Bayesian inference of reassortment networks reveals fitness benefits of reassortment in human influenza viruses Nicola F. Muller¨ a,b,c,1 , Ugne˙ Stolza,b , Gytis Dudasd , Tanja Stadlera,b, and Timothy G. Vaughana,b,1

aDepartment of Biosystems Science and Engineering, ETH Zurich, 4058 Basel, Switzerland; bSwiss Institute of Bioinformatics, 1015 Lausanne, Switzerland; cVaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, WA 98109; and dDepartment of Biological and Environmental Sciences, University of Gothenburg, SE-40530 Gothenburg, Sweden

Edited by David M. Hillis, The University of Texas at Austin, Austin, TX, and approved May 11, 2020 (received for review October 22, 2019)

Reassortment is an important source of genetic diversity in seg- ding of segment trees within these, allowing us to infer these mented viruses and is the main source of novel pathogenic parameters from available sequence data. influenza viruses. Despite this, studying the reassortment process The reassortment process modeled in this way differs from has been constrained by the lack of a coherent, model-based infer- other recombination processes in that it is known where on the ence framework. Here, we introduce a coalescent-based model genome recombination of genetic material occurs and in that that allows us to explicitly model the joint coalescent and reas- there is no ordering of the segments. The lack of linkage between sortment process. In order to perform inference under this model, segments means that at a reassortment event, any subset of we present an efficient Markov chain Monte Carlo algorithm to segments can originate from either parent. sample rooted networks and the embedding of phylogenetic trees In order to perform inference under such a model, the reas- within networks. This algorithm provides the means to jointly sortment network and the embedding of each segment tree infer coalescent and reassortment rates with the reassortment within that network must be jointly inferred. This is similar to network and the embedding of segments in that network from the well-known and challenging problem of inferring ancestral full-genome sequence data. Studying reassortment patterns of recombination graphs (ARGs). While many approaches to infer- different human influenza datasets, we find large differences ring ARGs exist, some are restricted to tree-based networks (12, in reassortment rates across different human influenza viruses. 13), meaning that the networks consist of a base tree where Additionally, we find that reassortment events predominantly recombination edges always attach to edges on the base tree. occur on selectively fitter parts of reassortment networks show- Other approaches (e.g., ref. 14) rely on approximations (15) ing that on a population level, reassortment positively contributes and are not applicable to the reassortment model due to its to the fitness of human influenza viruses. aforementioned lack of segment ordering. Completely general inference methods exist (16), but these are again not directly phylogenetics | phylodynamics | infectious diseases | BEAST | MCMC

