Felsenstein’s article describing the application of the bootstrap to evolutionary trees is one of the most cited papers of all time. The bootstrap method, based on resampling and replications, is used extensively to assess the robustness of phylogenetic inferences. However, increasing numbers of sequences are now available for a wide variety of species, and phylogenies with hundreds or thousands of taxa are becoming routine. In that framework, Felsenstein’s bootstrap tends to yield very low supports, especially on deep branches. We propose a new version of phylogenetic bootstrap, in which the presence of inferred branches in replications is measured using a gradual “transfer” distance, as opposed to the original version using a binary presence/absence index. The resulting supports are higher, while not inducing falsely supported branches. Our method is applied to large mammal, HIV, and simulated datasets, for which it reveals the phylogenetic signal, while Felsenstein’s bootstrap fails to do so.

This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of public health. In general, no close analytic form for their occurrence probabilities is available, and crude Monte Carlo procedures fail. We show how recent intensive computer simulation techniques, such as interacting branching particle methods, can be used for estimation purposes, as well as for generating model paths that correspond to realizations of such events. Applications of these simulation-based methods to several epidemic models fitted from real datasets are also considered and discussed thoroughly.

The transfer distance (TD) was introduced in the classification framework and studied in the context of phylogenetic tree matching. Recently, Lemoine et al. (Nature 556(7702):452–456, 2018 . 10.1038/s41586-018-0043-0) showed that TD can be a powerful tool to assess the branch support on large phylogenies, thus providing a relevant alternative to Felsenstein’s bootstrap. This distance allows a reference branch in a reference tree to be compared to a branch b from another tree T (typically a bootstrap tree), both on the same set of n taxa. The TD between these branches is the number of taxa that must be transferred from one side of b to the other in order to obtain . By taking the minimum TD from to all branches in T we define the transfer index , denoted by , measuring the degree of agreement of T with . Let us consider a reference branch having p tips on its light side and define the transfer support (TS) as . Lemoine et al. ( 2018 ) used computer simulations to show that the TS defined in this manner is close to 0 for random “bootstrap” trees. In this paper, we demonstrate that result mathematically: when T is randomly drawn, TS converges in probability to 0 when n tends to . Moreover, we fully characterize the distribution of on caterpillar trees, indicating that the convergence is fast, and that even when n is small, moderate levels of branch support cannot appear by chance.

CRF19 is a recombinant form of HIV-1 subtypes D, A1 and G, which was first sampled in Cuba in 1999, but was already present there in 1980s. CRF19 was reported almost uniquely in Cuba, where it accounts for ∼25% of new HIV-positive patients and causes rapid progression to AIDS (∼3 years). We analyzed a large data set comprising ∼350 pol and env sequences sampled in Cuba over the last 15 years and ∼350 from Los Alamos database. This data set contained both CRF19 (∼315), and A1, D and G sequences. We performed and combined analyses for the three A1, G and D regions, using fast maximum likelihood approaches, including: (1) phylogeny reconstruction, (2) spatio-temporal analysis of the virus spread, and ancestral character reconstruction for (3) transmission mode and (4) drug resistance mutations (DRMs). We verified these results with a Bayesian approach. This allowed us to acquire new insights on the CRF19 origin and transmission patterns. We showed that CRF19 recombined between 1966 and 1977, most likely in Cuban community stationed in Congo region. We further investigated CRF19 spread on the Cuban province level, and discovered that the epidemic started in 1970s, most probably in Villa Clara, that it was at first carried by heterosexual transmissions, and then quickly spread in the 1980s within the “men having sex with men” (MSM) community, with multiple transmissions back to heterosexuals. The analysis of the transmission patterns of common DRMs found very few resistance transmission clusters. Our results show a very early introduction of CRF19 in Cuba, which could explain its local epidemiological success. Ignited by a major founder event, the epidemic then followed a similar pattern as other subtypes and CRFs in Cuba. The reason for the short time to AIDS remains to be understood and requires specific surveillance, in Cuba and elsewhere.