Disease-causing microbes that infect more than one type of animal can be difficult to control. This is especially true when they infect wildlife. For example, Mycobacterium bovis is a bacterium that causes tuberculosis in tens of thousands of cattle in Britain every year and also infects badgers and other wildlife. Controlling the infections in cattle is essential, as it helps prevent the bacteria from infecting humans, improves cattle welfare and reduces the substantial costs to the livestock industry.

Analysing the relatedness of M. bovis genomes from infected cattle and badgers may help scientists work out how often badgers infect cattle and vice versa. Scientists have collected data and M. bovis samples from infected badgers in Woodchester Park, in England, for over three decades. Using these data and additional information about M. bovis infecting nearby cattle may help scientists learn how the bacteria spreads and how to stop it.

Now, Crispell et al. show that complex patterns of contact between cattle and badgers likely drive the persistence of tuberculosis in cattle, also known as bovine tuberculosis. In three separate analyses, Crispell et al. compared the genomes of M. bovis found in cattle and badgers, the animals' locations, when they were infected, and whether they could have been in contact. The analyses found that M. bovis was likely to have been transmitted more frequently from badgers to cattle rather than from cattle to badgers. They also showed that transmission within each species happened more often than transmission between species.

If these results are confirmed by other studies, they may help scientists develop better strategies for controlling tuberculosis in British cattle. In particular, controversial control strategies – such as badger culls – could be more targeted to better combat tuberculosis in cattle but have less of an impact on badgers. These insights might also aid control efforts in other countries where bovine tuberculosis is a problem and an important source of human tuberculosis.

Control of a pathogen in a system where it can infect multiple species requires an understanding of the role of each host species in the infection dynamics (Haydon et al., 2002). For example, when each host species is capable of maintaining infection independently, control operations in one species can be rendered ineffective as a result of spillover from another. Mycobacterium bovis infection in cattle populations (resulting in bovine tuberculosis - bTB) is a problem around the world (Ayele et al., 2004; Cousins and Roberts, 2001; de Kantor and Ritacco, 2006; Godfray et al., 2013; Reviriego Gordejo and Vermeersch, 2006; Schmitt et al., 2002), with many wildlife species implicated in its spread and persistence in different bTB systems (Delahay et al., 2002; Gortazar et al., 2003; Miller and Sweeney, 2013; Nugent, 2005; Nugent et al., 2015). On the islands of Britain and Ireland, the current evidence suggests that effective control of infection in cattle is hindered by transmission from an infected wildlife population – the European badger (Meles meles) (Godfray et al., 2013).

Although a considerable amount of research demonstrates an association between M. bovis found in sympatric cattle and badger populations (Balseiro et al., 2013; Goodchild et al., 2012; Olea-Popelka et al., 2005; Vial et al., 2011; Woodroffe et al., 2005), quantification of the direction and extent of transmission remains elusive. Recent studies using whole genome sequences (WGS) have demonstrated a close genetic relationship among M. bovis isolates taken from sympatric cattle and wildlife populations (Biek et al., 2012; Glaser et al., 2016; Patané et al., 2017). However, the low genomic variability of M. bovis and imbalanced sampling across host species has limited the ability to identify the direction of transmission. Evidence to date suggests that, even with access to pathogen sequence data, obtaining directional estimates of transmission might only be possible at the population level and will require dense targeted sampling and fine-grained epidemiological metadata (Kao et al., 2016; Kao et al., 2014), as has previously been demonstrated in investigations of M. tuberculosis outbreaks in humans (Bryant et al., 2013; Gardy et al., 2011; Guthrie et al., 2018; Walker et al., 2012; Walker et al., 2018; Yang et al., 2017) and in tracing between cattle herds for outbreaks of M. bovis (Biek et al., 2012; Salvador et al., 2019). However, these approaches have yet to be applied to situations where dense multi-host pathogen data are available.

Since the 1970s, a high-density naturally infected badger population at Woodchester Park in southwest England has been the subject of detailed study (Delahay et al., 2013). Both the resident badgers and sympatric cattle herds are frequently infected with M. bovis, providing the potential for inter-species transmission of infection to occur in either direction (DEFRA, 2017; Delahay et al., 2013). The data and samples associated with bTB occurrence in and around Woodchester Park are uniquely detailed, with individual-level host life history data and archived M. bovis isolates available for both the cattle (Orton et al., 2018) and badger (Delahay et al., 2013) populations. By combining WGS of selected cattle and badger isolates, with detailed local population data from this exceptionally in-depth study system, our work aimed to quantify the relative roles of the local badger and cattle populations in the spread and persistence of M. bovis in an endemic area.

Based on previous evidence of transmission between cattle and badgers, and the success of combining detailed tracing methods with WGS for M. tuberculosis, our hypothesis is that M. bovis circulation in our endemic setting is not limited to a single maintenance host and that it involves bi-directional transmission between the two host populations. Our research aimed to test this hypothesis and to quantify transmission patterns by analysing the Woodchester Park data using a series of statistical and observational analyses linking pathogen genome data with diagnostic testing and population movement and demographic data for both cattle and badgers.

