Upon successfully curbing transmission in spring 2020, many European countries witnessed a resurgence in cases of COVID-19 in the late summer. The number of COVID-19 infections increased rapidly, and by the end of October, it was clear that the continent was deep into a second epidemic wave. This forced governments to reimpose lockdowns and social restrictions in an effort to contain the resurgence. Although these measures reduced infection rates across Europe3, several countries witnessed a stabilization at high levels or even a new surge in infections. The spread of more transmissible variants, in particular B.1.1.7 (Alpha variant or 20I (V1)), which was first identified in the UK4, has considerably exacerbated the challenge to contain COVID-19.

Already early on in the pandemic, modelling studies warned about new waves due to partial relaxation of restrictions5 or seasonal variations6. By mid-April, the European Commission constructed a roadmap to lifting coronavirus containment measures7, recommending a cautious and coordinated manner to revive social and economic activities. However, the early start of the devastating second wave demonstrated that there was insufficient adherence to these measured recommendations. Cross-border travel, and mass tourism in particular, has been implicated as a major instigator of the second wave. Genomic surveillance demonstrated that a new variant (lineage B.1.1778, 20E (EU1) (, which emerged in Spain in early summer, has spread to multiple locations in Europe2. Although this variant quickly grew into the dominant circulating SARS-CoV-2 strain in several countries, it did not appear to be associated with a higher intrinsic transmissibility2.

Although it appears clear that travel considerably contributed to the second wave in Europe, it remains challenging to assess how it may have restructured and reignited the epidemic in the different European countries. Even without resuming travel, relaxing containment measures when low-level transmission is ongoing risks the proliferation of locally circulating strains. Phylodynamic analyses may provide insights into the relative importance of persistence versus the introduction of new lineages, but such analyses are complicated for SARS-CoV-2 for different reasons. Phylogenetic reconstructions may be poorly resolved owing to the relatively limited SARS-CoV-2 sequence diversity9. This is further confounded by the degree of genetic mixing that can be expected from unrestricted travel before the lockdowns in spring 2020.

Mobility data predicts SARS-CoV-2 spread

We analysed SARS-CoV-2 B.1 (20A) genomes from 10 European countries for which a minimal number of genomes from the second wave were already available on 3 November 2020. Using a two-step procedure that relied on subsampling relative to country-specific case counts (see Methods), we compiled a dataset of close to 4,000 genomes sampled between 29 January and 31 October 2020 (Extended Data Table 1). To achieve maximum resolution in our evolutionary reconstructions, we constructed a Bayesian time-measured phylogeographical model that integrates mobility and epidemiological data. Our approach simultaneously infers phylogenetic history and ancestral movement throughout this history while also identifying the drivers of spatial spread10. We used the latter functionality to determine the most appropriate mobility or connectivity measure. Specifically, we considered international air transportation data, the Google COVID-19 Aggregated Mobility Research Dataset (also referred to here as ‘mobility data’), and the social connectedness index of Facebook, as covariates of phylogeographical spread (Extended Data Fig. 1). The Google mobility dataset contains anonymized mobility flows aggregated over users who have turned on the location history setting, which is off by default (see Methods). The social connectedness index reflects the structure of social networks and has been suggested to correlate with the geographical spread of COVID-1911. To help to inform the phylogenetic coalescent time distribution, we parameterized the viral population size trajectories through time as a function of epidemiological case count data for the countries under investigation.

Analyses using both time-homogeneous and time-inhomogeneous models offered strong support for mobility data as a predictor of spatial diffusion whereas air transportation data and the social connectedness index offered no predictive value (Extended Data Table 2). The fact that mobility data encompassing both air and land-based transport are required to explain COVID-19 spread highlights the need to consider both types of transport in containment strategies. To ensure that containment strategies were accommodated by our reconstructions, we further extended our time-inhomogeneous approach to model biweekly variation in the overall rate of spread between countries as a function of mobility (see Methods and Extended Data Table 2).

