MERS-CoV spillover at the camel-human interface

1Middle East respiratory syndrome coronavirus (MERS-CoV), endemic in camels in the Arabian Peninsula, is the causative agent of zoonotic infections and limited outbreaks in humans. The virus, first discovered in 2012, has caused more than 2000 infections and over 700 deaths, according to the World Health Organization (WHO). Its epidemiology remains obscure, largely because infections are observed among the most severely affected individuals, such as older males with comorbidities. While contact with camels is often reported, other patients do not recall contact with any livestock, suggesting an unobserved community contribution to the outbreak. Previous studies on MERS-CoV epidemiology have used serology to identify factors associated with MERS-CoV exposure in potential risk groups. Such data have shown high seroprevalence in camels and evidence of contact with MERS-CoV in workers with occupational exposure to camels. Separately, epidemiological modelling approaches have been used to look at incidence reports through time, space and across hosts.

2Although such epidemiological approaches yield important clues about exposure patterns and potential for larger outbreaks, much inevitably remains opaque to such approaches due to difficulties in linking cases into transmission clusters in the absence of detailed information. Where sequence data are relatively cheap to produce, genomic epidemiological approaches can fill this critical gap in outbreak scenarios. These data often yield a highly detailed picture of an epidemic when complete genome sequencing is performed consistently and appropriate metadata collected. Sequence data can help discriminate between multiple and single source scenarios, which are fundamental to quantifying risk. Sequencing MERS-CoV has been performed as part of initial attempts to link human infections with the camel reservoir, nosocomial outbreak investigations and routine surveillance. A large portion of MERS-CoV sequences come from outbreaks within hospitals, where sequence data have been used to determine whether infections were isolated introductions or were part of a larger hospital-associated outbreak. Similar studies on MERS-CoV have taken place at broader geographic scales, such as cities.

3It is widely accepted that recorded human MERS-CoV infections are a result of at least several introductions of the virus into humans and that contact with camels is a major risk factor for developing MERS, per WHO guidelines. Previous studies attempting to quantify the actual number of spillover infections have either relied on case-based epidemiological approaches or employed methods agnostic to signals of population structure within sequence data. Here, we use a dataset of 274 MERS-CoV genomes to investigate transmission patterns of the virus between humans and camels.

4Here, we use an explicit model of metapopulation structure and migration between discrete subpopulations, referred to here as demes, derived from the structured coalescent. Unlike approaches that model host species as a discrete phylogenetic trait of the virus using continuous-time Markov processes (or simpler, parsimony based, approaches), population structure models explicitly incorporate contrasts in deme effective population sizes and migration between demes. By estimating independent coalescence rates for MERS-CoV in humans and camels, as well as migration patterns between the two demes, we show that long-term viral evolution of MERS-CoV occurs exclusively in camels. Our results suggest that spillover events into humans are seasonal and might be associated with the calving season in camels. However, we find that MERS-CoV, once introduced into humans, follows transient transmission chains that soon abate. Using Monte Carlo simulations we show that for MERS-CoV circulating in humans is much lower than the epidemic threshold of 1.0 and that correspondingly the virus has been introduced into humans hundreds of times.

5The structured coalescent approach we employ (see Materials and methods) identifies camels as a reservoir host where most of MERS-CoV evolution takes place (Figure 1), while human MERS outbreaks are transient and terminal with respect to long-term evolution of the virus (Figure 1—figure supplement 1). Across 174 MERS-CoV genomes collected from humans, we estimate a median of 56 separate camel-to-human cross-species transmissions (95% highest posterior density (HPD): 48–63). While we estimate a median of 3 (95% HPD: 0–12) human-to-camel migrations, the 95% HPD interval includes zero and we find that no such migrations are found in the maximum clade credibility tree (Figure 1). Correspondingly, we observe substantially higher camel-to-human migration rate estimates than human-to-camel migration rate estimates (Figure 1—figure supplement 2). This inference derives from the tree structure wherein human viruses appear as clusters of highly related sequences nested within the diversity seen in camel viruses, which themselves show significantly higher diversity and less clustering. This manifests as different rates of coalescence with camel viruses showing a scaled effective population size of 3.49 years (95% HPD: 2.71–4.38) and human viruses showing a scaled effective population of 0.24 years (95% HPD: 0.14–0.34).

