock rate (Page 6).
3) I have an additional comment (as reviewing editor):
You note that you select simulations with 1002500 tips – how do you initialize the R0 < 1 simulations to end up with at least 100 tips? The tree size will presumably differ with different R0, as will the number of simulations you run that don't meet the size condition.
Given that you also sample in the last 10 years of the simulation. A very different fraction of the process will potentially end up in the last 10 years under the different parameters. Accordingly, the relationship between R0, TBL and clustering will be complex, and the fact that the results don't seem to be informative about R0 may be partly a result of this "simulation bias" and sampling period.
Thank you for this comment. In the first version of the manuscript, I did not consider a factor that could influence the results of the analysis: the sampling period.
To answer this comment, I performed an additional analysis. First, I tested whether different sampling periods can lead to differences in TBL and clustering rates (all else being equal). I tested three different values (5, 10, and 20 years of sampling), and found that indeed, shorter sampling periods resulted in lower clustering rates and longer terminal branches. This is probably because with shorter sampling periods the proportion of samples at the edges of the sampling window is larger. These samples are less likely to be clustered, as only one side of the transmission chain is present in the sample set (Page 3, Ln 108; Appendix 3).
The sampling period could potentially influence the analysis of scenarios with different R0. It is possible that scenarios with R0 < 1 result in generally shorter trees (because the lineage goes extinct within the first 10 years), potentially leading to a difference in the sampling period. Therefore, I repeated the analyses of transmission rates, infectious period, R0, and the example. In these new analyses I added an additional condition for the simulation to be accepted. If the tree height was lower than 10 years, the simulation was rejected. In this way I ensured that all simulations had similar sampling periods (~ 10 years). The results did not change, meaning that the sampling period did not bias the results of these analysis.
Regarding the settings: all simulations are initialized as a single individual, simulations that result in less than 100 tips are discarded. For R0 < 1, a larger number of simulations needs to be discarded, as trees are tendentially smaller.
4) R1 notes that more comments on the sources of data that could help to disentangle the impact of differences in latency vs transmission would be helpful. Presumably that's a populationrepresentative sampling that would enable knowing the fraction of cases that are of the two cocirculating types, over time? Or good estimates of the infectious duration? Or either, or both.
At least in theory, all the parameters of the model can be estimated with phylodynamic analyses. However, this is quite challenging for MTB data sets. In addition to clustering rates and TBL, researchers can use complementary data to understand the epidemiological dynamics. For example, the change through time in the proportion of cases belonging to a certain type can be used as a proxy for the relative reproductive number (i.e., if a type is increasing in proportion within a population, it should have a larger R0 compared to other types). Similarly, if the absolute number of cases is increasing, R0 should be greater than one. However, there can be confounding factors, such as the migration of strains from other regions. Finally, the length of the infectious and latent period can be estimated (with some assumptions) from prevalence surveys and notification data. Usually this is done at the population level, the same analysis on individual lineages, or clones, could provide useful insights on the heterogeneity of MTB populations.
I included this paragraph in the discussion (Page 7, Ln 243255).
5) Please address minor points on clarity and communication raised by the reviewers. In addition, could you comment on the mutation rate during latency, and what might the result be if mutations were not occurring during latency at the rate that they do in active disease?
I addressed all points raised by the reviewers (see below). Regarding latency and clock rates, first a clarification: here, with latency, I simply refer to the time between being infected and becoming infectious, not to a particular bacterial metabolic state (as often done in the TB literature). In any case, the effect of latency and clock rate are additive. For example: in a type with longer latency and lower clock rate during latency (which would lead to lower clock rate overall), the longer latency would result in lower clustering rates and longer TBL, while the lower clock rate has the opposite effect. The outcome will be determined by the magnitude of the changes: if the variation in clock rates is large enough to compensate for the longer latency, clustering rates will be larger and TBL shorter, otherwise clustering rates will be lower, and TBL longer.
I included this point in the discussion (Page 9, Ln 328333).
Reviewer #1 (Recommendations for the authors):
Overall, the manuscript was fairly clear and straightforward to interpret, with a few comments below. The main concern I had was with the overarching conclusion that TBLs are noninformative about R0. The results show that transmission rates are associated with TBL/clustering, but the argument is that R0 is not because it depends on the ratio between the transmission rate and removal rate, each of which can alter those metrics. But it would be reasonable to make assumptions about the infectious duration, for example within a lineage and/or location, enabling comparison between variants within a lineage, within lineage over time or space, etc. Holding infectious duration constant, comparisons of R0 would then be possible through TBL or clustering. Moreover, in some cases, the infectious duration can be directly estimated (i.e. by performing a prevalence study and comparing with notifications), enabling the relation of R0 to TBL/clustering directly through transmission rates. These issues should be addressed and/or the conclusions about lack of ability to infer R0 differences should be tempered a bit. This wouldn't diminish the importance of the study, as explaining the relationship between all of these parameters and these metrics is the valuable task that this article undertakes.