Dynamic viral transmission through time

We use our probabilistic model of spatial spread informed by genomic, mobility and epidemiological data to characterize the dynamics of spread throughout the epidemic in Europe. We first focus on the ratio of introductions over the total viral flow in and out of each country over time and the genetic structure of country-specific transmission chains (Fig. 1). For the latter, we use a normalized entropy measure that quantifies the degree of phylogenetic interspersion of country-specific transmission chains in the SARS-CoV-2 phylogeny (see Methods). Although estimates for individual dispersal between pairs of countries can also be obtained (Extended Data Fig. 2), we remain cautious in interpreting these as direct pathways of spread because the genome sampling only covers a restricted set of European countries. The mobility to and from each country within our 10-country sample covers between 64% and 96% of the mobility of these countries to and from all countries within Europe (Extended Data Table 3 and Extended Data Fig. 3), except for Norway (27%), for which other Scandinavian countries account for considerable mobility connections (61%), and the UK (49%), for which Ireland accounts for a large fraction of mobility connections (38%).

Fig. 1: Mobility, genome sampling, case counts and phylogeographical summaries through time for 10 European countries.
figure 1

a, The country-specific Google mobility influx in the 10 countries during 2-week intervals. b, The weekly genome sampling by country used in the phylogeographical analysis. c, For each country, the ratio of introductions over the total viral flow from and to that country (in 2-week intervals) and a monthly normalized entropy measure summarizing the phylogenetic structure of country-specific transmission chains are shown. The posterior mean ratios of introductions are depicted with circles that have a size proportional to the total number of transitions from and to that country and the grey surface represents the 95% highest posterior density (HPD) intervals. The posterior mean normalized entropies and 95% HPD intervals are depicted by dotted lines. These normalized entropy measures indicate how phylogenetically structured the epidemic is in each country, and ranges from 0 (perfectly structured, for example, a single country-specific cluster) to 1 (unstructured interspersion of country-specific sequences across the entire SARS-CoV-2 phylogeny). The introduction ratios and normalized entropy measures are superimposed on the incidence of COVID-19 (daily cases per 106 people) reported for each country through time (coloured density plot). The two vertical dashed lines represent the summer time interval (15 June and 15 August 2020) for which we subsequently evaluate introductions versus persistence (see Fig. 2).

According to the proportion of introductions, we estimate more viral import than export events for Switzerland, Norway, the Netherlands and Belgium throughout most of the time period under investigation. According to the estimated phylogenetic entropy, these countries also experienced many independent transmission chains since the epidemic started to unfold. This is consistent with country-specific studies; for the first wave in Belgium, for example, about 331 individual introductions were estimated in the ancestry of a limited sample of 740 genomes12. For Portugal, we also estimate higher proportions of introductions early in the first wave but with a subsequent decline to predominantly export events. France, Italy and Spain, on the other hand, are characterized by a relatively high viral export during the first wave. The proportion of introductions remained relatively low for Italy and Spain after the first wave, whereas in France these proportions were high from mid-June until the end of July. However, the absolute number of transitions in our sample are low during this time period. These countries also had comparatively lower entropy values early in the epidemic, with an increase for France by the start of summer and a more gradual increase over time for Italy. In Spain, however, the genetic complexity of the SARS-CoV-2 transmission chains remained limited. In the UK and Germany, the viral flow in and out of the country was initially relatively balanced. A recent large-scale genomic analysis in the UK indicates that this can imply very high absolute numbers of cross-country transmissions, as more than 2,800 independent introduction events were identified from the analysis of 26,181 genomes13. Although our sample is limited compared to this UK-focused analysis13, our reconstructions also recover major influx from Spain, France and Italy during the first wave in the UK (Extended Data Fig. 2). We estimate an increase in the proportion of introductions for the UK from mid-June, indicating an important viral import relative to export around this time. The phylogenetic entropy also peaked around this time. In Germany, the proportions increased slightly later in the summer with a concomitant rise in phylogenetic entropy.

