SMILE

Stochastic Models for the Inference of Life Evolution

Presentation

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.

Directions

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.

Contact

You can reach us by email (amaury.lambert - at - upmc.fr) or (smile - at - listes.upmc.fr).

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Publication

2015

The reconstructed tree in the lineage-based model of protracted speciation

A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree produced by a given model of diversification. Etienne and Rosindell in Syst Biol 61(2):204–213, (2012) proposed a lineage-based model of diversification, called protracted speciation, where species remain incipient during a random duration before turning good species, and showed that this can explain the slowdown in lineage accumulation observed in real phylogenies. However, they were unable to provide a general likelihood formula. Here, we present a likelihood formula for protracted speciation models, where rates at which species turn good or become extinct can depend both on their age and on time. Our only restrictive assumption is that speciation rate does not depend on species status. Our likelihood formula utilizes a new technique, based on the contour of the phylogenetic tree and first developed by Lambert in Ann Probab 38(1):348–395, (2010). We consider the reconstructed trees spanned by all extant species, by all good extant species, or by all representative species, which are either good extant species or incipient species representative of some good extinct species. Specifically, we prove that each of these trees is a coalescent point process, that is, a planar, ultrametric tree where the coalescence times between two consecutive tips are independent, identically distributed random variables. We characterize the common distribution of these coalescence times in some, biologically meaningful, special cases for which the likelihood reduces to an elegant analytical formula or becomes numerically tractable.

Publication

2020

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.

Upcoming seminars

seminar

TBA

Sarah PENNINGTON (U Bath)

June 2, 2020 at 10 - Collège de France


seminar

TBA

Bastien MALLEIN (U Sorbonne Paris Nord)

June 23, 2020 at 10 - Collège de France


Resources

Planning des salles du Collège de France.
Intranet du Collège de France.