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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October 19, 2020

Amaury interviewed by the French mathematical society

Amaury Lambert est mathématicien, professeur à Sorbonne Université et professeur associé au département de biologie de l’École normale supérieure. Il anime l’équipe SMILE au Collège de France. Sa recherche se situe à l’intersection de l’évolution, de l’écologie et des probabilités. Il nous explique ci-dessous sa réponse de mathématicien travaillant à l’interface avec la biologie face à la crise sanitaire.

Publication

2017

How does geographical distance translate into genetic distance?

Geographic structure can affect patterns of genetic differentiation and speciation rates. In this article, we investigate the dynamics of genetic distances in a geographically structured metapopulation. We model the metapopulation as a weighted directed graph, with N vertices corresponding to N homogeneous subpopulations. The dynamics of the genetic distances is then controlled by two types of transitions -mutation and migration events between islands. Under a large population-long chromosome limit, we show that the genetic distance between two subpopulations converges to a deterministic quantity that can asymptotically be expressed in terms of the hitting time between two random walks in the metapopulation graph. Our result shows that the genetic distance between two subpopulations does not only depend on the direct migration rates between them but on the whole metapopulation structure.

Publication

2019

Positive association of the oriented percolation cluster in randomly oriented graphs

Consider any fixed graph whose edges have been randomly and independently oriented, and write \(\{S \leadsto i\}\) to indicate that there is an oriented path going from a vertex \(s \in S\) to vertex \(i\). Narayanan (2016) proved that for any set \(S\) and any two vertices \(i\) and \(j\), \(\{S \leadsto i\}\) and \(\{S \leadsto j\}\) are positively correlated. His proof relies on the Ahlswede-Daykin inequality, a rather advanced tool of probabilistic combinatorics. In this short note, I give an elementary proof of the following, stronger result: writing \(V\) for the vertex set of the graph, for any source set \(S\), the events \(\{S \leadsto i\}\), \(i \in V\), are positively associated -- meaning that the expectation of the product of increasing functionals of the family \(\{S \leadsto i\}\) for \(i \in V\) is greater than the product of their expectations.

Publication

2018

Chromosome Painting

We consider a Moran model with recombination in a haploid population of size N. At each birth event, with probability 1−ρN the offspring copies one parent's chromosome, and with probability ρN she inherits a chromosome that is a mosaic of both parental chromosomes. We assume that at time 0 each individual has her chromosome painted in a different color and we study the color partition of the chromosome that is asymptotically fixed in a large population, when we look at a portion of the chromosome such that ρ:=limN→∞ρNN2→∞. To do so, we follow backwards in time the ancestry of the chromosome of a randomly sampled individual. This yields a Markov process valued in the color partitions of the half-line, that was introduced by \cite{esser}, in which blocks can merge and split, called the partitioning process. Its stationary distribution is closely related to the fixed chromosome in our Moran model with recombination. We are able to provide an approximation of this stationary distribution when ρ≫1 and an error bound. This allows us to show that the distribution of the (renormalised) length of the leftmost block of the partition (i.e. the region of the chromosome that carries the same color as 0) converges to an exponential distribution. In addition, the geometry of this block can be described in terms of a Poisson point process with an explicit intensity measure.

Publication

2015

Mass extinction in poorly known taxa

Since the 1980s, many have suggested we are in the midst of a massive extinction crisis, yet only 799 (0.04\%) of the 1.9 million known recent species are recorded as extinct, questioning the reality of the crisis. This low figure is due to the fact that the status of very few invertebrates, which represent the bulk of biodiversity, have been evaluated. Here we show, based on extrapolation from a random sample of land snail species via two independent approaches, that we may already have lost 7\% (130,000 extinctions) of the species on Earth. However, this loss is masked by the emphasis on terrestrial vertebrates, the target of most conservation actions. Projections of species extinction rates are controversial because invertebrates are essentially excluded from these scenarios. Invertebrates can and must be assessed if we are to obtain a more realistic picture of the sixth extinction crisis.

Publication

2016

The impact of selection, gene conversion, and biased sampling on the assessment of microbial demography

Recent studies have linked demographic changes and epidemiological patterns in bacterial populations using coalescent-based approaches. We identified 26 studies using skyline plots and found that 21 inferred overall population expansion. This surprising result led us to analyze the impact of natural selection, recombination (gene conversion), and sampling biases on demographic inference using skyline plots and site frequency spectra (SFS). Forward simulations based on biologically relevant parameters from Escherichia coli populations showed that theoretical arguments on the detrimental impact of recombination and especially natural selection on the reconstructed genealogies cannot be ignored in practice. In fact, both processes systematically lead to spurious interpretations of population expansion in skyline plots (and in SFS for selection). Weak purifying selection, and especially positive selection, had important effects on skyline plots, showing patterns akin to those of population expansions. State-of-the-art techniques to remove recombination further amplified these biases. We simulated three common sampling biases in microbiological research: uniform, clustered, and mixed sampling. Alone, or together with recombination and selection, they further mislead demographic inferences producing almost any possible skyline shape or SFS. Interestingly, sampling sub-populations also affected skyline plots and SFS, because the coalescent rates of populations and their sub-populations had different distributions. This study suggests that extreme caution is needed to infer demographic changes solely based on reconstructed genealogies. We suggest that the development of novel sampling strategies and the joint analyzes of diverse population genetic methods are strictly necessary to estimate demographic changes in populations where selection, recombination, and biased sampling are present.

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