## SMILE: Stochastic Models for the Inference of Life Evolution

### Principal Investigator: Amaury LAMBERT, Pr. Sorbonne Université

Probabilistic models of evolution can be used to infer the historical patterns of species diversification from the knowledge of genotypes and phenotypes of contemporary species: identification of source regions of biodiversity in geographical space or in niche space, reconstruction of traits of ancestral species, inference of diversification rate shifts across paleontological time...

The approaches used in evolution modeling can be divided into: a) the top-down approach, used in phylogenetics and comparative systematics, where macro-evolutionary processes are described by simple stochastic models that have little empirical justification and are usually treated by sophisticated statistical methods (e.g., Markov chain Monte Carlo in tree space); the bottom-up approach, used in population genetics and ecology, where evolution emerges from the interaction of its microscopic components, namely organisms and their genes, which handles microscopic, measurable parameters (fecundity, survival probability, dispersal probability, mutation rate, recombination rate...), and builds models on this microscopic description.

The most used approach in data analysis is the top-down approach. It proposes simple null models of species diversification and of genotype/phenotype evolution, and rates them according to their ability to reproduce present day data. Our first line of research consists in developing mathematical and numerical techniques for the analysis of such models. Mathematical progress relies in particular on the theory of branching processes and coalescent processes. Numerical methods include likelihood computation, peeling algorithms and MCMC on trees augmented with the history of extinct lineages. This research will not only solve some current challenges in phylogenetics but also help get round computationally demanding statistical procedures, which in turn should pave the way for new ways of modeling evolution.

However, the relative good performance of a phenomenological model is rarely informative of the biological reality of evolution at the microscopic level. In addition, there is no guarantee that the model selected as the best one, indeed is a good one. In contrast, in bottom-up models, the confidence we have in the model stems from the knowledge we have of the microscopic scale and in particular from the fact that microscopic parameters are measurable. In addition, scaling limit techniques can yield macroscopic objects which emerge as the limit of the fine scale description. The standard coalescent is the best example of such a universal object, emerging from a very general class of models with large, fixed population size. Our second line of research is to contribute to push this effort further by proposing other models of macro-evolution arising as scaling limits of microscopically described biological populations. This line contributes to the utilization of possibly slightly more complex, but more reliable models for phylogenetic trees and for the evolutionary dynamics of quantitative traits. Our group focuses on the spatial structuring of populations on large time scales (dynamic landscapes) and on phenotypic evolution driven by intraspecific selection, under the assumption of rare mutations (adaptive dynamics).

Our third line of research concerns the history of genetic sequences in the macro-evolutionary timescale. In particular, we study the evolutionary constraints governing the order in which successive mutations occur at the same locus or at different loci. We are interested in the origin of such constraints and in the subsequent predictability of evolutionary pathways in the case when they are strong and pervasive.

Our way of doing research is to promote the discussion between personalities from different research areas or from different backgrounds. This is reflected by the wealth of specialties represented in our group: probability, statistics, bio-informatics, ecology, evolutionary biology.

## Selected Publication 2010-2022

- Zhao, L., Wymant, C., Blanquart, F., Golubchik, T., Gall, A., Bakker, M., Bezemer, D., Hall, M., Ong, S.H., Albert, J., et al. (2022). Phylogenetic estimation of the viral fitness landscape of HIV-1 set-point viral load. * Virus Evol* 8, veac022.

- Fedosov, A., Achaz, G., Gontchar, A., and Puillandre, N. (2022). MOLD, a novel software to compile accurate and reliable DNA diagnoses for taxonomic descriptions.

**Mol Ecol Resour.**- Wymant, C., Bezemer, D., Blanquart, F., Ferretti, L., Gall, A., Hall, M., Golubchik, T., Bakker, M., Ong, S.H., Zhao, L., et al. (2022). A highly virulent variant of HIV-1 circulating in the Netherlands.

*375, 540–545.*

**Science**- Leducq, V., Jary, A., Bridier-Nahmias, A., Daniel, L., Zafilaza, K., Damond, F., Goldstein, V., Duval, A., Blanquart, F., Calvez, V., et al. (2022). Nosocomial transmission clusters and lineage diversity characterized by SARS-CoV-2 genomes from two large hospitals in Paris, France, in 2020.

