Stochastic Models for the Inference of Life Evolution

SMILE | Stochastic Models for the Inference of Life Evolution | Collège de France


SMILE is an interdisciplinary research group gathering mathematicians, bio-informaticians and biologists.
SMILE is affiliated to the Institut de Biologie de l'ENS, in Paris.
SMILE is hosted within the CIRB (Center for Interdisciplinary Research in Biology) at Collège de France.
SMILE is supported by Collège de France and CNRS.
Visit also our homepage at CIRB.


SMILE is hosted at Collège de France in the Latin Quarter of Paris. To reach us, go to 11 place Marcelin Berthelot (stations Luxembourg or Saint-Michel on RER B).
Our working spaces are rooms 107, 121 and 122 on first floor of building B1 (ask us for the code). Building B1 is facing you upon exiting the traversing hall behind Champollion's statue.


You can reach us by email (amaury.lambert - at - ; (guillaume.achaz - at - or (smile - at -

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Exchangeable coalescents, ultrametric spaces, nested interval-partitions: A unifying approach

Kingman’s (1978) representation theorem (J. Lond. Math. Soc. (2) 18 (1978) 374–380) states that any exchangeable partition of ℕ can be represented as a paintbox based on a random mass-partition. Similarly, any exchangeable composition (i.e., ordered partition of ℕ) can be represented as a paintbox based on an interval-partition (Gnedin (1997) Ann. Probab. 25 (1997) 1437–1450). Our first main result is that any exchangeable coalescent process (not necessarily Markovian) can be represented as a paintbox based on a random nondecreasing process valued in interval-partitions, called nested interval-partition, generalizing the notion of comb metric space introduced in Lambert and Uribe Bravo (2017) (p-Adic Numbers Ultrametric Anal. Appl. 9 (2017) 22–38) to represent compact ultrametric spaces. As a special case, we show that any Λ-coalescent can be obtained from a paintbox based on a unique random nested interval partition called Λ-comb, which is Markovian with explicit transitions. This nested interval-partition directly relates to the flow of bridges of Bertoin and Le Gall (2003) (Probab. Theory Related Fields 126 (2003) 261–288). We also display a particularly simple description of the so-called evolving coalescent (Pfaffelhuber and Wakolbinger (2006) Stochastic Process. Appl. 116 (2006) 1836–1859) by a comb-valued Markov process. Next, we prove that any ultrametric measure space U, under mild measure-theoretic assumptions on U, is the leaf set of a tree composed of a separable subtree called the backbone, on which are grafted additional subtrees, which act as star-trees from the standpoint of sampling. Displaying this so-called weak isometry requires us to extend the Gromov-weak topology of Greven, Pfaffelhuber and Winter (2009) (Probab. Theory Related Fields 145 (2009) 285–322), that was initially designed for separable metric spaces, to nonseparable ultrametric spaces. It allows us to show that for any such ultrametric space U, there is a nested interval-partition which is (1) indistinguishable from U in the Gromov-weak topology; (2) weakly isometric to U if U has a complete backbone; (3) isometric to U if U is complete and separable.



The speed of vaccination rollout and the risk of pathogen adaptation

Vaccination is expected to reduce disease prevalence and to halt the spread of epidemics. But pathogen adaptation may erode the efficacy of vaccination and challenge our ability to control disease spread. Here we examine the influence of the speed of vaccination rollout on the overall risk of pathogen adaptation to vaccination. We extend the framework of evolutionary epidemiology theory to account for the different steps leading to adaptation to vaccines: (1) introduction of a vaccine-escape variant by mutation from an endemic wild-type pathogen, (2) invasion of this vaccine-escape variant in spite of the risk of early extinction, (3) spread and, eventually, fixation of the vaccine-escape variant in the pathogen population. We show that the risk of pathogen adaptation is maximal for intermediate speed of vaccination rollout. On the one hand, slower rollout decreases pathogen adaptation because selection is too weak to avoid early extinction of the new variant. On the other hand, faster rollout decreases pathogen adaptation because it reduces the influx of adaptive mutations. Hence, vaccinating faster is recommended to decrease both the number of cases and the likelihood of pathogen adaptation. We also show that pathogen adaptation is driven by its basic reproduction ratio, the efficacy of the vaccine and the effects of the vaccine-escape mutations on pathogen life-history traits. Accounting for the interplay between epidemiology, selection and genetic drift, our work clarifies the influence of vaccination policies on different steps of pathogen adaptation and allows us to anticipate the effects of public-health interventions on pathogen evolution.Significance statement Pathogen adaptation to host immunity challenges the efficacy of vaccination against infectious diseases. Are there vaccination strategies that limit the emergence and the spread of vaccine-escape variants? Our theoretical model clarifies the interplay between the timing of vaccine escape mutation events and the transient epidemiological dynamics following the start of a vaccination campaign on pathogen adaptation. We show that the risk of adaptation is maximized for intermediate vaccination coverage but can be reduced by a combination of non pharmaceutical interventions and maximizing the speed of the vaccination rollout. These recommendations may have important implications for the choice of vaccination strategies against the ongoing SARS-CoV-2 pandemic.Competing Interest StatementThe authors have declared no competing interest.Funding StatementThis study was funded by a grant from CNRS MITI to SG.Author DeclarationsI confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.YesI confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals.YesI understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).YesI have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.YesThis is a theoretical study.



Cultural transmission of reproductive success impacts genomic diversity, coalescent tree topologies and demographic inferences

Cultural Transmission of Reproductive Success (CTRS) has been observed in many human populations as well as other animals. It consists in a positive correlation of non-genetic origin between the progeny size of parents and children. This correlation can result from various factors, such as the social influence of parents on their children, the increase of children{\textquoteright}s survival through allocare from uncle and aunts, or the transmission of resources. Here, we study the evolution of genomic diversity through time under CTRS. We show that CTRS has a double impact on population genetics: (1) effective population size decreases when CTRS starts, mimicking a population contraction, and increases back to its original value when CTRS stops; (2) coalescent trees topologies are distorted under CTRS, with higher imbalance and higher number of polytomies. Under long-lasting CTRS, effective population size stabilises but the distortion of tree topology remains, which yields U-shaped Site Frequency Spectra (SFS) under constant population size. We show that this CTRS{\textquoteright} impact yields a bias in SFS-based demographic inference. Considering that CTRS was detected in numerous human and animal populations worldwide, one should be cautious that inferring population past histories from genomic data can be biased by this cultural process.

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