6We believe that the small number of inferred human-to-camel migrations are induced by the migration rate prior, while some are derived from phylogenetic proximity of human sequences to the apparent ‘backbone’ of the phylogenetic tree. This is most apparent in lineages in early-mid 2013 that lead up to sequences comprising the MERS-CoV clade dominant in 2015, where owing to poor sampling of MERS-CoV genetic diversity from camels the model cannot completely dismiss humans as a potential alternative host. The first sequences of MERS-CoV from camels do not appear in our data until November 2013. Our finding of negligible human-to-camel transmission is robust to choice of prior (Figure 1—figure supplement 2).

7The repeated and asymmetric introductions of short-lived clusters of MERS-CoV sequences from camels into humans leads us to conclude that MERS-CoV epidemiology in humans is dominated by zoonotic transmission (Figure 1 and Figure 1—figure supplement 1). We observe dense terminal clusters of MERS-CoV circulating in humans that are of no subsequent relevance to the evolution of the virus. These clusters of presumed human-to-human transmission are then embedded within extensive diversity of MERS-CoV lineages inferred to be circulating in camels, a classic pattern of source-sink dynamics. Our findings suggest that instances of human infection with MERS-CoV are more common than currently thought, with exceedingly short transmission chains mostly limited to primary cases that might be mild and ultimately not detected by surveillance or sequencing. Structured coalescent analyses recover the camel-centered picture of MERS-CoV evolution despite sequence data heavily skewed towards non-uniformly sampled human cases and are robust to choice of prior. Comparing these results with a currently standard discrete trait analysis approach for ancestral state reconstruction shows dramatic differences in host reconstruction at internal nodes (Figure 1—figure supplement 3). Discrete trait analysis reconstruction identifies both camels and humans as important hosts for MERS-CoV persistence, but with humans as the ultimate source of camel infections. A similar approach has been attempted previously, but this interpretation of MERS-CoV evolution disagrees with lack of continuing human transmission chains outside of Arabian peninsula, low seroprevalence in humans and very high seroprevalence in camels across Saudi Arabia. We suspect that this particular discrete trait analysis reconstruction is false due to biased data, that is, having nearly twice as many MERS-CoV sequences from humans than from camels and the inability of the model to account for and quantify vastly different rates of coalescence in the phylogenetic vicinity of both types of sequences. We can replicate these results by either applying the same model to current data (Figure 1—figure supplement 3) or by enforcing equal coalescence rates within each deme in the structured coalescent model (Figure 1—figure supplement 4).

8We use the posterior distribution of MERS-CoV introduction events from camels to humans (Figure 1) to model seasonal variation in zoonotic transfer of viruses. We identify four months (April, May, June, July) when the odds of MERS-CoV introductions are increased (Figure 2) and four when the odds are decreased (August, September, November, December). Camel calving is reported to occur from October to February, with rapidly declining maternal antibody levels in calves within the first weeks after birth. It is possible that MERS-CoV sweeps through each new camel generation once critical mass of susceptibles is reached, leading to a sharp rise in prevalence of the virus in camels and resulting in increased force of infection into the human population. Strong influx of susceptibles and subsequent sweeping outbreaks in camels may explain evidence of widespread exposure to MERS-CoV in camels from seroepidemiology.

9Although we find evidence of seasonality in zoonotic spillover timing, no such relationship exists for sizes of human sequence clusters (Figure 2B). This is entirely expected, since little seasonality in human behaviour that could facilitate MERS-CoV transmission is expected following an introduction. Similarly, we do not observe any trend in human sequence cluster sizes over time (Figure 2B, Spearman, ), suggesting that MERS-CoV outbreaks in humans are neither growing nor shrinking in size. This is not surprising either, since MERS-CoV is a camel virus that has to date, experienced little-to-no selective pressure to improve transmissibility between humans.

10Structured coalescent approaches clearly show humans to be a terminal host for MERS-CoV, implying poor transmissibility. However, we wanted to translate this observation into an estimate of the basic reproductive number to provide an intuitive epidemic behaviour metric that does not require expertise in reading phylogenies. The parameter determines expected number of secondary cases in a single infections as well as the distribution of total cases that result from a single introduction event into the human population (Equation 1, Materials and methods). We estimate along with other relevant parameters via Monte Carlo simulation in two steps. First, we simulate case counts across multiple outbreaks totaling 2000 cases using Equation 1 and then we subsample from each case cluster to simulate sequencing of a fraction of cases. Sequencing simulations are performed via a multivariate hypergeometric distribution, where the probability of sequencing from a particular cluster depends on available sequencing capacity (number of trials), numbers of cases in the cluster (number of successes) and number of cases outside the cluster (number of failures). In addition, each hypergeometric distribution used to simulate sequencing is concentrated via a bias parameter, that enriches for large sequence clusters at the expense of smaller ones (for its effects see Figure 3—figure supplement 1). This is a particularly pressing issue, since a priori we expect large hospital outbreaks of MERS to be overrepresented in sequence data, whereas sequences from primary cases will be sampled exceedingly rarely. We record the number, mean, standard deviation and skewness (third standardised moment) of sequence cluster sizes in each simulation (left-hand panel in Figure 3) and extract the subset of Monte Carlo simulations in which these summary statistics fall within the 95% highest posterior density observed in the empirical MERS-CoV data from structured coalescent analyses. We record values, as well as the number of case clusters (equivalent to number of zoonotic introductions), for these empirically matched simulations. A schematic of this Monte Carlo procedure is shown in Figure 3—figure supplement 2. Since the total number of cases is fixed at 2000, higher results in fewer larger transmission clusters, while lower results in many smaller transmission clusters.