Introductions thrive in low incidence

To assess the effect of summer travel on the second wave in the different countries, we use our genomic–mobility reconstruction to estimate both the number of lineages persisting in each country and the number of newly introduced lineages, and how these proliferated early in the second wave. We focus on a 2-month time period between 15 June 2020—when many EU and Schengen-area countries opened their borders to other countries—and 15 August 2020, before which the majority of holiday return travel is expected for many countries. We identify the number of lineages circulating in each country on 15 August and determine whether they result from a lineage that persisted since 15 June or from a unique introduction after this date (independent of the number of descendants for this lineage on 15 August; Extended Data Fig. 4). In Fig. 2, we plot (1) the ratio of these unique introductions over the total unique lineages (unique introductions and persisting lineages); (2) the proportion of descendant lineages on 15 August that resulted from the unique introductions over the total descendants circulating on this date; and (3) the proportion of descendant tips (sampled genomes) after 15 August that resulted from the unique introductions over the total number of descendant tips (see Methods and Extended Data Fig. 4). We estimate a posterior mean proportion of unique introductions that is close to or higher than 0.5 except for Spain and Portugal. This indicates that by 15 August, a relatively large fraction of circulating lineages in each country was produced by new introductions over summer. Because the B.1.177/20E (EU1) variant that was predominantly disseminated through summer travel does not appear to be particularly more transmissible2, this is unlikely to be due to strong intrinsic advantages of the newly introduced viruses.

Fig. 2: Posterior estimates for the relative importance of lineage introduction events in 10 European countries.
figure 2

We report three summaries (posterior mean and 95% HPD intervals) for each country: the ratio of unique introductions over the total number of unique persisting lineages and unique introductions between 15 June and 15 August 2020 (1), the ratio of descendant lineages from these unique introduction events over the total number of descendants circulating on 15 August 2020 (2) and the ratio of descendant taxa from these unique introductions over the total number of descendant taxa sampled after 15 August 2020 (3) (see Extended Data Fig. 4). The dots are numbered and the sizes are proportional to: (1) the total number of unique lineage introductions identified between 15 June and 15 August 2020; (2) the total number of lineages inferred on 15 August 2020; and (3) the total number of descendant tips after 15 August 2020.

The two proportions of descendants from these introductions on 15 August and after this date measure the relative success of newly introduced lineages compared to persisting lineages, indicating considerable variation in onward transmission. In Fig. 2, the country estimates are ordered according to decreasing average incidence during the 15 June–15 August time period, suggesting that incidence may shape the outcome of the introductions. In countries that experienced relatively high summer incidence (for example, Spain, Portugal, Belgium and France), the introductions lead to comparatively fewer descendants on 15 August or after. We find a significant overall association between the incidence and the difference in the logit-scaled proportion of unique introductions and the logit-scaled proportion of their descendants on 15 August (P = 0.007) as well as between the incidence and the difference in the logit-scaled proportion of unique introductions and the logit-scaled proportion of descendant tips after 15 August (P = 0.019) (Extended Data Fig. 5). With comparatively few descendants from introductions (Fig. 2), Norway may to some extent be an outlier because lineages estimated as persisting in this country could in fact be introductions from other Scandinavian countries that are not represented in our genome sample. We recover qualitatively similar, but more variable and statistically unsupported associations between the success of introductions and incidence for the 2-month time periods before and after the 15 June–15 August time period (Extended Data Fig. 5). This indicates that the comparatively higher proportion of introductions as well as the more stable and lower incidence between 15 June and 15 August provided the ideal conditions for a process of genetic drift by which introductions were able to fuel transmission.

Our estimates show that introductions in the UK particularly benefited from the conditions for successful onward transmission (Fig. 2), with a considerable fraction of introductions originating from Spain (Extended Data Fig. 6), reflecting the spread of B.1.177/20E (EU1), which rapidly became the most dominant strain in the UK2. Our analysis captures the expansion of this variant as well as that of B.1.160/20A.EU2, which together account for more than 25% of the genomes in our dataset. Although Spain was indeed inferred to be the origin of B.1.177/20E (EU1), the UK also considerably contributed to its spread (Fig. 3). The earliest introduction from Spain to the UK was estimated around the time Spain opened most EU borders (21 June) (Fig. 3). Although introductions from Spain to other countries soon followed, we estimate a similar rate and amount of spread from the UK to other countries before these other countries also further disseminated the virus. Although inferred from a limited sample, this illustrates a dynamic pattern of spread and the importance of the early establishment of B.1.177/20E (EU1) in the UK that probably served as an important secondary centre of dissemination. We note, however, that this pattern may be affected by the intensive and continuous genomic surveillance in the UK, which may also be reflected in our subsample of the available data. Although the UK is also involved in the spread of B1.160/20A.EU2, this variant has been largely disseminated from France (Fig. 3). The fact that this variant expanded later in France and subsequently also started to spread later compared to B.1.177/20E (EU1) (Extended Data Fig. 7) may explain why the latter spread more successfully.