*12, 1094.*

**Sci Rep**- Foutel-Rodier, F., Lambert, A., and Schertzer, E. (2021). Exchangeable Coalescents, Ultrametric Spaces, Nested Interval-Partitions: A Unifying Approach.

*31, 2046–2090.*

**Ann. Appl. Probab.**- Lambert, A. (2021). A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic.

*16, 53.*

**Math. Model. Nat. Phenom.**- Cosentino, G., Bernard, M., Ambroise, J., Giannoli, J.-M., Guedj, J., Débarre, F., and Blanquart, F. (2021). SARS-CoV-2 viral dynamics in infections with Alpha and Beta variants of concern in the French community.

*S0163-4453(21) 00374-1.*

**J Infect**- Lambert, A., Pina, V.M., and Schertzer, E. (2021). Chromosome Painting: How Recombination Mixes Ancestral Colors.

*31, 826–864.*

**Ann. Appl. Probab.**- Czuppon, P., Blanquart, F., Uecker, H., and Débarre, F. (2021). The Effect of Habitat Choice on Evolutionary Rescue in Subdivided Populations.

*197, 625–643.*

**Am Nat**- Belloir, A., and Blanquart, F. (2021). Estimating the global reduction in transmission and rise in detection capacity of the novel coronavirus SARS-CoV-2 in early 2020.

*35, 100445.*

**Epidemics**- Cluzel, N., Lambert, A., Maday, Y., Turinici, G., and Danchin, A. (2020). [Biochemical and statistical lessons from the evolution of the SARS-CoV-2 virus: paths for novel antiviral warfare].

*343, 177–209.*

**C R Biol**- Puillandre, N., Brouillet, S., and Achaz, G. (2020). ASAP: Assemble Species by Automatic Partitioning.

*.*

**Mol Ecol Resour**- Abdi, B., Nguyen, T., Brouillet, S., Desire, N., Sayon, S., Wirden, M., Jary, A., Achaz, G., Assoumou, L., Palich, R., et al. (2020). No HIV-1 molecular evolution on long term antiretroviral therapy initiated during primary HIV-1 infection.

*.*

**AIDS**- Day, T., Parsons, T., Lambert, A., and Gandon, S. (2020). The Price equation and evolutionary epidemiology.

*375, 20190357.*

**Philos. Trans. R. Soc. Lond., B, Biol. Sci.**- Doulcier, G., Lambert, A., De Monte, S., and Rainey, P.B. (2020). Eco-evolutionary dynamics of nested Darwinian populations and the emergence of community-level heredity.

*9.*

**Elife**- Kerdoncuff, E., Lambert, A., and Achaz, G. (2020). Testing for population decline using maximal linkage disequilibrium blocks.

**Theor Popul Biol.**- Lambert, A., and Schertzer, E. (2020). Coagulation-transport equations and the nested coalescents.

*176, 77–147.*

**Probab. Theory Relat. Field**- Manceau, M., Marin, J., Morlon, H., and Lambert, A. (2020). Model-based inference of punctuated molecular evolution.

*37, 3308–3323*

**Mol. Biol. Evol.**- Marin, J., Achaz, G., Crombach, A., and Lambert, A. (2020). The genomic view of diversification.

**J. Evol. Biol.**- Bienvenu, F., Débarre, F., and Lambert, A. (2019). The split-and-drift random graph, a null model for speciation.

*129, 2010–2048.*

**Stochastic Processes and Their Applications**- Anciaux, Y., Lambert, A., Ronce, O., Roques, L., and Martin, G. (2019). Population persistence under high mutation rate: from evolutionary rescue to lethal mutagenesis.

*73, 1517–1532.*

**Evolution**- Manceau, M., and Lambert, A. (2019). The Species Problem from the Modeler’s Point of View.

*81, 878–898.*

**Bull. Math. Biol.**- Blanquart, F. (2019). Evolutionary epidemiology models to predict the dynamics of antibiotic resistance.