We hypothesised that the sampled M. bovis population was circulating within and between the sampled cattle and badger populations. Testing our hypothesis across multiple analyses, we found that, while none of these analyses are definitive in their own right, our results are consistent with our hypothesis and suggest that there has been a long history of within- and between-species transmission in the Woodchester Park area, and an important role for badgers in disease persistence.

Our choice of analytical methods was based in part on our awareness of underlying data biases. Ideally, sampling should be proportionate to prevalence in the host populations and matched over the same spatial and temporal ranges. Here, the combination of poor sensitivities of the standard tests for cattle (~50–80%; de la Rua-Domenech et al., 2006) and badgers (~50–70%; Chambers et al., 2009) and a reliance on historical archived isolates, meant data biases were unavoidable. Counterbalancing this weakness are the dense sampling of both host populations and the exceptionally detailed metadata.

Random Forest and Boosted Regression models identified strong epidemiological signatures of M. bovis transmission within and between host populations. Within species, metrics capturing the spatial, temporal, and network dynamics were all highly informative, indicative of M. bovis circulation being dependent on these factors. Between species, the variation observed between M. bovis sourced from cattle and badgers was found to be well explained by where the animals resided and when they were infected. Changes in these relationships could be exploited to rapidly identify changes in the epidemiology, as might be caused by badger social perturbation under culling operations (Tuyttens et al., 2000; Woodroffe et al., 2006).

The present study identified further evidence of within- and between-species transmission in the phylogenetic relationships between the M. bovis genomes (Figure 1). Five clades containing highly similar M. bovis genomes derived from infected cattle and badgers were identified, suggesting that substantial inter-species transmission had occurred. The presence of clades dominated by a single host species was also consistent with sustained within-species transmission. However, these phylogenetic relationships are particularly sensitive to sampling biases and should be interpreted with caution. For example, one interpretation of the basal location of the cattle-derived M. bovis genomes in the clades shown in Figure 1 is that they originated in cattle. Alternatively, this pattern could be the result of sampling the cattle population over a broader temporal range (from 1988 to 2013) than the badgers (2000 to 2011).

Further interrogation of the cattle and badger life histories associated with clade 4 (Figure 1) revealed evidence of prolonged persistence of this lineage in the badger population (Figure 2). Despite the cattle population being sampled over a longer time period, the badgers associated with clade 4 were predominantly infected earlier than the cattle and that strain persisted in the badgers for over 10 years. The remaining clades examined suggested that cattle could have been infected before badgers; however, it was not possible to determine whether badgers outside of Woodchester Park could be driving these interactions. Our results do suggest that inter-badger transmission is likely to be dominated by short-range interactions, given that short spatial distances (all less than 3.7 km) were highly informative in describing the genetic relationships examined in the machine learning analyses. Therefore, badgers further away from Woodchester Park are unlikely to be directly driving the patterns observed in our sampled badger population, and the ‘invading’ clades observed here are more parsimoniously explained by introductions of M. bovis from cattle. An additional limitation of these analyses is that no other wildlife species were sampled. Previous research by Delahay et al. (2007) found other mammal species infected with M. bovis in the area, albeit at lower prevalence (7.2% in Fallow deer and 6.8% in Muntjac deer) than the sampled badger population (~30%; Delahay et al., 2013).

Given considerable evidence in the present study for inter-species transmission of M. bovis, we next used BASTA, an analysis platform that can account for sampling biases (De Maio et al., 2018), to quantify these processes (Figure 3b). The BASTA analyses estimated transition rates between demes within a structured population. As the demes within the structured model were species-specific, the estimated between-species transition rates can be considered equivalent to transmission rates between populations of badgers and cattle. The most favoured two-deme model estimated badgers-to-cattle transmission rates were, on average, 10.4 times higher than cattle-to-badgers transmission rates (Figure 3a and b). However, the second most favoured four-deme model (which included a more complex population structure) estimated that inter-species transmission rates were close to equal. Although even structured coalescent models do not accurately reflect spatial contact patterns, that the simplest ‘two-deme’ model is favoured is encouraging (i.e. more spatially structured models do not perform better). However, the two-deme model may also have been favoured because of the limited genetic diversity available to estimate the evolutionary parameters and therefore further exploration with explicitly spatial approaches is an important next step.