Fig. 3: Phylogeographical estimates of SARS-CoV-2 spread in 10 European countries.
figure 3

a, The maximum clade credibility tree summary of the Bayesian inference. Colours correspond to the countries in the legend. The two clades corresponding to B1.160/20A.EU2 and B1.177/20E (EU1) are highlighted in grey. b, c, Circular migration flow plots for B1.160/20A.EU2 (b) and B1.177/20E (EU1) (c) based on the posterior expectations of the Markov jumps. In these plots, migration flow out of a particular location starts close to the outer ring and ends with an arrowhead more distant from the destination location. d, Posterior mean estimates with 95% HPD intervals over time for four types of Markov jumps for B1.177/20E (EU1): from Spain to the UK, from Spain to other countries, from the UK and from other countries.


Our Bayesian phylogeographical approach builds on a rich history of identifying drivers of spatial spread, with applications to various pathogens at different spatial scales, ranging from air transportation for influenza at a global scale10 to gravity model transmission for Ebola in West Africa14. Such studies use a relatively limited genomic sample to gain insights into viral transmission dynamics. This is also the case in our application to SARS-CoV-2 in Europe for which we further extend the phylodynamic data integration approach to confront the lack of resolution offered by SARS-CoV-2 genomic data. A concerted effort in containing international spread further sets apart the COVID-19 pandemic from these earlier events. For this reason, we have now incorporated variation in mobility over time to account for the effect of these measures. Our reconstructions show that the composition of lineages circulating towards the end of the summer was to an important extent shaped by introductions in most of the European countries. The relative success of onward transmission of the introduced lineages appears to be shaped by the local incidence of COVID-19 during summer.

Our results should be interpreted in light of several important limitations. In addition to a limited overall size, the genome data only cover a selection of European countries, suggesting that we are missing transmission events that involve unsampled countries. This may be important for Norway, for example, which according to our mobility data, is largely connected to other Scandinavian countries. We also lack sampling from eastern Europe, which was to a large extent spared by border controls and lockdowns during the first wave, but witnessed high excess mortality rates during the second wave. The emergence of more transmissible variants has led to more intensified genomic surveillance, so similar phylodynamic reconstructions may now be performed on a wider scale.

The pandemic exit strategy offered by vaccination programmes is a source of optimism that also sparked proposals by EU member states to issue vaccine passports in a bid to revive travel and rekindle the economy. In addition to implementation challenges and issues of fairness, there are risks associated with such strategies when immunization is incomplete, as probably will be the case for the European population this summer. A recent modelling study for the UK suggests that vaccination in adults alone is unlikely to completely halt the spread of cases of COVID-19 and that lifting containment measures early and suddenly can lead to a large wave of infections15. A gradual release of restrictions was shown to be critical for minimizing the infection burden15. We believe that travel policies may be a key consideration in this respect because similar conditions may arise to the ones that we demonstrated to provide fertile ground for viral dissemination and resurgence in 2020. This may now also involve the spread of variants that are more transmissible and/or evade the immune responses triggered by vaccines and previous infections. Well-coordinated European strategies will therefore be required to manage the spread of SARS-CoV-2 and reduce future waves of infection, with hopefully a more unified implementation than hitherto observed.


Data reporting

No statistical methods were used to predetermine sample size. The experiments were not randomized and the investigators were not blinded to allocation during experiments and outcome assessment.

Sequence data and subsampling

We used a two-step genome data collection procedure. We first evaluated the available genomes from European countries in GISAID16 on 3 November 2020. We selected genomes from Belgium, France, Germany, Italy, the Netherlands, Norway, Portugal, Spain, Switzerland and the UK primarily based on the availability of genome data from both the first and second wave at that time but also because of their high ratio of genomes to positive cases. A total of 39,812 genomes were available for these countries on 3 November 2020; the available number of genomes per country is listed in Extended Data Table 1. Portugal represented an exception because data for this country were limited to the first wave at that time, but we included genomes from Portugal because of its potential importance as a summer travel location.