11We find that observed phylogenetic patterns of sequence clustering strongly support below 1.0 (middle panel in Figure 3). Mean value observed in matching simulations is 0.72 (95% percentiles 0.57–0.90), suggesting the inability of the virus to sustain transmission in humans. Lower values for in turn suggest relatively large numbers of zoonotic transfers of viruses into humans (right-hand panel in Figure 3). Median number of cross-species introductions observed in matching simulations is 592 (95% percentiles 311–811). Our results suggest a large number of unobserved MERS primary cases. Given this, we also performed simulations where the total number of cases is doubled to 4000 to explore the impact of dramatic underestimation of MERS cases. In these analyses, values tend to decrease even further as numbers of introductions go up, although very few simulations match currently observed MERS-CoV sequence data (Figure 3—figure supplement 3).

12Overall, our analyses indicate that MERS-CoV is poorly suited for human-to-human transmission, with an estimated and sequence sampling likely to be biased towards large hospital outbreaks (Figure 3—figure supplement 1). All matching simulations exhibit highly skewed distributions of case cluster sizes with long tails (Figure 3—figure supplement 4), which is qualitatively similar to the results of. We find that simulated sequence cluster sizes resemble observed sequence cluster sizes in the posterior distribution, with a slight reduction in mid-sized clusters in simulated data (Figure 3—figure supplement 5). Given these findings, and the fact that large outbreaks of MERS occurred in hospitals, the combination of frequent spillover of MERS-CoV into humans and occasional outbreak amplification via poor hygiene practices appear sufficient to explain observed epidemiological patterns of MERS-CoV.

13Recombination has been shown to occur in all genera of coronaviruses, including MERS-CoV. In order to quantify the degree to recombination has shaped MERS-CoV genetic diversity, we used two recombination detection approaches across partitions of taxa corresponding to inferred MERS-CoV clades. Both methods rely on sampling parental and recombinant alleles within the alignment, although each quantifies different signals of recombination. One hallmark of recombination is the ability to carry alleles derived via mutation from one lineage to another, which appear as repeated mutations taking place in the recipient lineage, somewhere else in the tree. The PHI (pairwise homoplasy index) test quantifies the appearance of these excessive repeat mutations (homoplasies) within an alignment. Another hallmark of recombination is clustering of alleles along the genome, due to how template switching, the primary mechanism of recombination in RNA viruses, occurs. 3Seq relies on the clustering of nucleotide similarities along the genome between sequence triplets – two potential parent-donors and one candidate offspring-recipient sequences.

14Both tests can give spurious results in cases of extreme rate heterogeneity and sampling over time, but both tests have not been reported to fail simultaneously. PHI and 3Seq methods consistently identify most of the apparent ‘backbone’ of the MERS-CoV phylogeny as encompassing sequences with evidence of recombination (Figure 4—figure supplement 1). Neither method can identify where in the tree recombination occurred, but each full asterisk in Figure 4—figure supplement 1 should be interpreted as the minimum partition of data that still captures both donor and recipient alleles involved in a recombination event. This suggests a non-negligible contribution of recombination in shaping existing MERS-CoV diversity. As done previously, we show large numbers of homoplasies in MERS-CoV data (Figure 4—figure supplement 2) with some evidence of genomic clustering of such alleles. These results are consistent with high incidence of MERS-CoV in camels, allowing for co-infection with distinct genotypes and thus recombination to occur.