Significance hrough rapid evolution, human influenza viruses are able to evade host immunity in populations around the globe. In T Genetic recombination processes, such as reassortment, make addition to mutation, reassortment of the different physically it complex or impossible to use standard phylogenetic and unlinked segments of influenza genomes provides an impor- phylodynamic methods. This is due to the fact that the shared tant source of viral diversity (1). If a cell is infected by more evolutionary history of individuals has to be represented by a than one virus, progenitor viruses can carry segments from more phylogenetic network instead of a tree. We therefore require than one parent (2). With the exception of accidental release novel approaches that allow us to coherently model these pro- of antigenically lagged human influenza viruses (3), reassort- cesses and that allow us to perform inference in the presence ment remains the sole documented mechanism for generating of such processes. Here, we introduce an approach to infer pandemic influenza strains (e.g., refs. 4–6). reassortment networks of segmented viruses using a Markov To characterize reassortment events, tanglegrams, comparison chain Monte Carlo approach. Our approach allows us to study between tree heights (7, 8), or ancestral state reconstructions (9) different aspects of the reassortment process and allows us are typically deployed. These approaches identify discordance to show fitness benefits of reassortment events in seasonal between different segment tree topologies or differences in human influenza viruses. pairwise distances between isolates across segment trees. Tangle- grams in particular require a substantial amount of subjectivity Author contributions: N.F.M., T.S., and T.G.V. designed research; N.F.M., U.S., and T.G.V. and have been described as potentially misleading (10). performed research; N.F.M., G.D., and T.G.V. analyzed data; N.F.M., U.S., G.D., T.S., and While the reassortment process has been intensively studied T.G.V. wrote the paper; and N.F.M., U.S., and T.G.V. implemented software.y (e.g., refs. 7–9 and 11), there is currently no explicit model-based The authors declare no competing interest.y inference approach available. We address this by introducing a This article is a PNAS Direct Submission.y coalescent-based model for the reassortment of viral lineages. This open access article is distributed under Creative Commons Attribution License 4.0 In this phylogenetic network model, ancestral lineages carry (CC BY).y genome segments, of which only a subset may be ancestral to Data deposition: All other data, such as log files of BEAST2 runs, as well as scripts to ana- sampled viral genomes. As in a normal coalescent process, net- lyze and plot results, are available on GitHub at https://github.com/nicfel/Reassortment- work lineages coalesce (merge) with each other backward in Material. The source code for the BEAST2 package CoalRe itself is available on GitHub at https://github.com/nicfel/CoalRe. The python scripts to plot phylogenetic networks is time at a rate inversely proportional to the effective popula- available on GitHub at https://github.com/evogytis/baltic.y tion size. We model reassortment (splitting) events as a result 1 To whom correspondence may be addressed. Email: [email protected] or of a constant-rate Poisson process on network lineages. At such [email protected] a splitting event, the ancestry of segments on the original lin- This article contains supporting information online at https://www.pnas.org/lookup/suppl/ eage diverges, with a random subset following each new lineage. doi:10.1073/pnas.1918304117/-/DCSupplemental.y We thus explicitly model reassortment networks and the embed- First published July 6, 2020.

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Fig. 2. Comparison of estimates between the coalescent with reassortment and assuming that each segment codes for an independent realization of the same coalescent process. (A) Comparison of the relative width of the 95% HPD interval of segment tree node heights using 10 random subsets. The vertical axis shows the distribution of ratios of the relative width of the 95% HPD intervals of the coalescent with reassortment over the coalescent assuming independent segment evolution. These values demonstrate a strong reduction in node height uncertainty when using the coalescent with reassortment over the coalescent with independent segments. (B) Comparison between the distribution of posterior clade support of segment trees found the MCC segment trees using 10 random subsets. (C) Comparison between the inferred effective population sizes. When assuming each segment is an independent realization of the same coalescent process, the effective population sizes are inferred to be much smaller and much more certain. (D) Comparison between the inferred clock rates. The coalescent with reassortment infers lower clock rates.

and upper bound of the 95% HPD interval, by the median node more representative of those between geographically more sepa- height estimate to get the relative width of the HPD interval rated lineages. These events therefore provide information about for each clade. As shown in Fig. 2A, using the coalescent with larger effective population sizes. Coalescent events across differ- reassortment reduces the uncertainty of node height estimates ent segments that occur close to the tips are less likely to have of segment tree nodes by 35% for p2009-like H1N1 up to over encountered reassortment events. In the coalescent with reas- 50% for influenza B. sortment, they are therefore interpreted as one event, whereas Next, we computed the distribution of clade supports for in the coalescent with independent segments, they are inter- clades represented in the maximum clade credibility (MCC) preted as eight. Coalescent events deeper in the tree are more trees (as described by ref. 17) inferred using the two approaches. likely between lineages that encountered reassortment events As shown in Fig. 2B, segment tree clades are far better resolved and are therefore more likely to provide independent informa- when using the coalescent with reassortment for all datasets. tion about the population process. The coalescent with indepen- We then compared the effective population sizes and evolu- dent segments assumes that all coalescent events provide the tionary rates inferred using the two approaches. The coalescent same amount of information about the population process and with reassortment infers higher effective population sizes for will consequently favor information about the population pro- all datasets (Fig. 2C). This also influences the inferred clock cess closer to the tips. This leads to differences in the estimated rates, since lower effective population sizes put stronger weight effective population sizes, which then leads to differences in the on shorter branches and therefore larger clock rates (Fig. 2C). estimated clock rates. We explain this discrepancy as follows. While we currently do We also compared the performance of the two approaches not account for population structure, the datasets we analyze by inferring tip dates (18). The tips (leaf nodes) are the only are in part shaped by population structure, such as geographic nodes in the trees or network for which we can actually pre- structure. Ignoring this structure likely affects the coalescent sume to know the true age, which is set by the sample collection with reassortment differently compared with assuming indepen- time. To compare the two approaches, we compiled 1,000 smaller dent segments. Coalescent events closer to the tips are more influenza A/H3N2 datasets, each composed of 20 genomes. Of likely between lineages that are, for example, geographically those datasets, 500 were randomly sampled from an random more closely related and can be assumed to occur rapidly and interval of 2 y between 1995 and 2019. The remaining 500 provide information about low effective population size values. datasets were assembled using a random sampling interval of Coalescent events deeper in the tree on the other hand are 10 y between 1995 and 2019. From each of these datasets, we