In the process of quantifying inter-species transmission rates, the BASTA analyses also provide counts of the number of transmission events within and between the sampled badgers and cattle (Figure 3c). These counts provide a conservative estimate of the minimum number of transitions between the sampled animals and their ancestors. Although it is not appropriate to directly compare the counts within- and between-species, they do demonstrate that, at a minimum, within-species transmission occurs at least twice as frequently as between-species transmission. The high degree of within-species transmission estimated here is consistent both with the results of other studies that highlight the importance of cattle-to-cattle transmission (Costello et al., 1998; Gilbert et al., 2005; Goodchild and Clifton-Hadley, 2001; Green et al., 2008; Menzies and Neill, 2000), and the persistent long-term infection observed in the Woodchester Park badger population (Delahay et al., 2013).

The high-density badger population in Woodchester Park is likely to be similar to populations found in other parts of southwest England (Judge et al., 2017). However, broader representativeness should be confirmed by comparison to sympatric cattle and badger populations elsewhere in Britain and Ireland, particularly in areas with high bTB incidence. In addition, we selected only isolates of spoligotype SB0263, as this was the dominant type in the badger population. The selection of SB0263 could artificially inflate the badgers-to-cattle transition rates estimated here, as the high prevalence of this spoligotype in the badgers could be a reflection of host preference. However, though there are known phenotypic differences between spoligotypes, there is no evidence that these fundamentally change the epidemiology (Garbaccio et al., 2014; Wright et al., 2013). In addition, many different M. bovis spoligotypes have been observed in sympatric badger and cattle populations (Smith et al., 2003) and SB0263 is not only one of the most common spoligotypes in the UK (Smith et al., 2003), it is also highly prevalent in the cattle around Woodchester Park.

If the transmission interactions estimated in our research are replicated elsewhere, this could help to explain the failure of efforts to address recurrent and persistent infection in cattle herds that co-exist with badger populations (Gallagher et al., 2013; Karolemeas et al., 2011). In addition, the bi-directional transmission of M. bovis between species has the potential to combine local persistence in badgers with the long-distance mobility of the cattle. In line with a recent evidence review (Godfray et al., 2018), our research also suggests that coordinated bTB control in both cattle and badgers may be necessary to control infection in cattle. More generally, our analyses illustrate the complex interplay that underpins multi-host pathogen problems and demonstrate that, despite this complexity, appropriately defined suites of methods can be used to overcome issues of data biases and identify important epidemiological properties of these systems.

All sequence data used for these analyses has been uploaded on to the National Centre for Biotechnology Information Short Read Archive (NCBI-SRA). Due to the sensitivity of the associated metadata, only the sampling date and species will be provided with these sequences.

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Thank you for submitting your article "Combining genomics and epidemiology to analyse bi-directional transmission of Mycobacterium bovis in a multi-host system" for consideration by eLife. Your article has been reviewed by three peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Neil Ferguson as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Christian Gortazar (Reviewer #3).

The reviewers have discussed the reviews with one another, and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

This is a population genomics study of the transmission of M. bovis between two nonhuman animal hosts, cattle and badgers, a matter of considerable ecological and practical interest.

Summary:

This is an analysis of the multispecies badger-cattle transmission system using genomic and epidemiological data to characterize the transmission of M. bovis between these species, a matter of considerable interest.

Strengths include the sizable and detailed data set, and the relatively clear exposition of what analyses were done.

Essential revisions:

The major required revision is to place the work in the context of clear hypotheses, predictions of these hypotheses for the results of analyses, and interpretation of the analyses as they inform our judgment on those hypotheses. As currently written, like many pathogen genomics papers, this paper presents analyses and results, but leaves the rationale for the analyses and the interpretation of the results in terms of scientific hypotheses unclear. While this is not atypical for papers in the field, it makes it very hard for an interested non-specialist in the subject matter (ecology of M. bovis) to appreciate the paper. For a general interest journal like eLife, it is problematic because the reader is left with an unclear sense of what has and has not been shown.

It seems that the major hypotheses being tested revolve around the extent to which badgers are a reservoir for cattle M. bovis infection. Put somewhat more precisely, finding that they are a reservoir would mean that badger-badger transmission sustains the infection, that badger-to-cattle transmission is frequent and is the source (immediate or ultimate) of most cattle infections.

There are four main types of analysis in this paper. In a revised version we would expect each of these to be motivated explicitly by "we hypothesized x and tested it using this method and found that results were/were not consistent with x”. This is the main missing item in the paper.

1) Random forest and boosted regressions. The reason for doing both is unclear, and the boosted regressions are not described much at all. The RF method seems perhaps to be testing the plausibility of the idea that genetic distance indicates likely transmission. This seems more or less borne out by the main results where spatial and social proximity have strong explanatory roles (the sign is not stated but I assume that epi distance and genetic distance are positively related). I'm not sure that I'd expect such a relationship to hold over the full scale of distances (beyond some distance I would think there would be no relationship anymore) but this is a detail. The finding that "same host" has no role in the RF is quite weird – usually isolates from the same host would be nearly identical. No explanation is given for why the many different network and spatial measures are used, or which one expects to be positive in such a complex model, especially assuming that this is multivariable, so they are all conditional on the others. Overall, the RF seems maybe to be consistent with the data being of high quality and with transmission being related to short genetic distance, but not to clearly refute or confirm any hypothesis. Please clarify why these analyses were done and what the results mean.

