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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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.



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.

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