We aligned the genomes from each country using MAFFT v.7.45317 and trimmed the 5′ and 3′ ends and only retained unique sequences from each location. To further mitigate the disparities in sampling, we subsampled each country proportionally to the cumulative number of cases on 21 October 2020 (the most recently sampled sequence at the time) by setting an arbitrary threshold of 6.5 sequences per 10,000 cases, with a minimum number of 100 sequences per country. To maximize the temporal and spatial coverage in each country, we binned genomes by epi-week and sampled as evenly as possible, sampling from a different region within the country when available. Only sequences from the B.1 lineage with the D614G substitution and exact sampling dates were selected for the analyses. From the final aligned sequence set, we removed 12 potential outliers, based on a root-to-tip regression applying TempEst v.1.5.318 to a maximum-likelihood tree inferred with IQTREE v.2.0.319, yielding a dataset of 2,909 genomes (Extended Data Table 1).

Because of the nature of genome sequence accumulation, fewer recently sampled genomes were available for most countries on 3 November 2020 (relative to the case counts at this time). Because our primary goal was to assess the persistence and introduction of lineages leading up to the second wave, we sought to augment our dataset with more recent genomes, having already performed analyses on the initial dataset. In the section on Bayesian evolutionary reconstructions, we outline how we updated these analyses accordingly. On 5 January 2021, we updated our dataset by adding more than 1,000 non-identical sequences collected between 1 August and 31 October (out of a total of 56,395 available genomes; the available and selected numbers of genomes per country are listed in Extended Data Table 1). For Portugal, we extended this period back to 22 June (the most recent sampling date for the previous Portuguese selection). We downloaded all new B.1 sequences with the D614G substitution collected during the selected time period from GISAID and performed the following subsampling. The number of genomes to add per country was obtained by raising the threshold ratio of sequences/cases to 8.5 and increasing the minimum number of sequences to 200. To bias the temporal coverage towards more recent samples, the genomes from each country were binned by week and sampled such that the number of sequences added per week was proportional to an exponential function of the form et/4, where t = 0 represents 1 August and t = 13 is 31 October. For Portugal, we did not use this preferential sampling as we needed to include close to all available genomes to increase the number of genomes to 200. The selected sequences were deduplicated and outliers were removed as described in the previous paragraph. With the additional selection of 1,050 genomes, we obtained a dataset of 3,959 genomes (Extended Data Table 1).

Mobility data

We analysed four different mobility and connectivity measures: air traffic flows, a social connectedness index provided by Facebook, as well as aggregated Facebook20 and Google international mobility data. Air traffic flow data were obtained from the International Air Transport Association ( and based on the number of origin–destination tickets while also taking into account connections at intermediate airports21. We used monthly air traffic data between the 10 European countries under investigation for the time period between January 2020 and October 2020. The social connectedness index (SCI) is an anonymized snapshot of active Facebook users and their friendship networks to measure the intensity of social connectedness between countries ( In practice, the SCI measures the relative probability of a Facebook friendship link between two users of the application in different countries. We used the SCI calculated for the 10 European countries represented in our genomic sample as of August 2020.

The Google COVID-19 Aggregated Mobility Research Dataset contains anonymized mobility flows aggregated over users who have turned on the location history setting (on a range of platforms23), which is off by default. To produce this dataset, machine learning is applied to logs data to automatically segment it into semantic trips24. To provide strong privacy guarantees, all trips were anonymized and aggregated using a differentially private mechanism25 to aggregate flows over time (see This research was done on the resulting heavily aggregated and differentially private data. No individual user data was ever manually inspected, only heavily aggregated flows of large populations were handled. All anonymized trips were processed in aggregate to extract their origin and destination location and time. For example, if users travelled from location a to location b within time interval t, the corresponding cell (abt) in the tensor would be n ± η, where η is Laplacian noise. The automated Laplace mechanism adds random noise drawn from a zero-mean Laplace distribution and yields (εδ)-differential privacy guarantee of ε = 0.66 and δ = 2.1 × 10−29 per metric. Specifically, for each week W and each location pair (A,B), we compute the number of unique users who took a trip from location A to location B during week W. To each of these metrics, we add Laplace noise from a zero-mean distribution of scale 1/0.66. The parameter ε controls the noise intensity in terms of its variance and δ represents the deviation from pure ε privacy. The closer these parameters are to zero, the stronger the privacy guarantees. We used aggregated mobility flows between the 10 European countries and summarized them by 2-week or monthly time periods between January 2020 and October 2020.