I addressed this in the answer to point (1) I report here again the main point.
In empirical studies, TBL and clustering rates could be used to estimate R0 only if the clock rate, the sampling proportion, the sampling period, the length of the infectious period, and the length of the latency period are ALL known or held fixed. If the infectious period is fixed, but the other factors are not, R0 would not necessarily correlate with clustering rates and TBL. To show this more clearly, I modified the example, which now consists of two types with identical infectious periods, but different latency, transmission, and clock rates. One type has R0 = 0.9, and the other has R0 = 1.1 (because of different transmission rates). The shrinking type resulted in higher clustering rates and shorter TBL (because of differences in clock rates and latency). This is described in the response to point (2)
I think some confusion on these issues was generated by the order in which I presented the results. To make these points clearer I modified the structure of the Results section (Pages. 35). I also amended the abstract (Ln 21) and expanded the discussion (Page 7, Ln 234242).
Reviewer #2 (Recommendations for the authors):
First, this is a cool and timely paper, and I really like the approach.
There are however some things I believe could be clarified and perhaps explored a little bit further.
Page 7 "An example": Drawing up an example of how different characteristics of cocirculating TBtypes can result in contraintuitive findings is great. In the example, a less transmissible type nevertheless has an R0 > 1 whereas a more transmissible variant has R0 < 1. Looking at table 2, it seems evident that the more transmissible Type 2 is contracting (R0<1) due to higher cure/death rates and higher sampling compared to the less transmissible Type 1, whereas it exhibits shorter TBLs and higher clustering due to shorter latency and a slower molecular clock compared to Type 1.
I have a few questions/comments which I hope will clear this up a little bit on my part:
 I think the example would be easier to follow if you explained which of the parameters influenced the R0, TBL and clustering rate, as I have tried to do above. If my summary is not correct, I guess that illustrates that this is a bit complex for many readers.
The summary of the original example is correct, there is only one missing aspect: the shorter TBL and larger clustering rates of Type 2 are indeed caused by shorter latency and lower clock rate. But, the larger transmission rate contributed to these trends as well.
In response to points 2 and 9 I changed the settings of the example, which is now simpler. In the updated version, the differences in R0 are due to different transmission rates, because the sampling and death rates are identical between the two types (therefore they have also identical infectious period). The shorter TBL and larger clustering rates of type 2 are now due to its shorter latency and lower clock rate (while the transmission rate is contrasting this trend).
I reworked the explanation of the example, because in the new version the two types are more similar to each other, it should be clearer what factors are influencing R0, TBL and clustering rates (Page 6).
 This is a bit embarrassing, but what specifically should sampling rate be interpreted as here, and throughout the paper? If I get this right, sampling represents both observation and removal (the patient is sampled, and hence also cured and does not transmit further)?
Yes, correct, the sampling rate ε is the rate at which infectious individuals are diagnosed and treated. It is assumed that these individuals stop being infectious immediately, hence they are removed from compartment I.
I added this information to the text (Page 3, Ln 9294).
 I think it would also be cool with a little description of the two types in more biological/medical lingo. If I understand correctly, Type 2 is more transmissible, and also characterized by rapid onset of disease (short latency), followed by rapid death, selfcure or healthseeking. This actually makes sense, and the only reason R0 < 1 is that healthseeking, cure and death rates are even more elevated than transmissibility?
Yes, this was correct for the original analysis. However, it was pointed by R1 that there is no direct evidence for such divergent sampling and death rates within the same community. This is a fair criticism, I personally think that different durations of the infectious period (together with different transmission rates) could in part explain different TBL and clustering rates between e.g., L1 and L2, but the evidence supporting this is indeed indirect.
In any case, I clarified the differences between the two types in the text (Page 6).
Page 3: If I'm not wrong, the model used is a form of birthdeath model? Perhaps this could be spelled out, and if not, explain how it differs from a BD model.
Yes, it is a BD model, I added this information (Page 3, Ln 88).
Suppl figures: I believe the numbering of the suppl figures in relation to the text is wrong in quite a few instances
Fixed it. Thanks, and sorry for this.
[Editors' note: further revisions were suggested prior to acceptance, as described below.]