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Fig. 4. Estimates of reassortment rates on fit and unfit edges. (A) Here, we show the number of reassortment events on fit and unfit edges of the networks divided by the total length of fit and unfit edges. Fit edges are defined as having a sampled descendant at least 2 y into the future. Every other edge is considered unfit. These rates are shown for different human influenza viruses on the x axis. The violin plots denote the distribution of theses ratios over the posterior distribution of networks. (B) Here, we show the difference between fit and unfit reassortment rates. Values above 0 indicate that reassortment events are more likely to occur on fitter, while values below 0 indicate that reassortment events are more likely to occur less fit edges.

transmitted. If reassortment events are beneficial, lineages that all nine datasets, we find the short-term reassortment rate to are the result of reassortment events should have a higher sur- be approximately 0.2 reassortment events per lineage per year, vival probability and are therefore more likely to persist further which is consistent with the reassortment rate estimates for unfit into the future. edges (SI Appendix, Fig. S12). To test if reassortment is beneficial, we calculated the num- Finally, we sought to rule out the possibility that these pat- ber of reassortment events on fit edges and on unfit edges for all terns are simply a property of our reassortment model. To do networks in the posterior distribution of the MCMC. We then this, we simulated networks under the coalescent with reassort- divided this number by the total length of fit respectively unfit ment with the reassortment rates and effective population sizes edges. As shown in Fig. 4, reassortment events occur at a higher fixed to the mean values estimated from the empirical data and rate on fit edges of the H3N2 and influenza B networks than they the network tip times fixed to those from the same data. In do on unfit edges. This suggests that reassortment is beneficial to these simulated networks, each edge has the same fitness. We the fitness of influenza A/H3N2 and influenza B viruses. then recomputed the same fit/unfit reassortment rate statistics For the other human influenza viruses, fitness benefits of reas- from these simulated networks (SI Appendix, Fig. S13) and found sortment are less pronounced. For p2009-like H1N1 and H2N2, that the patterns we observed in the empirical data completely the sampling time windows (both) or number of samples (H2N2) disappeared. This strongly suggests that the elevated rate of reas- was however rather small, and the results are likely driven by a sortment on fit lineages is not due to the particulars of our model lack of data. p1918-like H1N1 on the other hand had relatively but is instead a real effect. few reassortment events, overall driven by a low reassortment rate, and the results are likely driven by a lack of reassortment Conclusion events. These same general patterns hold when the definition We here present a Bayesian approach to jointly infer the reas- of what is a fit edge is changed to having descendants at least sortment network, the embedding of segment trees, and the cor- 4 or 6 y into the future (SI Appendix, Figs. S9 and S10). For responding evolutionary parameters. We show that this approach p2009-like H1N1, where the overall sampling interval is only 10 y, is able to retrieve reassortment rates, effective population size, the evidence for fitness benefits of reassortment events, however, and reassortment events from simulated data. decreases when using 4 and 6 y instead of 2 y. We have used this approach to show that there are large dif- We conducted further analysis to probe the robustness of our ferences in the rates of reassortment across different influenza result for H3N2, for which densely sampled sequences of long viruses and that reassortment events occur predominantly in time intervals are available. We analyzed two more influenza fitter parts of the corresponding reassortment networks. We pro- A/H3N2 datasets, one sampled between 1980 and 2005 and one pose that this is due to selection favoring lineages that have sampled from 2005 until the present. For both datasets, we find reassorted. Although we have deployed a relatively simple way higher rates of reassortment on fit edges (SI Appendix, Fig. S11). of defining which edges of a network are fit and which are not, Over shorter time frames, the effect of fitness is less visible since future approaches could more directly incorporate fitness mod- selection has not had enough time to filter out less fit strains. In els into these network-type approaches (20, 21). Additionally, turn, this means that if we look at datasets sampled over short our ability to infer which segments coreassort will allow us to times (for example, over 2 y), we should estimate reassortment further investigate if coreassortment between specific segments rates consistent with the estimated rates on unfit edges. To test drive these fitness benefits. this, we compiled 9 datasets, each with 100 to 200 sequences Even if one is not directly interested in reassortment patterns, sampled from 2 seasons between 2000 and 2018. Averaged over our approach allows phylogenetic and phylodynamic inferences

