Stochastic Models for the Inference of Life Evolution


SMILE is an interdisciplinary research group gathering probabilists, statisticians, bio-informaticians and biologists.
SMILE is affiliated to the Stochastics and Biology group of LPSM (Lab of Probability, Statistics and Modeling) at Sorbonne Université (ex Université Pierre et Marie Curie Paris 06).
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.

Recent contributions of the SMILE group related to SARS-Cov2 and COVID-19.


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 - or (smile - at -

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The impact of selection, gene conversion, and biased sampling on the assessment of microbial demography

Recent studies have linked demographic changes and epidemiological patterns in bacterial populations using coalescent-based approaches. We identified 26 studies using skyline plots and found that 21 inferred overall population expansion. This surprising result led us to analyze the impact of natural selection, recombination (gene conversion), and sampling biases on demographic inference using skyline plots and site frequency spectra (SFS). Forward simulations based on biologically relevant parameters from Escherichia coli populations showed that theoretical arguments on the detrimental impact of recombination and especially natural selection on the reconstructed genealogies cannot be ignored in practice. In fact, both processes systematically lead to spurious interpretations of population expansion in skyline plots (and in SFS for selection). Weak purifying selection, and especially positive selection, had important effects on skyline plots, showing patterns akin to those of population expansions. State-of-the-art techniques to remove recombination further amplified these biases. We simulated three common sampling biases in microbiological research: uniform, clustered, and mixed sampling. Alone, or together with recombination and selection, they further mislead demographic inferences producing almost any possible skyline shape or SFS. Interestingly, sampling sub-populations also affected skyline plots and SFS, because the coalescent rates of populations and their sub-populations had different distributions. This study suggests that extreme caution is needed to infer demographic changes solely based on reconstructed genealogies. We suggest that the development of novel sampling strategies and the joint analyzes of diverse population genetic methods are strictly necessary to estimate demographic changes in populations where selection, recombination, and biased sampling are present.



A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic

In our model of the COVID-19 epidemic, infected individuals can be of four types, according whether they are asymptomatic (\$$A\$$) or symptomatic (\$$I\$$), and use a contact tracing mobile phone app (\$$Y\$$) or not (\$$N\$$). We denote by \$$f\$$ the fraction of \$$A\$$'s, by \$$y\$$ the fraction of \$$Y\$$'s and by \$$R_0\$$ the average number of secondary infections from a random infected individual. We investigate the effect of non-digital interventions (voluntary isolation upon symptom onset, quarantining private contacts) and of digital interventions (contact tracing thanks to the app), depending on the willingness to quarantine, parameterized by four cooperating probabilities. For a given `effective' \$$R_0\$$ obtained with non-digital interventions, we use non-negative matrix theory and stopping line techniques to characterize mathematically the minimal fraction \$$y_0\$$ of app users needed to curb the epidemic. We show that under a wide range of scenarios, the threshold \$$y_0\$$ as a function of \$$R_0\$$ rises steeply from 0 at \$$R_0=1\$$ to prohibitively large values (of the order of 60-70\% up) whenever the effective \$$R_0\$$ is above 1.3. Our results show that moderate rates of adoption of a contact tracing app can reduce \$$R_0\$$ but are by no means sufficient to reduce it below 1 unless it is already very close to 1 thanks to non-digital interventions.

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