*12, 365–383.*

**Evol Appl**- Achaz, G., Lambert, A., and Schertzer, E. (2018). The Sequential Loss of Allelic Diversity.

*50, 13–29.*

**Adv. Appl. Probab.**- Manceau, M., and Lambert, A. (2018). The Species Problem from the Modeler’s Point of View. **Bull. Math. Biol.**

- Parsons, T. L., Lambert, A., Day, T., and Gandon, S. (2018). Pathogen evolution in finite populations: slow and steady spreads the best.* J R Soc Interface* 15.

- Vakirlis, N., Hebert, A. S., Opulente, D. A., Achaz, G., Hittinger, C. T., Fischer, G., Coon, J. J., and Lafontaine, I. (2018). A Molecular Portrait of De Novo Genes in Yeasts.

*, 631–645.*

**Mol. Biol. Evol.**35- Landoulsi, Z., Laatar, F., Noé, E., Mrabet, S., Ben Djebara, M., Achaz, G., Nava, C., Baulac, S., Kacem, I., Gargouri-Berrechid, A., et al. (2018). Clinical and genetic study of Tunisian families with genetic generalized epilepsy: contribution of CACNA1H and MAST4 genes.

**Neurogenetics***19*, 165–178.

- Achaz, G. (2018). 4 - Which Model(s) Explain Biodiversity? In Biodiversity and Evolution, P. Grandcolas, and M.-C. Maurel, eds. (Elsevier), p. 39–61.

- Schertzer, E., and Simatosi, F. (2018). Height and contour processes of Crump-Mode-Jagers forests (I): general distribution and scaling limits in the case of short edges.

**Electron. J. Probab.***23*, 67.

- Blanquart, F., Lehtinen, S., Lipsitch, M., and Fraser, C. (2018). The evolution of antibiotic resistance in a structured host population.

**J R Soc Interface***15*.

- Lambert, A. (2018). The coalescent of a sample from a binary branching process.

**Theoretical Population Biology***122*, 30–35.

-Duchamps, J.-J., and Lambert, A. (2018). Mutations on a random binary tree with measured boundary.

**Ann. Appl. Probab.***28*, 2141–2187.

- Aguilée, R., Gascuel, F., Lambert, A., and Ferriere, R. (2018). Clade diversification dynamics and the biotic and abiotic controls of speciation and extinction rates.

*9, 3013.*

**Nat Commun**- Débarre, F., Rode, N.O., and Ugelvig, L.V. Gender equity at scientific events. Evolution Letters 0.

- Lambert, A. (2018). Random ultrametric trees and applications. * ESAIM: Proceedings & Surveys* 60 70-89.

- Schertzer, E. (2018). Renewal structure of the Brownian taut string.

*128, 487–504.*

**Stoch. Process. Their Appl.**- Bridel, S., Olsen, A.-B., Nilsen, H., Bernardet, J.-F., Achaz, G., Avendaño-Herrera, R., and Duchaud, E. (2018). Comparative Genomics of Tenacibaculum dicentrarchi and “Tenacibaculum finnmarkense” Highlights Intricate Evolution of Fish-Pathogenic Species. * Genome Biol Evol *10, 452–457.

- Rego-Costa, A., Debarre, F., and Chevin, L.-M. (2018). Chaos and the (un)predictability of evolution in a changing environment.

*72, 375–385.*

**Evolution**- Matuszewski, S., Hildebrandt, M. E., Achaz, G., and Jensen, J. D. (2018). Coalescent Processes with Skewed Offspring Distributions and Nonequilibrium Demography.

*208, 323–338.*

**Genetics**- Newman, C. M., Ravishankar, K., and Schertzer, E. (2017). Perturbations of Voter model in one-dimension.

**Electron. J. Probab.***22*.

- Bienvenu, F., Akçay, E., Legendre, S., and McCandlish, D. M. (2017). The genealogical decomposition of a matrix population model with applications to the aggregation of stages.

*115, 69–80.*

**Theor Popul Biol**- Lambert, A. (2017). Probabilistic models for the (sub)tree(s) of life.

*31, 415–475.*

**Braz. J. Probab. Stat.**- Manceau, M., Lambert, A., and Morlon, H. (2017). A Unifying Comparative Phylogenetic Framework Including Traits Coevolving Across Interacting Lineages.