15Owing to these findings, we performed a sensitivity analysis in which we partitioned the MERS-CoV genome into two fragments and identified human outbreak clusters within each fragment. We find strong similarity in the grouping of human cases into outbreak clusters between fragments (Figure 4A). Between the two trees in Figure 4B four (out of 54) ‘human’ clades are expanded where either singleton introductions or two-taxon clades in fragment 2 join other clades in fragment 1. For the reverse comparison, there are five ‘human’ clades (out of 53) in fragment 2 that are expanded. All such clades have low divergence (Figure 4B) and thus incongruences in human clades are more likely to be caused by differences in deme assignment rather than actual recombination. And while we observe evidence of distinct phylogenetic trees from different parts of the MERS-CoV genome (Figure 4B), human clades are minimally affected and large portions of the posterior probability density in both parts of the genome are concentrated in shared clades (Figure 4—figure supplement 3). Additionally, we observe the same source-sink dynamics between camel and human populations in trees constructed from separate genomic fragments as were observed in the original full genome tree (Figures 1 and 4B).

16Observed departures from strictly clonal evolution suggest that while recombination is an issue for inferring MERS-CoV phylogenies, its effect on the human side of MERS outbreaks is minimal, as expected if humans represent a transient host with little opportunity for co-infection. MERS-CoV evolution on the reservoir side is complicated by recombination, although is nonetheless still largely amenable to phylogenetic methods. Amongst other parameters of interest, recombination is expected to interfere with molecular clocks, where transferred genomic regions can give the impression of branches undergoing rapid evolution, or branches where recombination results in reversions appearing to evolve slow. In addition to its potential to influence tree topology, recombination in molecular sequence data is an erratic force with unpredictable effects. We suspect that the effects of recombination in MERS-CoV data are reigned in by a relatively small effective population size of the virus in Saudi Arabia (see next section) where haplotypes are fixed or nearly fixed, thus preventing an accumulation of genetic diversity that would then be reshuffled via recombination. Nevertheless the evolutionary rate of the virus appears to fall firmly within the expected range for RNA viruses: regression of nucleotide differences to Jordan-N3/2012 genome against sequence collection dates yields a rate of subs/site/year, Bayesian structured coalescent estimate from primary analysis (95% HPDs: ) subs/site/year.

17Here, we attempt to investigate MERS-CoV demographic patterns in the camel reservoir. We supplement camel sequence data with a single earliest sequence from each human cluster, treating viral diversity present in humans as a sentinel sample of MERS-CoV diversity circulating in camels. This removes conflicting demographic signals sampled during human outbreaks, where densely sampled closely related sequences from humans could be misconstrued as evidence of demographic crash in the viral population.

18Despite lack of convergence, neither of the two demographic reconstructions show evidence of fluctuations in the scaled effective population size of MERS-CoV over time (Figure 5). We recover a similar demographic trajectory when estimating over time with a skygrid tree prior across the genome split into ten fragments with independent phylogenetic trees to account for confounding effects of recombination (Figure 5—figure supplement 1). However, we do note that coalescence rate estimates are high relative to the sampling time period, with a mean estimate of at 3.49 years (95% HPD: 2.71–4.38), and consequently MERS-CoV phylogeny resembles a ladder, as often seen in human influenza A virus phylogenies.

19This empirically estimated effectived population can be compared to the expected effective population size in a simple epidemiological model. At endemic equilibrium, we expect scaled effective population size to follow, where is the equilibrium rate of transmission and is the equilibrium number of infecteds. We assume that is constant and is equal to the rate of recovery. Given a 20 day duration of infection in camels, we arrive at infections per year. Given extremely high seroprevalence estimates within camels in Saudi Arabia, we expect camels to usually be infected within their first year of life. Therefore, we can estimate the rough number of camel infections per year as the number of calves produced each year. We find there are 830,000 camels in Saudi Arabia and that female camels in Saudi Arabia have an average fecundity of 45%. Thus, we expect new calves produced yearly and correspondingly 186,750 new infections every year, which spread over 20 day intervals gives an average prevalence of infections. This results in an expected scaled effective population size years.

20Comparing expected to empirical we arrive at a ratio of 80.3 (64.0–103.5). This is less than the equivalent ratio for human measles virus and is in line with the expectation from neutral evolutionary dynamics plus some degree of transmission heterogeneity and seasonal troughs in prevalence. Thus, we believe that the ladder-like appearance of the MERS-CoV tree can likely be explained by entirely demographic factors.