2) Phylogenetic reconstruction. Here most of the clades have high probability of ancestral nodes being in cattle, seemingly inconsistent with the badger-reservoir hypothesis. Please comment on how these results should be interpreted.

3) The epidemiological descriptive data, where badgers seemed to have it long before cattle. Seems consistent with the reservoir hypothesis, though badgers are also much more widely sampled. Please make this explicit (modified if it has been misunderstood).

4) The structured coalescent analyses, in which badger-to-cattle transmissions seem to be much more common than the reverse under nearly all models, including the best-supported ones. One aspect that confuses me is that presumably the different lifespans of the hosts lead to different durations of the infection, so I am not sure if number of transmissions per unit time is the best measure of transmission. But taken at face value this seems consistent with the reservoir hypothesis. Please clarify what you think the interpretation is, and in particular (two reviewers wondered) whether these can be interpreted as the ratio of rates (transmissions per unit time), of basic or effective reproductive numbers (transmissions per infection), or something else that has physical interpretation.

Assuming that the Reviewing Editor, a nonexpert in the substantive field, has understood the above correctly, please modify the discussion to give careful consideration of the contrasting observations (3 and 4 support the hypothesis, 2 argues against it) and how they can be reconciled. If the authors can convincingly do that and answer (even with uncertainty) a clear scientific question, this could become publishable.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Combining genomics and epidemiology to analyse bi-directional transmission of Mycobacterium bovis in a multi-host system" for further consideration at eLife. Your revised article has been favorably evaluated by Neil Ferguson (Senior Editor), a Reviewing Editor, and one reviewer.

This paper has been extensively revised, and the scientific logic is now far clearer. There are some remaining issues that need to be addressed before acceptance, as outlined below:

1) The sampling selected for genetically similar isolates in the two host species, which will (I believe in all cases) increase the estimated transition rates above that which is typical for all strains. For example, any spoligotypes that are not transmitted between the species will not be counted. This is an important caveat to the conclusions about the frequency of interspecies transfer and needs to be explicit in the Discussion.

2) The phylogeny and BASTA analyses document interspecies transfer in both directions. The regression trees seemingly show the relevance of within-species transmission. Neither alone nor together do they answer the question of reservoir – is transmission in either species sufficient on its own for maintenance of the infection and continuing spillover into the other? The Discussion recommends integrated control, and intuitively this seems sensible, but on their own evidence of transmission within each species and between the two does not prove that essentially R_0{ii} >1 for either species, where ii represents transmission from species i to species i, and this is a condition for i to be a reservoir. I believe that the data are formally consistent with the possibility that eradication in either species would eradicate in the other (seems unlikely, as it requires a big role for interspecies transmission) or, more plausibly, that eradication in one species would eliminate it in the other because R0 within that species <1. If this reasoning is wrong, please refute. If it is right, please note this in the discussion and soften the call for integrated control.

3) Is there any way to quantify the ratio of within to between-species transmissions? This is hinted at frequently, but the numbers are never given.

4) The inclusion of a factor in the RF and BRT analyses does not guarantee that it is included in the expected direction. Can the authors report the direction of the effect for each included factor and explain any discrepancies from expectation, e.g. that overlapping lifespan = lower distance?

5) Can the authors explain, in Figure 3 a)what "mean posterior probability of each rate" means (I think it means posterior probability that it is positive) and b) why the ratio of transition counts and ratio of transition rates is so different?

6) No clear answer was given to essential revision 4, which asked in what if any sense these transition rate ratios can be interpreted as reproductive number ratios or something else epidemiological. Please comment on this in the Discussion. Also please edit carefully to use "transition" rather than "transmission" or explain why both these terms appear (as far as I can tell interchangeably) in the text.

Essential revisions:

The major required revision is to place the work in the context of clear hypotheses, predictions of these hypotheses for the results of analyses, and interpretation of the analyses as they inform our judgment on those hypotheses. As currently written, like many pathogen genomics papers, this paper presents analyses and results, but leaves the rationale for the analyses and the interpretation of the results in terms of scientific hypotheses unclear. While this is not atypical for papers in the field, it makes it very hard for an interested non-specialist in the subject matter (ecology of M. bovis) to appreciate the paper. For a general interest journal like eLife, it is problematic because the reader is left with an unclear sense of what has and has not been shown.

It seems that the major hypotheses being tested revolve around the extent to which badgers are a reservoir for cattle M. bovis infection. Put somewhat more precisely, finding that they are a reservoir would mean that badger-badger transmission sustains the infection, that badger-to-cattle transmission is frequent and is the source (immediate or ultimate) of most cattle infections.

