SMILE

Stochastic Models for the Inference of Life Evolution

SMILE | Stochastic Models for the Inference of Life Evolution | Collège de France

Presentation

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.

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 - college-de-france.fr) ; (guillaume.achaz - at - college-de-france.fr) or (smile - at - listes.upmc.fr).

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Publication

2022

A minimal yet flexible likelihood framework to assess correlated evolution

An evolutionary process is reflected in the sequence of changes of any trait (e.g. mor- phological, molecular) through time . Yet, a better understanding of evolution would be procured by characterizing correlated evolution, or when two or more evolutionary pro- cesses interact. Many previously developed parametric methods often require significant computing time as they rely on the estimation of many parameters. Here we propose a minimal likelihood framework modelling the joint evolution of two traits on a known phylogenetic tree. The type and strength of correlated evolution is characterized by few parameters tuning mutation rates of each trait and interdependencies between these rates. The framework can be applied to study any discrete trait or character ranging from nucleotide substitution to gain or loss of a biological function. More specifically, it can be used to 1) test for independence between two evolutionary processes, 2) iden- tify the type of interaction between them and 3) estimate parameter values of the most likely model of interaction. In its current implementation, the method takes as input a phylogenetic tree together with mapped discrete evolutionary events on it and then maximizes the likelihood for one or several chosen scenarios. The strengths and limits of the method, as well as its relative power when compared to a few other methods, are assessed using both simulations and data from 16S rRNA sequences in a sample of 54 γ-enterobacteria. We show that even with datasets of fewer than 100 species, the method performs well in parameter estimation and in the selection of evolutionary scenario.

Publication

2020

From individual-based epidemic models to McKendrick-von Foerster PDEs: A guide to modeling and inferring COVID-19 dynamics


We present a unifying, tractable approach for studying the spread of viruses causing complex diseases, requiring to be modeled with a large number of types (infective stage, clinical state, risk factor class...). We show that recording for each infected individual her infection age, i.e., the time elapsed since she was infected,
1. The age distribution \$$n(t,a)\$$ of the population at time \$$t\$$ is simply described by means of a first-order, one-dimensional partial differential equation (PDE) known as the McKendrick--von Foerster equation;
2. The frequency of type \$$i\$$ at time \$$t\$$ is simply obtained by integrating the probability \$$p(a,i)\$$ of being in state \$$i\$$ at age \$$a\$$ against the age distribution \$$n(t,a)\$$.
The advantage of this approach is three-fold. First, regardless of the number of types, macroscopic observables (e.g., incidence or prevalence of each type) only rely on a one-dimensional PDE ``decorated'' with types. This representation induces a simple methodology based on the McKendrick-von Foerster PDE with Poisson sampling to infer and forecast the epidemic. This technique is illustrated with French data of the COVID-19 epidemic.
Second, our approach generalizes and simplifies standard compartmental models using high-dimensional systems of ODEs to account for disease complexity. We show that such models can always be rewritten in our framework, thus providing a low-dimensional yet equivalent representation of these complex models.
Third, beyond the simplicity of the approach and its computational advantages, we show that our population model naturally appears as a universal scaling limit of a large class of fully stochastic individual-based epidemic models,
where the initial condition of the PDE emerges as the limiting age structure of an exponentially growing population starting from a single individual.

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