21In this study we aimed to understand the drivers of MERS coronavirus transmission in humans and what role the camel reservoir plays in perpetuating the epidemic in the Arabian peninsula by using sequence data collected from both hosts (174 from humans and 100 from camels). We showed that currently existing models of population structure can identify distinct demographic modes in MERS-CoV genomic data, where viruses continuously circulating in camels repeatedly jump into humans and cause small outbreaks doomed to extinction (Figure 1—figure supplement 1). This inference succeeds under different choices of priors for unknown demographic parameters (Figure 1—figure supplement 2) and in the presence of strong biases in sequence sampling schemes (Figure 3). When rapid coalescence in the human deme is not allowed (Figure 1—figure supplement 4) structured coalescent inference loses power and ancestral state reconstruction is nearly identical to that of discrete trait analysis (Figure 1—figure supplement 3). When allowed different deme-specific population sizes, the structured coalescent model succeeds because a large proportion of human sequences fall into tightly connected clusters, which informs a low estimate for the population size of the human deme. This in turn informs the inferred state of long ancestral branches in the phylogeny, that is, because these long branches are not immediately coalescing, they are most likely in camels.

22From sequence data, we identify at least 50 zoonotic introductions of MERS-CoV into humans from the reservoir (Figure 1), from which we extrapolate that hundreds more such introductions must have taken place (Figure 3). Although we recover migration rates from our model (Figure 1—figure supplement 2), these only pertain to sequences and in no way reflect the epidemiologically relevant per capita rates of zoonotic spillover events. We also looked at potential seasonality in MERS-CoV spillover into humans. Our analyses indicated a period of three months where the odds of a sequenced spillover event are increased, with timing consistent with an enzootic amongst camel calves (Figure 2). As a result of our identification of large and asymmetric flow of viral lineages into humans we also find that the basic reproduction number for MERS-CoV in humans is well below the epidemic threshold (Figure 3). Having said that, there are highly customisable coalescent methods available that extend the methods used here to accommodate time varying migration rates and population sizes, integrate alternative sources of information and fit to stochastic nonlinear models, which would be more appropriate for MERS-CoV. Some distinct aspects of MERS-CoV epidemiology could not be captured in our methodology, such as hospital outbreaks where is expected to be consistently closer to 1.0 compared to community transmission of MERS-CoV. Outside of coalescent-based models, there are population structure models that explicitly relate epidemiological parameters to the branching process observed in sequence data, but often rely on specifying numerous informative priors and can suffer from MCMC convergence issues.

23Strong population structure in viruses often arises through limited gene flow, either due to geography, ecology or evolutionary forces. On a smaller scale, population structure can unveil important details about transmission patterns, such as identifying reservoirs and understanding spillover trends and risk, much as we have done here. When properly understood naturally arising barriers to gene flow can be exploited for more efficient disease control and prevention, as well as risk management.

24Severe acute respiratory syndrome (SARS) coronavirus, a Betacoronavirus like MERS-CoV, caused a serious epidemic in humans in 2003, with over 8000 cases and nearly 800 deaths. Since MERS-CoV was also able to cause significant pathogenicity in the human host it was inevitable that parallels would be drawn between MERS-CoV and SARS-CoV at the time of MERS discovery in 2012. Although we describe the epidemiology of MERS-CoV from sequence data, indications that MERS-CoV has poor capacity to spread human-to-human existed prior to any sequence data. SARS-CoV swept through the world in a short period of time, but MERS cases trickled slowly and were restricted to the Arabian Peninsula or resulted in self-limiting outbreaks outside of the region, a pattern strongly indicative of repeat zoonotic spillover. Infectious disease surveillance and control measures remain limited, so much like the SARS epidemic in 2003 or the H1N1 pandemic in 2009, zoonotic pathogens with are probably going to be discovered after spreading beyond the original location of spillover. Even though our results show that MERS-CoV does not appear to present an imminent global threat, we would like to highlight that its epidemiology is nonetheless concerning.

25Pathogens Bacillus anthracis, Andes hantavirus, monkeypox and influenza A are able to jump species barriers but only influenza A viruses have historically resulted in pandemics. MERS-CoV may join the list of pathogens able to jump species barriers but not spread efficiently in the new host. Since its emergence in 2012, MERS-CoV has caused self-limiting outbreaks in humans with no evidence of worsening outbreaks over time. However, sustained evolution of the virus in the reservoir and continued flow of viral lineages into humans provides the substrate for a more transmissible variant of MERS-CoV to possibly emerge. Previous modelling studies suggest a positive relationship between initial in the human host and probability of evolutionary emergence of a novel strain which passes the supercritical threshold of. This leaves MERS-CoV in a precarious position; on one hand its current of 0.7 is certainly less than 1, but its proximity to the supercritical threshold raises alarm. With very little known about the fitness landscape or adaptive potential of MERS-CoV, it is incredibly challenging to predict the likelihood of the emergence more transmissible variants. In light of these difficulties, we encourage continued genomic surveillance of MERS-CoV in the camel reservoir and from sporadic human cases to rapidly identify a supercritical variant, if one does emerge.