There are four main types of analysis in this paper. In a revised version we would expect each of these to be motivated explicitly by "we hypothesized x and tested it using this method and found that results were/were not consistent with x”. This is the main missing item in the paper.

Thank you for highlighting this critical issue. The following changes were completed in response:

– Added description of our hypothesis and three objectives to the end of the Introduction.

– Added statements into the Results section to explicitly link each result to an objective and our hypothesis.

– Added similar explicit linking statements into the Materials and methods section.

1) Random forest and boosted regressions. The reason for doing both is unclear, and the boosted regressions are not described much at all. The RF method seems perhaps to be testing the plausibility of the idea that genetic distance indicates likely transmission. This seems more or less borne out by the main results where spatial and social proximity have strong explanatory roles (the sign is not stated but I assume that epi distance and genetic distance are positively related). I'm not sure that I'd expect such a relationship to hold over the full scale of distances (beyond some distance I would think there would be no relationship anymore) but this is a detail. The finding that "same host" has no role in the RF is quite weird – usually isolates from the same host would be nearly identical. No explanation is given for why the many different network and spatial measures are used, or which one expects to be positive in such a complex model, especially assuming that this is multivariable, so they are all conditional on the others. Overall, the RF seems maybe to be consistent with the data being of high quality and with transmission being related to short genetic distance, but not to clearly refute or confirm any hypothesis. Please clarify why these analyses were done and what the results mean.

Thank you for highlighting this. We have made the following changes:

– Additional analyses using Boosted Regression models were completed to allow the two methods to be more directly compared (Appendix 1—figures 2, 3 and 4 were updated and changes were made in the Results section of the main manuscript and to Appendix 1: Metric importance in Random Forest and Boosted Regression Analysis).

– Additional text was included to provide clarity regarding the use of these analyses in the Results section.

– The reference to the “same host” epidemiological metric has been removed. This metric wasn’t informative in the machine learning analyses because there were too little data available (only 201 of the 12,483 badger-to-badger comparisons were between genomes sourced from the same animal).

– The trends in relationship between each predictor variable and the genetic distances were examined using partial dependence plots. The relationships were found to be non-linear and variable and given that partial dependence plots can be misleading when highly correlated predictor variables are present in the model. Therefore, we only added broad statements about direction in the Results section.

– Additional analyses were described in the Results section, which investigated the influence of missing data and highly correlated predictor variables.

2) Phylogenetic reconstruction. Here most of the clades have high probability of ancestral nodes being in cattle, seemingly inconsistent with the badger-reservoir hypothesis. Please comment on how these results should be interpreted.

We agree that these results were inconsistent with our hypothesis. Re-examining our analyses, it was clear that the ancestral character estimation method used was highly sensitive to sampling biases and therefore these analyses were removed. The BASTA analyses we describe conducted similar analyses but BASTA is considered more robust because these analyses can account for the known sampling biases in our dataset. The following changes were made:

– Removed text referring to ancestral character estimation throughout manuscript.

– Figure 1 and its legend were updated to remove reference to the ancestral character estimation.

– Provided additional text in the Discussion noting that clades 1,2, 3, and 5, which appear to have a cattle origin, are likely to originate from outside of Woodchester Park where we have no badger isolates and therefore sampling biases may influence any observations of a cattle origin.

– Added additional explanatory text in the Results section to highlight the influence of sampling biases.

3) The epidemiological descriptive data, where badgers seemed to have it long before cattle. Seems consistent with the reservoir hypothesis, though badgers are also much more widely sampled. Please make this explicit (modified if it has been misunderstood).

The epidemiological description (Figure 2) is restricted to the animals associated with clade 4 in Figure 1. The observation that the badgers in this figure were sampled over a broader temporal window is a reflection of the clade 4 strain rather than our sampling. In fact, in our research the cattle population was sampled over a broader temporal window (1988-2013) as compared to the badger population (2000-2011). To clarify this the following changes were made:

– Additional text added to the legend of Figure 3.

– Minor changes were made to Figure 2 and its legend.

– Included four additional supplementary figures to Figure 1 (Figure 1—figure supplements 1, 2, 3, and 4) documenting the life histories of the animals associated with clades 1, 2, 3 and 5. These are referred to in the Results section.

4) The structured coalescent analyses, in which badger-to-cattle transmissions seem to be much more common than the reverse under nearly all models, including the best-supported ones. One aspect that confuses me is that presumably the different lifespans of the hosts lead to different durations of the infection, so I am not sure if number of transmissions per unit time is the best measure of transmission. But taken at face value this seems consistent with the reservoir hypothesis. Please clarify what you think the interpretation is, and in particular (two reviewers wondered) whether these can be interpreted as the ratio of rates (transmissions per unit time), of basic or effective reproductive numbers (transmissions per infection), or something else that has physical interpretation.