*66, 551–568.*

**Syst. Biol.**- Lambert, A., and Uribe Bravo, G. (2017). The Comb Representation of Compact Ultrametric Spaces.

*9, 22–38.*

**P-Adic Numbers Ultrametric Anal. Appl.**- Tomasetti, C., Durrett, R., Kimmel, M., Lambert, A., Parmigiani, G., Zauber, A. & Vogelstein, B., (2017), Role of stem-cell divisions in cancer risk.

*548, E13–E14.*

**Nature**- Ferretti, L., Ledda, A., Wiehe, T., Achaz, G., and Ramos-Onsins, S.E. (2017). Decomposing the Site Frequency Spectrum: The Impact of Tree Topology on Neutrality Tests.

*207, 229–240.*

**Genetics**- Lapierre, M., Lambert, A. & Achaz, G. (2017), Accuracy of Demographic Inferences from the Site Frequency Spectrum: The Case of the Yoruba Population.

*206, 439–449.*

**Genetics**- Débarre, F. (2017), Fidelity of parent-offspring transmission and the evolution of social behavior in structured populations.

*420, 26–35.*

**J. Theor. Biol.**- Gangloff, S., Achaz, G., Francesconi, S., Villain, A., Miled, S., Denis, C., and Arcangioli, B. (2017). Quiescence unveils a novel mutational force in fission yeast.

**Elife**6. e27469.

- Blanquart, F., Wymant, C., Cornelissen, M., Gall, A., Bakker, M., Bezemer, D., Hall, M., Hillebregt, M., Ong, S. H., Albert, J., et al. (2017). Viral genetic variation accounts for a third of variability in HIV-1 set-point viral load in Europe.

*15, e2001855.*

**PLoS Biol.**-Blanquart, F., Lehtinen, S., and Fraser, C. (2017). An evolutionary model to predict the frequency of antibiotic resistance under seasonal antibiotic use, and an application to Streptococcus pneumoniae.

*. 284.*

**Proc. Biol. Sci**- Lehtinen, S., Blanquart, F., Croucher, N. J., Turner, P., Lipsitch, M., and Fraser, C. (2017). Evolution of antibiotic resistance is linked to any genetic mechanism affecting bacterial duration of carriage.

*114, 1075–1080.*

**Proc. Natl. Acad. Sci. U.S.A.**- Bailey, S. F., Blanquart, F., Bataillon, T., and Kassen, R. (2017). What drives parallel evolution?: How population size and mutational variation contribute to repeated evolution.

*39, 1–9.*

**Bioessays**- Lapierre, M., Blin, C., Lambert, A., Achaz, G., and Rocha, E. P. C. (2016). The Impact of Selection, Gene Conversion, and Biased Sampling on the Assessment of Microbial Demography.

*33, 1711–1725.*

**Mol. Biol. Evol.**- Delaporte, C., Achaz, G. & Lambert, A. (2016), Mutational pattern of a sample from a critical branching population.

*1–38.*

**J. Math. Biol.**- Alexander, H. K., Lambert, A. & Stadler, T. (2016), Quantifying Age-dependent Extinction from Species Phylogenies.

*65, 35–50.*

**Syst. Biol.**- Ferretti, L., Schmiegelt, B., Weinreich, D., Yamauchi, A., Kobayashi, Y., Tajima, F., and Achaz, G. (2016). Measuring epistasis in fitness landscapes: The correlation of fitness effects of mutations.

*396, 132–143.*

**J. Theor. Biol.**- Suez, M., Behdenna, A., Brouillet, S., Graça, P., Higuet, D. & Achaz, G. (2016), MicNeSs: genotyping microsatellite loci from a collection of (NGS) reads.

*16, 524–533.*

**Mol Ecol Resour**- Hartnett, A. T., Schertzer, E., Levin, S. A. & Couzin, I. D. (2016), Heterogeneous Preference and Local Nonlinearity in Consensus Decision Making.

*116, 038701.*

**Phys. Rev. Lett.**- Bienvenu, F., and Legendre, S. (2015). A new approach to the generation time in matrix population models.