26All MERS-CoV sequences were downloaded from GenBank and accession numbers are given in Supplementary file 1. Sequences without accessions were kindly shared by Ali M. Somily, Mazin Barry, Sarah S. Al Subaie, Abdulaziz A. BinSaeed, Fahad A. Alzamil, Waleed Zaher, Theeb Al Qahtani, Khaldoon Al Jerian, Scott J.N. McNabb, Imad A. Al-Jahdali, Ahmed M. Alotaibi, Nahid A. Batarfi, Matthew Cotten, Simon J. Watson, Spela Binter, and Paul Kellam prior to publication. Sequences available on GenBank but not associated with publications were shared by Meriadeg Ar Gouilh, Emad M. Elassal, Monica Galiano, Krista Queen and Ying Tao. Fragments of some strains submitted to GenBank as separate accessions were assembled into a single sequence. Only sequences covering at least 50% of MERS-CoV genome were kept, to facilitate later analyses where the alignment is split into two parts in order to account for effects of recombination. Sequences were annotated with available collection dates and hosts, designated as camel or human, aligned with MAFFT, and edited manually. Protein coding sequences were extracted and concatenated, reducing alignment length from 30,130 down to 29,364, which allowed for codon-partitioned substitution models to be used. The final dataset consisted of 174 genomes from human infections and 100 genomes from camel infections (Supplementary file 1).

27For our primary analysis, the MultiTypeTree module of BEAST v2.4.3 was used to specify a structured coalescent model with two demes – humans and camels. At time of writing structured population models are available in BEAST v2 but not in BEAST v1. We use the more computationally intensive MultiTypeTree module over approximate methods also available in BEAST v2, such as BASTA, MASCOT, and PhyDyn. Structured coalescent model implemented in the MultiTypeTree module estimates four parameters: rate of coalescence in human viruses, rate of coalescence in camel viruses, rate of migration from the human deme to the camel deme and rate of migration from the camel deme to the human deme. Analyses were run on codon position partitioned data with two separate HKY+ nucleotide substitution models specified for codon positions 1 + 2 and 3. A relaxed molecular clock with branch rates drawn from a lognormal distribution was used to infer the evolutionary rate from date calibrated tips. Default priors were used for all parameters except for migration rates between demes for which an exponential prior with mean 1.0 was used. All analyses were run for 200 million steps across ten independent Markov chains (MCMC runs) and states were sampled every 20,000 steps. Due to the complexity of multitype tree parameter space 50% of states from every analysis were discarded as burn-in, convergence assessed in Tracer v1.6 and states combined using LogCombiner distributed with BEAST v2.4.3. Three chains out of ten did not converge and were discarded altogether. This left 70,000 states on which to base posterior inference. Posterior sets of typed (where migrating branches from structured coalescent are collapsed, and migration information is left as a switch in state between parent and descendant nodes) trees were summarised using TreeAnnotator v2.4.3 with the common ancestor heights option. A maximum likelihood phylogeny showing just the genetic relationships between MERS-CoV genomes from camels and humans was recovered using PhyML under a HKY+ nucleotide substitution model and is shown in Figure 1—figure supplement 5.

28As a secondary analysis to test robustness to choice of prior, we set up an analysis where we increased the mean of the exponential distribution prior for migration rate to 10.0. All other parameters were identical to the primary analysis and as before 10 independent MCMC chains were run. In this case, two chains did not converge. This left 80,000 states on which to base posterior inference. Posterior sets of typed trees were summarised using TreeAnnotator v2.4.3 with the common ancestor heights option.

29To better understand where statistical power of the structured coalescent model lies we set up a tertiary analysis where a model was set up identically to the first structured coalescent analysis, but deme population sizes were enforced to have the same size. This analysis allowed us to differentiate whether statistical power in our analysis is coming from effective population size contrasts between demes or the backwards-in-time migration rate estimation. Five replicate chains were set up, two of which failed to converge after 200 million states. Combining the three converging runs left us with 15,000 trees sampled from the posterior distribution, which were summarised in TreeAnnotator v2.4.3 with the common ancestor heights option.