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L ). θ , ~µ o 29 no. i θ l and L , ersn the represent ob h set the be to ste simply then is i ρ), = l L ρ 1 t | r the are and for P 17109 ( ~ is D) C t [1] l (l ∈ 2 ) ,

EVOLUTION On the other hand, if the ith event is a reassortment event on lineage l, the we define when two coalescent or reassortment nodes are the same. We event contribution is the probability density of an (observable) reassortment define two coalescent nodes to be the same if 1) the parent edges of those event to occur on that lineage, i.e.: nodes carry the same segments and 2) if the subtree below each segment includes exactly the same clades between the two coalescent nodes. We " #  1 |C(l)| define two reassortment nodes to be the same if 1) both parent edges carry P(event |L , θ, ρ) = ρ 1 − 2 × . i i 2 the same segments in the same relative orientation and 2) if the subtree below each segment includes exactly the same clades between the two reas- As we condition on sampling events, their event contribution is always sortment events. A side effect of this definition is that the more segments simply 1. we include in the summary, the more likely two nodes will be considered different nodes. While the number of coalescent and reassortment nodes in the network Interval Contribution. The interval contribution P(intervali|Li, θ, ρ) is the probability of not observing any event in a given time interval. Three dif- changes over the course of the MCMC, the number of coalescent nodes on ferent types of events can happen in the coalescent with reassortment: the segment trees is constant. In order to avoid dimensionality issues when sampling, coalescent, and reassortment events. Since we condition on the summarizing, we first compute the frequency of observing each coalescent times of the sampling events, only coalescent and reassortment events node over the course of the MCMC. We then weight this frequency by the number of coalescent events on segment trees this coalescent node cor- are produced. Given the total rate Λi (probability per unit time) with which these occur in the interval immediately prior to event i, the interval responds to. We next choose the network that maximizes those weighted contribution can be written as: clade credibilities as the MCC network. In order to compute the posterior support of each reassortment event in the MCC network, we next compute the frequency of observing each P(intervali|Li, θ, ρ) = exp [−Λi(ti − ti−1)]. reassortment event in the MCC network during the MCMC. The total rate is the sum of the coalescence rate λ(c) and the reassortment Since we require the network to be rooted, we track segments even after i the root of a segment tree is reached. These patterns are however not sup- rate λ(r). The coalescence rate depends on the number of lineages extant at i ported by any genetic information and follow the prior distribution only. For a particular time and the effective population size in the usual way: the summary of networks, we therefore remove segments from edges if the root of a segment tree has been reached. Additionally, we remove reassort- (c) |Li| 1 λ = . ment loops, i.e., events that start on one edge and then directly reattach to i 2 θ the same edge. Since the support for individual events can greatly depend The rate of observable reassortment events is: on how many segments are analyzed, we have also implemented an option to only summarize over a subset of the segments, while ignoring others.    |C(l)|−1 (r) X 1 λ = ρ |Li| − . i 2 Reassortment Distance. For any reassortment event where segments a and b l∈Li take different paths, follow segment a until it reaches a network edge that carries segment b. We repeat this for any pair of segments that took differ- (r) Note that λi is generally less than the total rate of reassortment events in ent paths to get the common ancestor height between any two segments. (r) We then define the reassortment distance and a reassortment event as the this interval, which would be simply ρ|Li|, as, i.e., λi excludes reassortment events that produce lineages carrying no ancestral segments. minimal difference between the height of the reassortment event and the common ancestor height of any pair of segments. This seeks to denote for The Parameter Priors. The term P(~µ, θ, ρ) denotes the joint prior distribution how long segments in the two parent viruses at the reassortment event of all model parameters. We factorize the prior distribution by writing it evolved independently. as the product of the