*185, 834–843.*

**Am. Nat.**- Schertzer, E., Staver, A. C., and Levin, S. A. (2015). Implications of the spatial dynamics of fire spread for the bistability of savanna and forest.

*70, 329–341.*

**J Math Biol**- Davila Felipe, M. & Lambert, A. (2015), Time Reversal Dualities for some Random Forests.

*12, 399–426.*

**ALEA Lat.****Am. J. Probab. Math. Stat.**- Debarre, F., Yeaman, S. & Guillaume, F. (2015), Evolution of Quantitative Traits under a Migration-Selection Balance: When Does Skew Matter?

*186, S37–S47.*

**Am. Nat.**- Gascuel, F., Ferrière, R., Aguilée & R., Lambert, A. (2015), How Ecology and Landscape Dynamics Shape Phylogenetic Trees.

*64, 590–607.*

**Syst. Biol.**- Clémençon, S., Cousien, A., Felipe M. D. & Tran, V. C. (2015), On computer-intensive simulation and estimation methods for rare-event analysis in epidemic models.

*34, 3696–3713.*

**Statist. Med.**- Lambert, A. & Ma, C. (2015), The Coalescent in Peripatric Metapopulations.

*52, 538–557.*

**J. Appl. Probab.**- Lambert, A., Morlon, H., Etienne, R. S. (2015), The reconstructed tree in the lineage-based model of protracted speciation.

*70, 367–397.*

**J. Math. Biol.**- Massol, F., & Débarre, F. (2015), Evolution of dispersal in spatially and temporally variable environments: The importance of life cycles.

*69, 1925–1937.*

**Evolution**- Newman, C. M., Ravishankar, K. & Schertzer, E. (2015), Brownian net with killing.

*125, 1148–1194.*

**Stochastic Processes and their Applications**- Regnier, C., Achaz, G., Lambert, A., Cowie, R. H., Bouchet, P. & Fontaine, B. (2015), Mass extinction in poorly known taxa.

*112, 7761–7766.*

**Proc. Natl. Acad. Sci. U. S. A.**- Suez, M., Behdenna, A., Brouillet, S., Graça, P., Higuet, D. & Achaz, G., (2015), MicNeSs: genotyping microsatellite loci from a collection of (NGS) reads.

**Mol Ecol Resour***16*, 524–533.

- Berdahl A., Torney C. J., Schertzer E. & Levin S. A. (2015), On the evolutionary interplay between dispersal and local adaptation in heterogeneous environments.

*. 69, 1390–1405.*

**Evolution**- Débarre F. (2015), Fitness costs in spatially structured environments. * Evolution, *12646.

- Lambert A. & Simatos F. (2015), Asymptotic Behavior of Local Times of Compound Poisson Processes with Drift in the Infinite Variance Case. * J. Theor. Probab.* 28, 41-91.

- Manceau M., Lambert A. & Morlon H. (2015), Phylogenies support out-of-equilibrium models of biodiversity.* Ecol Lett 18,* 347–356.

- Martin G. & Lambert A. (2015), A simple, semi-deterministic approximation to the distribution of selective sweeps in large populations. * Theor. Popul. Biol*. 101, 40-46.

- Etienne R. S., Morlon H. & Lambert A. (2014), Estimating the duration of speciation from phylogenies.

*, 2430–2440.*

**Evolution 68**- Ferretti L., Mamino M. & Bianconi G. (2014), Condensation and topological phase transitions in a dynamical network model with rewiring of the links.

*89, 042810.*

**Phys Rev E Stat Nonlin Soft Matter Phys**- Lambert A., Alexander H. K. & Stadler T. (2014), Phylogenetic analysis accounting for age-dependent death and sampling with applications to epidemics.

*352, 60–70.*

**J. Theor. Biol.**- Blanquart, F., Achaz, G., Bataillon, T., and Tenaillon, O. (2014). Properties of selected mutations and genotypic landscapes under Fisher’s Geometric Model.

*68, 3537-3554.*

**Evolution**- Achaz, G., Rodriguez-Verdugo, A., Gaut, B. S., and Tenaillon, O. (2014). The reproducibility of adaptation in the light of experimental evolution with whole genome sequencing.

