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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The genomic view of diversification

Evolutionary relationships between species are traditionally represented in the form of a tree, called the species tree. The reconstruction of the species tree from molecular data is hindered by frequent conflicts between gene genealogies. A standard way of dealing with this issue is to postulate the existence of a unique species tree where disagreements between gene trees are explained by incomplete lineage sorting (ILS) due to random coalescences of gene lineages inside the edges of the species tree. This paradigm, known as the multi-species coalescent (MSC), is constantly violated by the ubiquitous presence of gene flow revealed by empirical studies, leading to topological incongruences of gene trees that cannot be explained by ILS alone. Here we argue that this paradigm should be revised in favor of a vision acknowledging the importance of gene flow and where gene histories shape the species tree rather than the opposite. We propose a new, plastic framework for modeling the joint evolution of gene and species lineages relaxing the hierarchy between the species tree and gene trees. As an illustration, we implement this framework in a mathematical model called the genomic diversification (GD) model based on coalescent theory, with four parameters tuning replication, genetic differentiation, gene flow and reproductive isolation. We use it to evaluate the amount of gene flow in two empirical data-sets. We find that in these data-sets, gene tree distributions are better explained by the best fitting GD model than by the best fitting MSC model. This work should pave the way for approaches of diversification using the richer signal contained in genomic evolutionary histories rather than in the mere species tree.



Testing for Independence between Evolutionary Processes

Evolutionary events co-occurring along phylogenetic trees usually point to complex adaptive phenomena, sometimes implicating epistasis. While a number of methods have been developed to account for co-occurrence of events on the same internal or external branch of an evolutionary tree, there is a need to account for the larger diversity of possible relative positions of events in a tree. Here we propose a method to quantify to what extent two or more evolutionary events are associated on a phylogenetic tree. The method is applicable to any discrete character, like substitutions within a coding sequence or gains/losses of a biological function. Our method uses a general approach to statistically test for significant associations between events along the tree, which encompasses both events inseparable on the same branch, and events genealogically ordered on different branches. It assumes that the phylogeny and themapping of branches is known without errors. We address this problem from the statistical viewpoint by a linear algebra representation of the localization of the evolutionary events on the tree.We compute the full probability distribution of the number of paired events occurring in the same branch or in different branches of the tree, under a null model of independence where each type of event occurs at a constant rate uniformly inthephylogenetic tree. The strengths and weaknesses of themethodare assessed via simulations; we then apply the method to explore the loss of cell motility in intracellular pathogens.



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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