Finally, we also considered international mobility data from Facebook mobility data as an alternative to Google mobility data. These data are based on the numbers of Facebook users moving over large distances, such as air or train travel. Counts of international travel patterns are updated daily based only on users who have opted to share precise location data from their device with the Facebook mobile app through location services. Also in this case, we used aggregated mobility flows between the 10 European countries and summarized them by month between January 2020 and October 2020. Because international aggregate mobility data obtained from Google and Facebook are highly correlated (monthly Spearman correlation ranging from 0.84 to 0.92) (Supplementary Fig. 1), we only included the Google aggregate mobility data as a covariate in the phylogeographical analyses. We note that the mobility data are subject to limitations as these may not be representative of the population as whole and their representativeness may vary by location.

Bayesian evolutionary reconstructions

Joint sequence–trait inference with a time-homogeneous generalized linear model of discrete trait diffusion

We performed a Bayesian evolutionary reconstruction of timed phylogeographical history using BEAST 1.1026, incorporating the genome sequences, their country and date of sampling, epidemiological and mobility and/or connectivity data. Because of the relatively low degree of resolution offered by the sequence data, our full probabilistic model specification focuses on (1) relatively simple model specifications and (2) informing parameters by additional non-genetic data sources. We modelled sequence evolution using an HKY85 nucleotide substitution model with a gamma-distributed rate variation among sites and a strict molecular clock model. Our genome set includes three genomes from an early outbreak in Bavaria, which was caused by an independent introduction from China27,28. We therefore constrained these genomes as an outgroup in the analysis, which according to root-to-tip regression plots as a function of sampling time resulted in a better correlation coefficient and R2 compared to the best-fitting root under the heuristic mean residual squared criterion18 (Supplementary Fig. 2).

As a coalescent tree prior, we modelled the effective population size trajectory as a piecewise constant function that changes values at pre-specified times (following a previously published study29), with log-transformed population sizes modelled as a deterministic function of log-transformed counts of cases of COVID-19 (following a previous publication30). This reduces the nonparametric skygrid parameterization to a generalized linear model (GLM) formulation with an estimable regression intercept (α) and coefficient (β). In this parameterization, a coefficient estimate centred around 0 would imply constant population size dynamics through time. We specified 2-week intervals and summarized as a covariate the total case counts over these time intervals for the 10 countries of sampling (obtained from The earliest interval with non-zero cases counts was from 14 January 2020 to 28 January 2020; before 14 January 2020, the log-transformed and standardized case count covariate was set to the equivalent of 1 case. We also tested whether a lag time was required for the case count covariate using marginal likelihood estimation31. Specifically, we shifted the case counts by 1, 2, 3 and 4 weeks before summarizing them according to 2-week intervals and estimated the model fit of these covariates against case counts without lag time (Supplementary Table 1). To mitigate the computational burden associated with the marginal likelihood estimation procedure, we performed these analyses on a subset of 1,000 genomes (obtained using the Phylogenetic Diversity Analyzer tool32). We estimated the highest (log-transformed) marginal likelihood for a two-week lag time (Supplementary Table 1) and used this for the case count covariate in our analyses.

Similar to sequence evolution, we modelled the process of transitioning through discrete location states (countries of sampling) according to a continuous-time Markov chain (CTMC)33. We used a parameterization that models the log-transformed transition rates as a log-linear function of mobility and connectivity covariates10. The Bayesian implementation of this model simultaneously estimates the phylogenetic history, ancestral movement and the contribution of covariates to the movement patterns10. Although we mainly use this approach to obtain well-informed phylodynamic estimates, we also make use of its capacity to identify the most-relevant mobility measure to inform our reconstructions. As covariates we considered the SCI of Facebook, air transportation data and mobility data. For the two time-variable mobility measures, we used the average of the log-transformed and standardized monthly mobility measures as a single covariate in our time-homogeneous phylogeographical GLM model. In this GLM formulation, we estimate the positive effect sizes for each covariate as well as their inclusion probability through a spike-and-slab procedure10. Although we subsampled the number of SARS-CoV-2 genomes per country in proportion to case counts, they do not fully correspond because we used a minimum number of genomes for countries with low case counts. We therefore evaluated whether this resulted in signal for sampling bias by including an origin and destination covariate in the GLM based on the residuals for a regression analysis between genomes and case counts (following a previously published study14). We performed this analysis using a set of empirical trees (see ‘Time-inhomogeneous reconstructions’) applying both a time-homogeneous and time-inhomogeneous model, but found no support for these additional covariates (Supplementary Table 2).