30Due to concerns that recombination might affect our conclusions, as an additional secondary analysis, we also considered a scenario where alignments were split into two fragments (fragment 1 comprised of positions 1–21000, fragment 2 of positions 21000–29364), with independent clocks, trees and migration rates, but shared substitution models and deme population sizes. Fragment positions were chosen based on consistent identification of the region around nucleotide 21000 as a probable breakpoint by GARD by previous studies into SARS and MERS coronaviruses. All analyses were set to run for 200 million states, subsampling every 20,000 states. Chains not converging after 200 million states were discarded. 20% of the states were discarded as burn-in, convergence assessed with Tracer 1.6 and combined with LogCombiner. Three chains out of ten did not converge. This left 70,000 states on which to base posterior inference. Posterior sets of typed trees were summarised using TreeAnnotator v2.4.3 with the common ancestor heights option.

31A currently widely used approach to infer ancestral states in phylogenies relies on treating traits of interest (such as geography, host, etc.) as features evolving along a phylogeny as continuous time Markov chains with an arbitrary number of states. Unlike structured coalescent methods, such discrete trait approaches are independent from the tree (i.e. demographic) prior and thus unable to influence coalescence rates under different trait states. Such models have been used in the past to infer the number of MERS-CoV host jumps with results contradicting other sources of information. In order to test how a discrete trait approach compares to the structured coalescent we used our 274 MERS-CoV genome data set in BEAST v2.4.3 and specified identical codon-partitioned nucleotide substitution and molecular clock models to our structured coalescent analysis. To give the most comparable results, we used a constant population size coalescent model, as this is the demographic function for each deme in the structured coalescent model. Five replicate MCMC analyses were run for 200 million states, three of which converged onto the same posterior distribution. The converging chains were combined after removing 20 million states as burn-in to give a total of 27,000 trees drawn from the posterior distribution. These trees were then summarised using TreeAnnotator v2.4.5 with the common ancestor heights option.

32We extracted the times of camel-to-human introductions from the posterior distribution of multitype trees. This distribution of introduction times was then discretised as follows: for sample from the posterior, was if there as an introduction in month and year and 0 otherwise. We model the sum of introductions at month and year across the posterior sample with the hierarchical model:where represents the contribution of year to expected introduction count and represents the contribution of month to expected introduction count. Here,. We sampled posterior values from this model via the Markov chain Monte Carlo methods implemented in Stan. Odds ratios of introductions were computed for each month as.

33Here, we employ a Monte Carlo simulation approach to identify parameters consistent with observed patterns of sequence clustering (Figure 3—figure supplement 2). Our structured coalescent analyses indicate that every MERS outbreak is a contained cross-species spillover of the virus from camels into humans. The distribution of the number of these cross-species transmissions and their sizes thus contain information about the underlying transmission process. At heart, we expect fewer larger clusters if fundamental reproductive number is large and more smaller clusters if is small. A similar approach was used in to estimate for Zika introductions into Florida.

34Branching process theory provides an analytical distribution for the number of eventual cases in a transmission chain resulting from a single introduction event with and dispersion parameter. This distribution follows

35Here, represents the expected number of secondary cases following a single infection and represents the dispersion parameter assuming secondary cases follow a negative binomial distribution, so that smaller values represent larger degrees of heterogeneity in the transmission process.

36As of 10 May 2017, the World Health Organization has been notified of 1952 cases of MERS-CoV. We thus simulated final transmission chain sizes using Equation 1 until we reached an epidemic comprised of cases. 10,000 simulations were run for 121 uniformly spaced values of across the range [0.5–1.1] with dispersion parameter fixed to 0.1 following expectations from previous studies of coronavirus behavior. Each simulation results in a vector of outbreak sizes, where is the size of the ith transmission cluster and and is the number of clusters generated.

37Following the underlying transmission process generating case clusters, we simulate a secondary process of sampling some fraction of cases and sequencing them to generate data analogous to what we empirically observe. We sample from the case cluster size vector without replacement according to a multivariate hypergeometric distribution (see Algorithm 1: Multivariate hypergeometric sampling scheme). The resulting sequence cluster size vector contains entries, some of which are zero (i.e. case clusters not sequenced), but which reflects the number of human MERS-CoV sequences used in this study. Note that this ‘sequencing capacity’ parameter does not vary over time, even though MERS-CoV sequencing efforts have varied in intensity, starting out slow due to lack of awareness, methods and materials and increasing in response to hospital outbreaks later. As the default sampling scheme operates under equiprobable sequencing, we also simulated biased sequencing by using concentrated hypergeometric distributions where the probability mass function is squared (bias = 2) or cubed (bias = 3) and then normalized. Here, bias enriches the hypergeometric distribution so that sequences are sampled with weights proportional to. Thus, bias makes larger clusters more likely to be ‘sequenced’.