You are correct that the different lifespans animals will lead to durations of infection. However, the transmission rates estimated in BASTA (our structured coalescent approach) are done at the population level and for these analyses it is the time from infection to transmission that is important. In addition, the transmission rates are at the deme level rather than the individual level. Lastly, the average lifespan of dairy cattle (6.5 years) and badgers (5-8 years) are fairly similar.

In the manuscript, we had incorrectly referred to the transmission rates (Figure 3B) as “cattle-to-badger” or “badger-to-cattle”, which should have used “badgers” – this has been corrected.

Similarly, in reference to the estimation of the number of within and between species transition events (Figure 3D) we incorrectly used “badgers” and “cattle” – these have been corrected to “cow” and “badger”.

To help with the interpretation of the results of the BASTA analyses, an additional panel was added to Figure 3C. Figure 3C presents the median ratio of the badgers-to-cattle transmission rate divided by the cattle-to-badgers transmission rate estimated by each model analysed in BASTA. Additional references in the text for Figure 3C were added.

Assuming that the reviewing editor, a nonexpert in the substantive field, has understood the above correctly, please modify the Discussion to give careful consideration of the contrasting observations (3 and 4 support the hypothesis, 2 argues against it) and how they can be reconciled. If the authors can convincingly do that and answer (even with uncertainty) a clear scientific question, this could become publishable.

Thank you for this recommendation. In the revised manuscript the Discussion has been re-written. The aim of this re-write was to produce a shorter and clearer discussion that describes how each analysis and its results should be interpreted in the context of our hypothesis and the broader literature. We note that, while we understand why it seemed like the observations contradict each other, by recognising the role that biases played in the analysis 2, these are now consistent.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

This paper has been extensively revised, and the scientific logic is now far clearer. There are some remaining issues that need to be addressed before acceptance, as outlined below:

1) The sampling selected for genetically similar isolates in the two host species, which will (I believe in all cases) increase the estimated transition rates above that which is typical for all strains. For example, any spoligotypes that are not transmitted between the species will not be counted. This is an important caveat to the conclusions about the frequency of interspecies transfer and needs to be explicit in the Discussion.

Our analyses were limited to highly related genomes. There were very few examples of non-SB0263 isolates in the sampled badgers (>90%), and therefore, for this population, we believe our results are a good representation of the epidemiological characteristics of the system. Further, given the small number of samples of differing spoligotypes and the large genetic distances between them, we would likely be unable to improve the accuracy of our estimates even if we added these samples. However, we do agree that the selection of SB0263 may artificially inflate the importance of badger-to-cattle transmission over cattle-to-cattle transmission. This selection bias is alluded to in the Discussion:

“In addition, we have only considered spoligotype SB0263 and there are known phenotypic differences between spoligotypes, though such differences are unlikely to fundamentally change the epidemiology (Garbaccio et al., 2014; Wright et al., 2013).”

In addition, more detail is provided in the Materials and methods section:

“More than 90% of the badger-derived isolates were spoligotype SB0263. More than 75% (1096/1442) of the isolates available from cattle within 10km of Woodchester Park shared the same spoligotype and it is the second most common type found across England (Smith et al., 2003; Smith, Gordon, de la Rua-Domenech, Clifton-Hadley, and Hewinson, 2006).”

The section in the Discussion has been edited and expanded:

“In addition, we selected only isolates of spoligotype SB0263, since this was the dominant type in the badger population. […] In addition, many different M. bovis spoligotypes have been observed in sympatric badger and cattle populations (Smith et al., 2003) and SB0263 is not only one of the commonest spoligotypes in the UK (Smith et al., 2003), it is also highly prevalent in cattle around Woodchester Park.”

2) The phylogeny and BASTA analyses document interspecies transfer in both directions. The regression trees seemingly show the relevance of within-species transmission. Neither alone nor together do they answer the question of reservoir – is transmission in either species sufficient on its own for maintenance of the infection and continuing spillover into the other? The Discussion recommends integrated control, and intuitively this seems sensible, but on their own evidence of transmission within each species and between the two does not prove that essentially R_0{ii} >1 for either species, where ii represents transmission from species i to species i, and this is a condition for i to be a reservoir. I believe that the data are formally consistent with the possibility that eradication in either species would eradicate in the other (seems unlikely, as it requires a big role for interspecies transmission) or, more plausibly, that eradication in one species would eliminate it in the other because R0 within that species <1. If this reasoning is wrong, please refute. If it is right, please note this in the Discussion and soften the call for integrated control.

Thank you for highlighting this issue and we agree that the language used needs to be tightened.

We have replaced the use of the term ‘reservoir’ with respect to the badger population and have removed our statements suggesting the badgers are maintaining infection. Instead, we note that our evidence suggests that infection can persist in the badger population independently for over 10 years. We have softened our statement calling for coordinated control by changing “it will be necessary” to “it may be necessary” in the Discussion. Lastly, we have edited the final sentence of the abstract to state:

“If representative, our results suggest that control operations should target both cattle and badgers.”