We performed inference under the full model specification using Markov chain Monte Carlo (MCMC) sampling and used the BEAGLE library v.334 to increase computational performance. We specified standard transition kernels on all parameters, except for the regression coefficients of the piecewise-constant coalescent GLM model. For these parameters, we implemented new Hamiltonian Monte Carlo transition kernels to improve sampling efficiency. These kernels use principles from Hamiltonian dynamics and their approximate energy conserving properties to reduce correlation between successive sampled states, but require computation of the gradient of the model log-posterior with respect to the parameters of interest, in addition to efficient evaluation of the log-posterior that BEAGLE provides. To accomplish this, we extended our previous analytic derivation of the gradient of the log-transformed density from the skygrid coalescent model with respect to the log-transformed population sizes35 to now be with respect to the regression coefficients using the chain rule and their regression design matrix.

Owing to the dataset size, MCMC burn-in takes up considerable computational time. We therefore iterated through a series of BEAST inferences, initially only considering sequence evolution and subsequently adding the location data, to arrive at a tree distribution from which trees were taken as starting trees in our final analyses. The latter was composed of multiple independent MCMC runs that were run sufficiently long to ensure that their combined posterior samples achieved effective sample sizes larger than 100 for all continuous parameters.

Data augmentation through online BEAST

As we updated our dataset after the initial analyses of the 2,909 genome collection using the approach discussed (see ‘Bayesian evolutionary reconstructions’), we sought to capitalize on these efforts to limit the burn-in for subsequent analyses of the 3,959 dataset. Specifically, we adopted the distance-based procedure to insert new taxa into a time-measured phylogenetic tree sample as implemented in the BEAST framework for online inference36. We subsequently use the augmented tree as the starting tree for the analyses of the updated dataset.

Time-inhomogeneous reconstructions

To accommodate the time variability of the mobility measures, we constructed epoch model extensions of the discrete phylogeography approach that allow specifying arbitrary intervals over the evolutionary history and associating them with different model parameterizations37. As a complement to testing covariates of spatial diffusion using a time-homogeneous model, we used the epoch extension to specify monthly intervals, enabling us to incorporate monthly mobility matrices (air transportation data were available only as monthly numbers), but assuming time-homogeneous effect sizes and inclusion probabilities. Monthly covariates were again log-transformed and standardized after adding a pseudo-count to each entry in the monthly matrices.

In addition, we performed another analysis in which we relaxed the constant-through-time inclusion probability of the covariates. In this model specification, each interval is associated with a specific set of indicator variables to represent the inclusion or exclusion of covariates, but we pool information about predictor inclusion across the intervals using hierarchical graph modelling38. This approach uses a set of indicator variables to model covariate inclusion at the hierarchical level but enables interval-specific inclusion or predictors to diverge from the hierarchical level with a non-zero probability (with the number of differences modelled as a binomial distribution38), which was set to 0.10 in our study. We estimated hierarchical and interval-level inclusion using the spike-and-slab procedure38.

Finally, we performed an analysis using the time-inhomogeneous model in which the interval-specific transition rates are modelled as a function of the single covariate that is supported by the analyses above leveraging aggregate mobility. We incorporated more variability through time by specifying 2-week intervals (similar to the coalescent GLM interval specification). In addition, we add time-homogeneous random effects to the phylogeographical transition rate parameterization to account for potential biases in the ability of mobility to predict phylogeographical spread. Although the posterior mean estimates for these random effects vary, only very few indicate that individual phylogeographical transition rates significantly deviate from the mobility data (Supplementary Fig. 3). The time-inhomogeneous GLM approach that we use enables the modelling of relative differences in transition rates, but also the overall rate of migration between countries varies through time, and importantly, this is strongly affected by intervention strategies. To accommodate these dynamics, we further extend this model by incorporating a time-inhomogeneous overall CTMC rate scaler and parameterize it as a log-linear function of the total monthly between-country log-transformed and standardized mobility (time-variable rate scalar GLM in Extended Data Table 2). To generate realizations of the discrete location CTMC process and obtain estimates of the transitions (Markov jumps) between states under this model, we used posterior inference of the complete Markov jump history through time10,39.