The manuscript has been improved but there are some remaining issues that need to be addressed, as outlined below:
In response to the question about bias induced by having to choose among your simulations, I fear that you have misunderstood the question and therefore haven't addressed it. (The new exploration of the impact of sampling period is nice to have, though). You write: "Regarding the settings: all simulations are initialized as a single individual, simulations that result in less than 100 tips are discarded. For R0 < 1, a larger number of simulations needs to be discarded, as trees are tendentially smaller. "
This is a source of potentially large bias because the tree you obtain is likely not to meaningfully *have* an R0 of 0.9. To grow from 1 to 100, the mean number of offspring that is realised is definitely above 1 for an extended period, even if the parameter you set in the process was such that the *expected* number was less than 1. (I would be curious to see a birthdeath simulation with an R0 of 0.9 that grows from 1 to 100 tips and last over 10 years). The probability of this growth is not zero, but it's small, so the trees you obtain are not at all representative of R0 = 0.9 trees. This means that when the clustering differs or fails to differ, you can't interpret that as being able to identify (or not) trees from R=0.9 vs R=1.1.
Thank you for clarifying your comment, which indeed I had misunderstood in the first revision. This is an important point, before addressing it (see below), I want to clarify one detail regarding the simulations. To be accepted a simulation does not need to grow to 100 tips existing at the same time. Rather, 100 individuals must have existed over the whole simulated period. Therefore, the simulated lineages are not necessarily growing strongly, in fact some may go extinct before the end of the simulated period. These settings represent a muchreduced source of potential bias compared to what is written in the comment above.
I clarified the description of the simulation setup to avoid misunderstandings (page 10):
“A postsimulation condition was implemented by specifying the minimum and maximum number of tips in the phylogenetic tree necessary to accept the simulation. This threshold regards the total number of tips sampled during the simulated period, not the number of lineages existing at the most recent time point.”
The tree sizes will be different too, and from coalescent theory, we know that this alone will change the patterns of genetic diversity (and hence the clustering). I would hazard that if you took simulations from identical parameters (birth, death, sampling, etc all the same) but in one set you chose the rejection criterion to have the trees need to grow bigger or last longer than in the other set, you would also find differences in clustering as a sole function of the cutoff criterion.
I partially investigated this already in the first version of this manuscript (see Results at pages 34, and Appendix 4), although only for R0 = 1. In that analysis I found that different cutoff values on the minimum tree size did not change clustering rates or TBL. I now expanded this analysis and performed it also for different values of R0 confirming that the results are robust to different thresholds on the minimum tree size (see answer to next point).
Some portion of what you find is due probably due primarily to size and you could explore this, as well as not so dramatically biasing the trees you analyse by requiring extremely unlikely events before a tree gets into your sample.
Think of it the other way. If you took trees from a simulation with R0> 1 but you *only* looked at trees that went extinct before reaching 10 taxa, and then you did estimation or some other analysis on those trees, they would look very similar to trees with an R0 < 1 because those also die out. By removing the ones that grew you removed the information that R0 was set to be > 1. Conversely, here, by rejecting the vast majority of trees simulated under R0 < 1 that died out, you are removing the information that R0 was ever < 1.
I expanded the analyses investigating transmission and sampling rates (Appendix 5). I focused on these because they are the ones exploring the broadest range of R0 values (from 0.8 to 1.2). With the original settings I accepted only simulations that resulted in at least 100 tips over the whole simulated period. I repeated these analyses using 50 and 25 as alternative minimum tips thresholds, with these settings the potential bias should be reduced. In addition, I included a scenario with a larger threshold (200 tips), to observe how the results changed when increasing the potential source of bias.
For both transmission and sampling rates I confirmed the results of the original analysis for all thresholds. Increasing transmission rates (and therefore R0) resulted in larger clustering rates and shorter terminal branches. This trend was clear for all thresholds, and it was monotone over the entire range of R0 values (0.81.2). Conversely, the sampling rate did not strongly affect clustering rates and TBL. There might be a weak trend towards lower clustering rates for lower sampling rates, this was similar for all thresholds, and it was mostly visible for R0 values between 0.8 and 1 (Appendix 5 – figures 18, Appendix 5 – tables 18).
To explore the influence of different thresholds more directly, I compared the results obtained with the same settings and different thresholds. To limit the number of supplementary tables and figures I focused on the scenarios with R0 = 0.8, 1, and 1.2. When I compared the results obtained for R0 = 0.8, the scenario with potentially the largest bias, I found that the clustering rates and TBL were not identical when using different thresholds on the minimum tree size. There was a weak trend towards lower clustering rates for larger thresholds (on the minimum tree size), although this was not monotone for all SNP thresholds (Appendix 5 – figures 910, Appendix 5 – table 910). Additionally, for one of the analyses with R0 = 0.8 (λ = 1 and ε = 1.25) I found that larger thresholds also resulted in longer terminal branches, although the difference between the mean of the TBL distributions was smaller than 0.01 SNPs (0.3729, 0.3768, 0.3773, and 0.3815 for a threshold of 25, 50, 100, and 200 respectively). These trends were not present for larger values of R0, indicating that they are indeed a bias due to the minimum tree size, which affect scenarios with shrinking populations (Appendix 5 – figures 1113, Appendix 5 – tables 1113).
