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 LPMA (Lab of Probability and Random Models) at UPMC (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.


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 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.

Upcoming seminars


Canalization and genetic assimilation. Reassessing the radicality of the Waddingtonian concept of inheritance of acquired characters


March 5, 2018 at 12 - Collège de France


Titre à venir (EV)

Elisabeta VERGU (INRA)

March 12, 2018 at 11 - Collège de France


Titre à venir (TJ)

Thijs JANZEN (Carl von Ossietzky Universität)

March 14, 2018 at 14 - Collège de France


Titre à venir (MCL)


March 19, 2018 at 11 - Collège de France


Titre à venir (MGF)

Mauricio GONZALEZ FORERO (U St Andrews)

March 26, 2018 at 11 - Collège de France


Titre à venir (VL)


April 9, 2018 at 11 - Collège de France


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