Although the epoch model enables us to flexibly accommodate time-variable spatial dynamics, it considerably increases the computational burden associated with likelihood evaluations. To efficiently draw inferences under this model for our large dataset, we fit the time-inhomogeneous spatial diffusion process to a set of trees inferred under the time-homogeneous GLM diffusion model described above. Although likelihood evaluations remain computationally expensive, even with the speed-up offered by GPU computation with BEAGLE, eliminating simultaneous tree estimation tremendously reduces the parameter space, requiring only modest MCMC chain lengths to adequately explore it. Model and inference specifications for the different analyses are available as BEAST XML input files on GitHub ( and Zenodo (

Posterior summaries

We assessed MCMC mixing (for example, using effective sample sizes) and summarized continuous parameter estimates using Tracer v.1.7.140. Credible intervals were computed as 95% HPD intervals. Trees were visualized using FigTree v.1.4.4 (available at In terms of phylogeographical estimates, we mainly focused on (1) transitions to each location and from each location (based on Markov jump estimates) instead of pairwise transitions; (2) ratios of these transitions and (3) how these transitions structured transmission chains in individual countries. Transitions to and from each location avoid drawing conclusions about direct migration between countries, which can be tenuous given the incomplete genome coverage of Europe, while their ratios avoid using absolute numbers of transitions, which are highly sample-dependent. Phylogeographical inference is limited to reconstructing the transitions in the ancestral history of a sample of sequences, which will only be a small fraction of the actual migration events especially when these events result in insufficient onward transmission to be captured in our limited sample. In addition, SARS-CoV-2 genome data can be poorly resolved and identical genomes in different locations are consistent with hypotheses that involve both a sparse and a rich number of virus flows between these locations. As the data hold little information to distinguish these hypotheses, we only consider sparse scenarios by including only unique sequences for each location. A joint inference of sequence evolution and discrete spatial diffusion would err on the side of sparse hypotheses anyway because it will tend to cluster identical sequences that share a location. Despite the general underestimation of spatial dispersal, a phylogeographical inference is still likely to capture the transition events with important onward transmission, and evaluating the importance of such events relative to persistence is a major focus of this study. Cryptic transmission also complicates the ability to reconstruct spatial dispersal, but we expect this to be equally likely for introductions and persistence and therefore focus on their ratio for each location.

We provide three new tree sample tools in the BEAST codebase on GitHub ( to obtain posterior summaries of location transition histories using posterior tree distributions annotated with Markov jumps:

(1) TreeMarkovJumpHistoryAnalyzer enables the collection of Markov jumps and their timings from a posterior tree distribution annotated with Markov jumps histories in a .csv file for further analyses.

(2) TreeStateTimeSummarizer decomposes the total tree time into the times associated with contiguous partitions of a tree estimated to be in a particular location state, with the partitions determined by the Markov jumps. An arbitrary lower- and upper-time boundary can be specified to restrict the summary to a particular time interval in the evolutionary history. We use the time estimates for the separate partitions associated with each state to calculate an entropy measure that summarizes the genetic make-up of country-specific transmission chains. Specifically, we use for each location a normalized Shannon entropy:

$$-\frac{1}{\mathrm{ln}(n)}\mathop{\sum }\limits_{i}^{n}{p}_{i}\,\mathrm{ln}({p}_{i}),$$

where pi is the proportion of time associated with that location for partition i of a phylogeographical tree and n represents the number of partitions for that location in the tree.

(3) PersistenceSummarizer also uses posterior tree distributions annotated with Markov jumps to summarize the number of lineages at a particular point in time (evaluation time (Te); see Extended Data Fig. 5), which location states they are associated with, since what time point in the past they have maintained that state and how many sampled descendants they have after time Te (Extended Data Fig. 5). In addition, it enables summarizing how long these lineages have circulated independently before Te, so before sharing common ancestry with other lineages that maintained the same location state. This information allows us to determine how many lineages are circulating at Te that stem either from a unique persistent lineage (maintaining the same location states) or unique introduction event since a particular time before Te (ancestral time (Ta) in Extended Data Fig. 5). The association between incidence and the difference in the logit proportion of unique introductions and the logit proportion of their descendants on 15 August was evaluated using a P value obtained by a linear regression analysis.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this paper.