38After simulations were completed, we identified simulations in which the recovered distribution of sequence cluster sizes fell within the 95% highest posterior density intervals for four summary statistics of empirical MERS-CoV sequence cluster sizes recovered via structured coalescent analysis: number of sequence clusters, mean, standard deviation and skewness (third central moment). These values were 48–61 for number of sequence clusters, 2.87–3.65 for mean sequence cluster size, 4.84–6.02 for standard deviation of sequence cluster sizes, and 415.40–621.06 for skewness of sequence cluster sizes.

39We performed a smaller set of simulations with 2500 replicates and twice the number of cases, that is,, to explore a dramatically underreported epidemic. Additionally, we performed additional smaller set of simulations on a rougher grid of values (23 values, 0.50–1.05), with 5 values of dispersion parameter (0.002, 0.04, 0.1, 0.5, 1.0) and 3 levels of bias (1,2,3) to justify our choice of dispersion parameter that was fixed to 0.1 in the main analyses (Figure 3—figure supplement 6).

40Pseudocode describes the multivariate hypergeometric sampling scheme that simulates sequencing. Probability of sequencing a given number of cases from a case cluster depends on cluster size and sequences left (i.e. ‘sequencing capacity’). The bias parameter determines how probability mass function of the hypergeometric distribution is concentrated.

41Data: Array of case cluster sizes in outbreak, sequences available, total outbreak size, where.

42Result: Array of sequence cluster sizes sampled:.

43Draw from a hypergeometric distribution with successes, failures after trials;

44while do

45;

46;

47Compute the probability mass function (pmf) for all possible values of,

48, where is the pmf for a hypergeometric distribution with successes, failures after trials;

49Draw a sequence cluster size from array of potential sequence cluster sizes according to;

50end

51Add remaining sequences to last sequence cluster;

52In order to infer the demographic history of MERS-CoV in camels we used the results of structured coalescent analyses to identify introductions of the virus into humans. The oldest sequence from each cluster introduced into humans was kept for further analysis. This procedure removes lineages coalescing rapidly in humans, which would otherwise introduce a strong signal of low effective population size. These subsampled MERS-CoV sequences from humans were combined with existing sequence data from camels to give us a dataset with minimal demographic signal coming from epidemiological processes in humans. Sequences belonging to the outgroup clade where most of MERS-CoV sequences from Egypt fall were removed out of concern that MERS epidemics in Saudi Arabia and Egypt are distinct epidemics with relatively poor sampling in the latter. Were more sequences of MERS-CoV available from other parts of Africa we speculate they would fall outside of the diversity that has been sampled in Saudi Arabia and cluster with early MERS-CoV sequences from Jordan and sequences from Egyptian camels. However, currently there are no indications of what MERS-CoV diversity looks like in camels east of Saudi Arabia. A flexible skygrid tree prior was used to recover estimates of scaled effective population size at 50 evenly spaced grid points across six years, ending at the most recent tip in the tree (2015 August) in BEAST v1.8.4, under a relaxed molecular clock with rates drawn from a lognormal distribution and codon position partitioned (positions and ) HKY nucleotide substitution models. At time of writing advanced flexible coalescent tree priors from the skyline family, such as skygrid are available in BEAST v1 but not in BEAST v2. We set up five independent MCMC chains to run for 500 million states, sampling every states. This analysis suffered from poor convergence, where two chains converged onto one stationary distribution, two to another and the last chain onto a third stationary distribution, with high effective sample sizes. Demographic trajectories recovered by the two main stationary distributions are very similar and differences between the two appear to be caused by convergence onto subtly different tree topologies. This non-convergence effect may have been masked previously by the use of all available MERS-CoV sequences from humans which may have lead MCMC towards one of the multiple stationary distributions.

53To ensure that recombination was not interfering with the skygrid reconstruction, we also split our MERS-CoV alignment into ten parts 2937 nucleotides long. These were then used as separate partitions with independent trees and clock rates in BEAST v1.8.4. Nucleotide substitution and relaxed clock models were set up identically to the whole genome skygrid analysis described above. Skygrid coalescent tree prior was used jointly across all ten partitions for demographic inference. Five MCMC chains were set up, each running for 200 million states, sampling every 20,000 states.

54Sequence data and all analytical code is publicly available at https://github.com/blab/mers-structure. A copy is archived at https://github.com/elifesciences-publications/mers-structure.