3) Is there any way to quantify the ratio of within to between-species transmissions? This is hinted at frequently, but the numbers are never given.

It would be possible to quantify the ratio of the estimated number of within- and between-individual transmission events (from Figure 3C) but we don’t feel this is appropriate. These counts of the transmission events between individual animals can only be considered conservative estimates of the minimum number of events because they don’t account for multiple host transitions (badger or cow) on a single branch from a parent node to its child. In addition, we assumed that, where possible, the host animal represented the parent and one of the child nodes. In contrast, the more robust inter-species transmission rates are explicitly estimated at the population level and account for missed individuals on the transmission chains by allowing multiple host transitions on a single branch.

We included additional sentences describing the transmission event counts in the discussion in the Results section:

“The counts of events between individual animals outputted by BASTA represent the lower bound of the number of transmission events that occurred over the evolutionary history of the sampled M. bovis population because they are estimated on the transmission chains between the sampled and ancestral host animals and don’t account for missing individuals in these chains.”

Also, additional lines were added in the Discussion section:

“These counts provide a conservative estimate of the minimum number of transitions between the sampled animals and their ancestors. While it is not appropriate to directly compare the counts within- and between-species, they do demonstrate that, at a minimum, within-species transmission occurs at least twice as frequently as between-species transmission.”

Lastly, we created a supplementary figure to Figure 3 (Figure 3—figure supplement 1) that illustrates how the estimated transmission events were counted on each phylogeny in the posterior distribution of trees estimated by the two deme model in BASTA.

4) The inclusion of a factor in the RF and BRT analyses does not guarantee that it is included in the expected direction. Can the authors report the direction of the effect for each included factor and explain any discrepancies from expectation, e.g. that overlapping lifespan = lower distance?

Partial dependence plots were produced from the Random Forest analyses estimating the direction of the relationship between each epidemiological metric and genetic distances. These plots were added into Appendix 1—figures 5, 6, and 7. In addition, two new random metrics were included in the Random Forest and Boosted Regression analyses to provide an indication of the importance that could be attributed to a variable that had no relationship to the genetic distances (see updates to Appendix 1— figures 2, 3, and 4). Sentences describing the trends between the epidemiological trends and genetic distances have been included in Appendix 1:

“Partial dependence plots were used to estimate the direction of the effect between each of the epidemiological metrics (predictor variables) and the genetics distances (response variable) (Appendix 1—figure 5, Appendix 1—figure 6, and Appendix 1—figure 7). […] There was a lot of noise around these relationships, but these trends were in-line with our expectations that cattle and wildlife in close proximity in time and space are more likely to transmit infection to one another.”

5) Can the authors explain, in Figure 3 a) what "mean posterior probability of each rate" means (I think it means posterior probability that it is positive) and b) why the ratio of transition counts and ratio of transition rates is so different?

a) We apologise for the confusion. Based on the number of inter-species rates estimated, this value is either the posterior probability directly (for the first three models) or the mean calculated across the different inter-species transmission rates that were estimated and summed, as seen in Author response table 1 (derived from Figure 5).

To improve clarity, text has been added to the legend of Figure 3, clarifying how the numbers representing the posterior probabilities were calculated:

“The values above each vertical line represent the posterior probability of each rate, either as a mean of probabilities associated with multiple estimated rates (for the 3Deme_outerIsBadgers, 4Deme, 6Deme and 8Deme models) or a single probability (for the 2Deme, 3Deme_outerIsBoth, and 3Deme_outerIsCattle models).”

b) As stated in our response to point 3, the transmission counts represent the lower bounds on the number of events between individual animals. In contrast, the inter-species transmission rates are estimated at the population and can’t be directly compared to these counts. In addition, because the counts don’t account for missing individuals on the transmission chains from the ancestral individuals to the sampled animals, they are susceptible to sampling biases.

To avoid confusion panel C of Figure 3 was removed. In addition, the new panel C (previously D) has been edited to improve its clarity. The counts for within species and between species events have been separated and the number of badgers and cattle sampled at the tips of the phylogenies that the counts are derived from has been noted.

6) No clear answer was given to essential revision 4, which asked in what if any sense these transition rate ratios can be interpreted as reproductive number ratios or something else epidemiological. Please comment on this in the Discussion. Also please edit carefully to use "transition" rather than "transmission" or explain why both these terms appear (as far as I can tell interchangeably) in the text.

a) The relative transmission rates are the most appropriate calculations given the evolutionary analysis methods that were used in this paper. It isn’t appropriate to discuss these in terms of the reproductive ratio because we are calculating population-level rather than individual transmission rates. We note that direct estimates of reproductive numbers are possible but would require extensive additional work using different methods.

b) In our case the inter-population transition rates estimated here can be considered inter-species transmission rates because the populations we consider are species specific. As noted above in 6a above, these are estimates at the population rather than individual animal level.