*781, 211–231.*

**Adv. Exp. Med. Biol.**- Champagnat N. & Lambert A. (2013), Splitting trees with neutral Poissonian mutations II: Largest and oldest families.

*123(4) 1368-1414.*

**Stoch. Proc. Appl.**- Aguilée R., Claessen D. & Lambert A. (2013) Adaptive radiation driven by the interplay of eco-evolutionary and landscape dynamics. * Evolution *67(5) 1291-1306.

- Bansaye V. & Lambert A. (2013) Past, growth and persistence of source-sink metapopulations. * Theoret. Popul. Biol.* 88 31-46.

- Lambert A. & Stadler T. (2013) Birth-death models and coalescent point processes: The shape and probability of reconstructed phylogenies. * Theoret. Popul. Biol.* 90 113-128.

- Lambert A. & Steel M. (2013) Predicting the loss of phylogenetic diversity under non-stationary diversification models. * J. Theoret. Biol.* 337 111-124.

**Lambert A. & Popovic .L (2013), The coalescent point process of branching trees,**

--

**Vol. 23, No. 1, 99-144.**

*Annals of Applied Probability,*- Lambert A. & Trapman P. (2013), Splitting trees stopped when the first clock rings and Vervaat's transformation,

**Volume 50, Number 1 (2013), 208-227.**

*Journal of Applied Probability,*- Ishida, S., Picard, F., Rudolf, G., Noé, E., Achaz, G., Thomas, P., Genton, P., Mundwiller, E., Wolff, M., Marescaux, C., et al. (2013). Mutations of DEPDC5 cause autosomal dominant focal epilepsies.

*45, 552–555.*

**Nat. Genet.**- Loire, E., Higuet, D., Netter, P., and Achaz, G. (2013). Evolution of coding microsatellites in primate genomes.

*5, 283–295.*

**Genome Biol Evol**- Champagnat N. & Lambert A. (2012), Splitting trees with neutral Poissonian mutations I: Small families.

*122(3) 1003-1033.*

**Stoch. Proc. Appl.**- Mariadassou M., Bar-Hen A. & Kishino H. (2012), Taxon Influence: Assessing taxon-induced incongruities in phylogenetic inference,

*61 337-345.*

**Systematic Biology**- Stewart A. J., Parsons T. L. & Plotkin J. B. (2012), Environmental robustness and the evolvability of populations,

**66 (5) 1598-1612.**

*Evolution*- Draghi J. A., Parsons T. L. & Plotkin J. B. (2011), Epistasis increases the rate of conditionally neutral substitution in an adapting population,

**187 (4): 1139-1152.**

*Genetics*- Puillandre N., Lambert A., Brouillet S. & Achaz G. (2011), ABGD, Automatic Barcode Gap Discovery for primary species delimitation,

*21:8 1864-1877.*

**Molecular Ecology**- Lambert A. (2011), Species abundance distributions in neutral models with immigration or mutation and general lifetimes,

*63: 57-72.*

**Journal of Mathematical Biology**- Aguilée A., Lambert A. & Claessen D. (2011), Ecological speciation in dynamic landscapes,

*24: 2663-2677.*

**Journal of Evolutionary Biology**- Draghi J. A., Parsons T. L., Wagner G. P. & Plotkin J. B. (2010), Mutational robustness can facilitate adaptation,

**463 (7279): 353-355.**

*Nature*- Lambert A. (2010), The contour of splitting trees is a Lévy process,

*38 348-395.*

**Annals of Probability**## People

** Group leader:**Lambert Amaury, PR, Sorbonne Université

**Senior researchers:**

Achaz Guillaume, PR2, Université de Paris

Blanquart François, CRCN CNRS

**Godfroid Maxime, Postdoctoral fellow**

**Postdoctoral fellows &****PhD****Students:**Picot Aurore, Postdoctoral fellow

Lorenzi Jean-Noel, Postdoctoral fellow

Morel-Journel Thibaut, Postdoctoral fellow

Forest Thomas, PhD student

Kerdoncuff Elise, PhD student

Foutel-rodier Félix, PhD student

Gamblin Jasmine, PhD student

Thomas Guillaume, PhD student