individual parameter priors P(~µ), P(θ), and P(ρ). This asserts that our prior information on any one of these model parameters is Implementation. We implemented the MCMC framework for the coalescent independent of the prior information we have for the others. with reassortment as a BEAST2 package called CoalRe. This package includes the classes to do simulation and inference under the coalescent with reas- An MCMC Algorithm for Reassortment Networks. In order to perform MCMC sortment. The implementation is such that the tree likelihood calculations sampling of network and the embedding of segment trees within these net- are separate from the network framework, which allows using the various works, we introduce several MCMC operators (i.e., proposal distributions). different site and clock models implemented in BEAST2. Additionally, it can These operators often have analogs in operators used to explore different be used with other Bayesian approaches such as nested sampling or parallel phylogenetic trees. Here, we briefly summarize each of these operators, tempering. Further, model comparison as well as integration over evolution- providing the complete details in the supplement. ary models can be performed. The package can be downloaded by using Add/remove operator. The add/remove operator adds and removes reas- the package manager in BEAUti. The source code for the software pack- sortment events. An extension of the subtree prune and regraft move for age can be found here: https://github.com/nicfel/CoalRe. A tutorial on how networks (27) to jointly operate on segment trees as well. to set up an analysis using the coalescent with reassortment is available at Segment diversion operator. The segment diversion operator changes the https://taming-the-beast.org/tutorials/Reassortment-Tutorial (28). Networks path segments take at reassortment events. are logged in the extended Newick format (29) and can be visualized using, Exchange operator. The exchange operator changes the attachment of for example, https://icytree.org/ (30). Additionally, we provide python scripts edges in the network while keeping the network length constant. to plot networks based on https://github.com/evogytis/baltic. Subnetwork slide operator. The subnetwork slide operator changes the height of nodes in the network while allowing to change the topology. Simulations. In the simulation study, we simulated reassortment networks, Scale operator. The scale operator scales the heights of individual nodes or using the structured coalescent with randomly drawn effective population the whole network without changing the network topology. sizes and reassortment rates. To do so, we first sampled random effective Gibbs operator. The Gibbs operator efficiently samples any part of the net- population sizes from a log normal distribution (mean: 5; SD: 0.5) and work that is older than the segment tree roots and is thus not informed by reassortment rates from another log normal distribution (mean: 0.2; SD: any genetic data. 0.5). An average effective population size of 5 is similar to the estimated Empty segment preoperator. The empty segment preoperator augments effective population sizes of seasonal human influenza viruses (Fig. 2C), the network with edges that do not carry any segments for the duration of and an average reassortment rate of 0.2 per lineage per year is similar a move, to allow larger jumps in network space. to the later estimated reassortment rates for seasonal human influenza We validate the implementation of the coalescent with reassortment viruses (Fig. 3). We then randomly sampled the sampling times of 100 network prior as well as all operators in the supplement. taxa, each with 4 segments, from a uniform distribution between 0 and 20. We simulated reassortment networks alongside the embedding of the Summarizing Reassortment Networks. To summarize a distribution of net- segment trees using these parameters. For each segment tree, we next works, we use a similar strategy to the MCC strategy (as described by ref. simulated genetic sequences by using the Jukes–Cantor substitution model 17) used by phylogenetic inference software such as BEAST to summarize (31) with an evolutionary rate of 5 × 10−3 per site and year. We used the distributions of trees. We first compute all unique coalescent and reassort- Jukes–Cantor model in order to limit the uncertainty coming from the ment nodes that were encountered during the MCMC. To do so requires that substitution model, allowing us to test the performance of the coalescent