Any instances of the misuse of these terms in the manuscript were corrected. Additional text added into the discussion to clearly define our use of transmission and transition:

“The BASTA analyses estimated transition rates between demes within a structured population. Since the demes within the structured model were species-specific the estimated transition rates can be considered equivalent to transmission rates between populations of badgers and cattle.”

Author details

1. Joseph Crispell

   School of Veterinary Medicine, Veterinary Sciences Centre, University College Dublin, Dublin, Ireland

   Contribution

   Formal analysis, Visualization, Methodology, Writing—original draft, Writing—review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-0364-7112

2. Clare H Benton

   National Wildlife Management Centre, Animal & Plant Health Agency (APHA), London, United Kingdom

   Contribution

   Data curation, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

3. Daniel Balaz

   Roslin Institute, University of Edinburgh, Edinburgh, United Kingdom

   Contribution

   Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-3958-8748

4. Nicola De Maio

   European Molecular Biology Laboratory, European Bioinformatics Institute (EMBL-EBI), Cambridge, United Kingdom

   Contribution

   Software, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

5. Assel Ahkmetova

   Institute of Biodiversity, Animal Health & Comparative Medicine, College of Medical, Veterinary & Life Sciences, University of Glasgow, Glasgow, United Kingdom

   Contribution

   Data curation, Writing—review and editing

   Competing interests

   No competing interests declared

6. Adrian Allen

   Agri-Food & Biosciences Institute Northern Ireland (AFBNI), Belfast, United Kingdom

   Contribution

   Data curation, Writing—review and editing

   Competing interests

   No competing interests declared

7. Roman Biek

   Institute of Biodiversity, Animal Health & Comparative Medicine, College of Medical, Veterinary & Life Sciences, University of Glasgow, Glasgow, United Kingdom

   Contribution

   Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

8. Eleanor L Presho

   Agri-Food & Biosciences Institute Northern Ireland (AFBNI), Belfast, United Kingdom

   Contribution

   Data curation, Writing—review and editing

   Competing interests

   No competing interests declared

9. James Dale

   Animal & Plant Health Agency (APHA), London, United Kingdom

   Contribution

   Data curation, Writing—review and editing

   Competing interests

   No competing interests declared

10. Glyn Hewinson

    Centre for Bovine Tuberculosis, Institute of Biological, Environmental and Rural Sciences, University of Aberystwyth, Aberystwyth, United Kingdom

    Contribution

    Data curation, Writing—review and editing

    Competing interests

    No competing interests declared

11. Samantha J Lycett

    Roslin Institute, University of Edinburgh, Edinburgh, United Kingdom

    Contribution

    Methodology, Writing—review and editing

    Competing interests

    No competing interests declared

    "This ORCID iD identifies the author of this article:" 0000-0003-3159-596X

12. Javier Nunez-Garcia

    Genomics Medicine Ireland, Dublin, Ireland

    Contribution

    Data curation, Writing—review and editing

    Competing interests

    No competing interests declared

13. Robin A Skuce

    Agri-Food & Biosciences Institute Northern Ireland (AFBNI), Belfast, United Kingdom

    Contribution

    Data curation, Writing—review and editing

    Competing interests

    No competing interests declared

14. Hannah Trewby

    Quadram Institute Bioscience, Norwich, United Kingdom

    Contribution

    Data curation, Methodology, Writing—review and editing

    Competing interests

    No competing interests declared

15. Daniel J Wilson

    Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, Nuffield Department of Population Health, University of Oxford, Oxford, United Kingdom

    Contribution

    Software, Methodology, Writing—review and editing

    Competing interests

    No competing interests declared

    "This ORCID iD identifies the author of this article:" 0000-0002-0940-3311

16. Ruth N Zadoks

    Institute of Biodiversity, Animal Health & Comparative Medicine, College of Medical, Veterinary & Life Sciences, University of Glasgow, Glasgow, United Kingdom

    Contribution

    Supervision, Methodology, Writing—review and editing

    Competing interests

    No competing interests declared

    "This ORCID iD identifies the author of this article:" 0000-0002-1164-8000

17. Richard J Delahay

    National Wildlife Management Centre, Animal & Plant Health Agency (APHA), London, United Kingdom

    Contribution

    Conceptualization, Data curation, Methodology, Writing—review and editing

    For correspondence

    Dez.Delahay@apha.gsi.gov.uk

    Competing interests

    No competing interests declared

18. Rowland Raymond Kao

    1. Roslin Institute, University of Edinburgh, Edinburgh, United Kingdom
    2. Royal (Dick) School of Veterinary Studies, University of Edinburgh, Edinburgh, United Kingdom

    Contribution

    Conceptualization, Data curation, Supervision, Funding acquisition, Methodology, Writing—review and editing

    For correspondence

    rowland.kao@ed.ac.uk

    Competing interests

    No competing interests declared

    "This ORCID iD identifies the author of this article:" 0000-0003-0919-6401

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