We have now found a second putative recombination event with Rf1 as recombinant. Note that this is also consistent with the network in Figure 1. On the other hand, also note that the branching order in the SARS-CoV clade (the bottom 7 taxa in Figure 3) has changed a bit. This could mean that more recombination events are present in the SARS-CoV clade, as we also see in Figure 1.
One interesting follow-up question is whether the two (or more) networks produced by TriLoNet can be combined into a single higher-level network, in order to show multiple reticulations simultaneously (see  for an algorithm that could be useful).
Another interesting observation from these networks is that there is no sign of recombination involving the pangolin coronaviruses MP789 and PCoV_GX-P1E. It rather looks like these viruses evolved from common ancestors of SARS-CoV-2 and RaTG13, but it is important to note that we cannot exclude a recombination event on the basis of these networks. The relationship between SARS-CoV-2 and pangolin coronaviruses is still being debated in the literature [2,7,8,9].
Some limitations of the algorithms were noticed during this study. Firstly, the depicted networks are purely topological, i.e., the branch lengths do not represent anything. Adapting these algorithms to take branch length information into account could possibly improve their accuracy for this data set since the extant taxa have precise time stamps and for recent divergence events these times can be estimated quite accurately, see .
Another limitation is that we had to remove several taxa from the original data set  before the TreeChild algorithm could find a solution. By removing taxa, we reduced the number of reticulations needed to display the trees, making the TreeChild algorithm run in reasonable time. We made sure to include a diverse set of taxa (based on their pairwise distances ) to represent as much of the subgenus as possible.
Rosanne used several other algorithms, taxon selections and also used trees based on genes rather than fixed-length blocks (which we did above, following Guido’s post), see her thesis on github.
Although rooted phylogenetic network methods are often limited in the number of taxa that can be analysed and/or the complexity of the networks that can be constructed, we have seen that these methods can be useful for constructing hypothetical evolutionary histories. Moreover, although the constructed networks are not identical, we have seen that they share certain key properties, which are also consistent with previous research.
Rosanne Wallin, Leo van Iersel, Mark Jones, Steven Kelk and Leen Stougie
 Leo van Iersel, Remie Janssen, Mark Jones, Yukihiro Murakami and Norbert Zeh. A Practical Fixed-Parameter Algorithm for Constructing Tree-Child Networks from Multiple Binary Trees. arXiv:1907.08474
 Maciej F. Boni, Philippe Lemey, Xiaowei Jiang, Tommy Tsan-Yuk Lam, Blair W. Perry, Todd A. Castoe, Andrew Rambaut and David L. Robertson. Evolutionary origins of the SARS-CoV-2 sarbecovirus lineage responsible for the COVID-19 pandemic. Nat Microbiol 5, 1408–1417 (2020). https://doi.org/10.1038/s41564-020-0771-4
 James Oldman, Taoyang Wu, Leo van Iersel and Vincent Moulton. TriLoNet: Piecing together small networks to reconstruct reticulate evolutionary histories. Molecular Biology and Evolution, 33 (8): 2151-2162 (2016). http://dx.doi.org/10.1093/molbev/msw068
 Fabio Pardi and Celine Scornavacca. Reconstructible phylogenetic networks: do not distinguish the indistinguishable. PLoS Comput Biol, 11(4), e1004135 (2015).
 Lam, Tommy Tsan-Yuk, Marcus Ho-Hin Shum, Hua-Chen Zhu, Yi-Gang Tong, Xue-Bing Ni, Yun-Shi Liao, Wei Wei, et al. Identifying SARS-CoV-2 Related Coronaviruses in Malayan Pangolins. Nature, 583, 282–285 (2020). https://doi.org/10.1038/s41586-020-2169-0
 Wang, Hongru, Lenore Pipes, and Rasmus Nielsen. Synonymous Mutations and the Molecular Evolution of SARS-Cov-2 Origins. [Preprint] Evolutionary Biology, April 21, 2020. https://doi.org/10.1101/2020.04.20.052019
 Li, Xiaojun, Elena E. Giorgi, Manukumar Honnayakanahalli Marichannegowda, Brian Foley, Chuan Xiao, Xiang-Peng Kong, Yue Chen, S. Gnanakaran, Bette Korber, and Feng Gao. Emergence of SARS-CoV-2 through Recombination and Strong Purifying Selection. Science Advances, Vol. 6, no. 27 (2020). https://doi.org/10.1126/sciadv.abb9153