17110 | www.pnas.org/cgi/doi/10.1073/pnas.1918304117 Muller¨ et al. Downloaded by guest on September 26, 2021 Downloaded by guest on September 26, 2021 0 .M eVen,Tnlgasaemsedn o iuleauto fte congru- tree of evaluation visual for misleading are Tanglegrams Vienne, De M. D. 10. 2 .Ddlt .Lwo,A arig .Fls,Ifrneo oooosrecombination homologous of Inference Falush, D. Daarling, A. Lawson, D. Didelot, X. 12. Nelson I. M. 11. 6 .W loqit .A uhr,Uiyn etcladnnetcleouin A evolution: nonvertical and vertical Unifying Suchard, recombination. with A. M. coalescent of Bloomquist, the inference W. Approximating E. Genome-wide Cardin, 16. Siepel, J. N. A. McVean, Gronau, T. A. I. G. Hubisz, 15. J. M. Rasmussen, D. M. 14. Vaughan G. T. 13. 7 .Hld .R ocar,Loigfrtesi h oet umr refo posterior from tree Summary forest: the in trees for Looking Bouckaert, R. R. Heled, J. 17. 1 .A ee,C .Rsel .I hamn rdcigeouinfo h hp of shape the from evolution Predicting Shraiman, I. B. Russell, A. C. Neher, A. 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Scholtissek, C. 19. h rttocdnpstosadtetidhvn ifrn ae 3) This (39). rates different having third the and positions + codon HKY two assumed an We first under 36). the evolved (35, have tempering to parallel sequences using the (34) all 2.5.2 aligned BEAST in We sortment distribution. containing temporal set even final (33). an 3.8.31 a Muscle with using produce samples segments to 500 subsampling least used at we dataset, A/H2N2 5 of rate evolutionary slower the of had effect segments the all the considered where study additionally scenario we to information, genetic of order of amount consisted In the reducing segment nucleotides. evolving Each independently conditions. 1,000 idealized under reassortment with h aesqecsa nrf 2 eotie hs eune from sequences used these we obtained We dataset, oridata/gisaid at 32. found A/H2N2 be ref. influenza can github.com/nicfel/Reassortment-Material/blob/master/Applications/H2N2/ table in the acknowledgments as (https://gisaid.org; For GISAID sequences Influenza B). same the influenza the H1N1, from and seasonal downloaded and H3N2, (pandemic data (https://www.fludb.org) sequence Database Research using viruses influenza Analysis. and Availability Data Sequence (5 higher are 2C (Fig. rates evolutionary two (5 These lower year. and site per M .L u .J yet .J .Bon esotetpten fainiflez virus influenza avian of patterns Reassortment Brown, L. 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National feedback Swiss CR32I3-166258. summarize helpful by Grant their funded to are for T.S. how reviewers and N.F.M. anonymous manuscript. on two discussions the thank useful also for Huson Daniel at available ACKNOWLEDGMENTS. are results, plot license files and log analyze relevant to as scripts such allowing the https://github.com/nicfel/Reassortment-Material. as data, well other still with as All runs, thus data. comply BEAST2 these and of on to intact, based results order numbers of accession in reproduction the files leaving XML regulations, char- the sequence the from removed we A/H2N2 acters GISAID, influenza language from the obtained For were markup online. that available are sequences extensible datasets the run full to files (XML) the (https://www.fludb.org), Database conver- S14 ). Fig. assessed only , Appendix We (SI (42) which known. 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EVOLUTION