These results suggest that the threshold on the minimum tree size can bias the outcome of some analyses. However, with the settings used in this study this bias was negligible, and the results were robust to different thresholds. For the transmission rate, the trend towards larger clustering rates for higher transmission rates was clear also for scenarios with R0 equal or greater than one, these scenarios are scarcely affected by the bias, further indicating that this is a genuine trend due to the epidemiological process (Appendix 5 – figures 1 and 35). Conversely, for the sampling rate the observed trend was evident mostly for scenarios with R0 smaller than one, suggesting that it was caused by the threshold on the tree size (Appendix 5 – figures 2 and 68). In any case the differences were rather small, and I conclude that if there is any effect of the sampling rate on clustering and TBL, this is extremely weak.
I report all these new analyses in Appendix 5 (page 21). I also modified the manuscript (pages 45) to include the latest results.
I have asked for a revision because I think this point is not minor, as quite a bit of the paper is focused on clustering and R0 under simulations, and this same issue could impact many of them.
I agree that these aspects needed to be explored before publication. I would also like to point out that there are several factors that are not related to transmission, or R0, but influence the results of clustering and TBL (the most relevant are latency and the molecular clock rate). Therefore, this study would reach the same conclusion (i.e., that clustering rates and TBL cannot be used to identify differences in transmission or evolutionary success, unless all other factors are known or identical between subpopulations), also without including the analyses of scenarios with R0 < 1. Of course, it is much better to include these analyses, as they allow to explore the effect of the transmission and sampling rates, and therefore R0, on clustering rates and TBL, and I’m glad I could show that they are robust to different thresholds on the minimum tree size.
It would be interesting to explore a genuinely declining population (rather than one that is declining in expectation because R0 < 1 but growing in its actual realisation because you start with 1 taxon and branch, rejecting those simulations that do not grow). However, initialising that population is challenging because the results would depend on the initial genetic diversity.
The editor already identified a fundamental challenge. In a stable population (R0 = 1), 50% of the lineages existing at any time point are expected to die without transmitting further, with R0 = 0.8 this proportion rises to 60%. Therefore, if we initialize a population and consider all individuals, the clustering rate will be in large part determined by the initial genetic diversity, which has nothing to do with the simulated epidemiological processes. It would be possible to repeat this analysis several times with different “starting populations”, characterized by different underlying genealogies. However, the set of possible starting conditions is extremely large, and I believe that these analyses could not alter the main findings of this study.
As a side note – under point 4 in the response, you note that "At least, in theory, all the parameters of the model can be estimated with phylodynamic analyses." But this paper finds a fundamental unidentifiability that suggests that these parameters are not identifiable: https://academic.oup.com/mbe/article/38/9/4010/6278301. They use likelihoods, not clustering, but since the likelihoods and portion clustered are fundamentally based on the branching times in the phylogenies it seems that their results would probably carry over.
Thank you for pointing this out. I removed that sentence from the manuscript, and I amended the conclusions (pages 910), to take into account these findings:
“Phylodynamic methods that estimate the parameters of an epidemiological model from genomic data are becoming available (Kühnert et al. 2016, Didelot et al. 2017, Volz and Siveroni 2018), however, these analyses have limits that cannot be overcome exclusively with phylogenetic data (Louca et al. 2021), and in any case they are challenging with current MTB data sets (Kühnert et al. 2018, Walter et al. 2022). Methodological advances, the integration of different types of data, and more complete and longer sampling series of MTB epidemics will allow to study epidemiological dynamics more accurately in the future. In the meantime, the results of clustering and TBL analyses should not be overinterpreted.”
https://doi.org/10.7554/eLife.76780.sa2Article and author information
Author details
Funding
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (PZ00P3_193473)
 Fabrizio Menardo
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
Acknowledgements
This work was founded by the SNF Ambizione grant PZ00P3_193473. Computations were performed on the ScienceCluster at the University of Zurich.
Senior Editor
 Eduardo Franco, McGill University, Canada
Reviewing Editor
 Caroline Colijn, Simon Fraser University, Canada
Reviewers
 Jason Andrews, Stanford University, United States
 Vegard Eldholm, Norwegian Institute of Public Health, Norway
Publication history
 Preprint posted: January 3, 2022 (view preprint)
 Received: January 4, 2022
 Accepted: June 15, 2022
 Version of Record published: June 28, 2022 (version 1)
Copyright
© 2022, Menardo
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
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