ERC SINGER - Stochastic dynamics of sINgle cells : Growth, Emergence and Resistance

Thématiques
- Mathématiques appliquées
- Processus stochastiques
- Evolution bactérienne
- Modélisation en hématologie
- Biologie
- Recherche
- Médical
A propos
Le projet que porte l’ERC SINGER vise à développer de nouveaux modèles stochastiques et déterministes pour des applications biologiques et médicales. Il s’agit d’un défi sociétal interdisciplinaire qui va chercher à développer des scénarios d’évolution des résistances ainsi que de meilleures stratégies pour les antibiotiques ou les chimiothérapies qui y sont liés.
L’objectif principal consiste à étudier de nouveaux problèmes mathématiques à plusieurs échelles, en nous inspirant des défis biologiques posés par les organismes unicellulaires. En collaborant étroitement avec des experts en biologie, nous cherchons à comprendre et à modéliser la complexité des populations évolutives, tout en contribuant au développement de nouvelles théories mathématiques pour relever ces défis passionnants
Le projet
Le projet se concentre sur la biologie éco-évolutive des populations asexuées de bactéries ou de cellules, en explorant comment la survie et la reproduction dépendent des traits phénotypiques ou génétiques. L'évolution de ces traits résulte de divers mécanismes, et le défi majeur consiste à prédire les scénarios d'évolution en prenant en compte ces mécanismes. Le projet tire parti des mesures récentes de cellules individuelles, où de petites populations et une grande variabilité sont observées, avec un impact significatif de l'environnement.
L'objectif principal est de développer des modèles stochastiques pour contrôler ces fluctuations et prédire leur comportement en réponse aux changements environnementaux.
L'approche mathématique adoptée englobe une classe de modèles et caractéristiques, visant à des applications médicales et biologiques pour les populations évoluant, se reproduisant, croissant et émergeant. Une collaboration étroite avec des biologistes permettra de résoudre des problèmes biologiques en posant de nouvelles questions mathématiques. Le projet s'inscrit dans une tradition de développement de nouveaux concepts mathématiques à partir de découvertes biologiques, en utilisant des modèles de population structurés et de croissance-fragmentation.
La méthodologie implique des processus stochastiques structurés à valeur de mesure générant une diversité de comportements macroscopiques. Les principaux outils comprennent les théorèmes des limites, les équations différentielles stochastiques, les processus de ramification avec interactions et les équations différentielles partielles non linéaires.
Le projet représente un défi mathématique en cherchant à réconcilier les approches stochastiques et Hamilton-Jacobi dans la modélisation éco-évolutive, en explorant de nouvelles échelles de temps et de taille, et en contrôlant les événements d'extinction. Il aborde également des problèmes médicaux, notamment la compréhension des mutations leucémiques et des temps de réponse dans des systèmes multi-échelles, avec des implications potentielles pour les traitements médicaux.
Les thèmes de recherche clés :
- la transition des processus stochastiques aux équations de Hamilton-Jacobi,
- la modélisation des mutations leucémiques et des temps de réponse dans des systèmes multi-échelles,
- la recherche de lignées et de chemins inversés dans des situations non linéaires,
- la modélisation de la croissance et de la fragmentation des bactéries multitype en lien avec la réponse aux antibiotiques.
En résumé, ce projet s'appuie sur des modèles mathématiques pour explorer les mécanismes d'évolution des populations biologiques à différentes échelles, en mettant l'accent sur les défis mathématiques et les applications potentielles en biologie et en médecine.
Les 2 axes du projet
- Axe 1 : Développement d’un cadre mathématique pour suivre de très petites sous-populations dans des approximations de grandes populations afin d'expliquer et de quantifier des comportements surprenants à long terme dans la dynamique évolutive des populations, comme l'émergence de "populations éteintes"
- Axe 2 : Modélisation et compréhension mathématique des scénarios d'évolution des résistances en collaboration étroite avec les biologistes afin de proposer de nouvelles stratégies tenant compte de ces scénarios.
Le projet est supporté par :
“Funded by the European Union (ERC, acronym, project number). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.”
Lien vers projets connexes
Membres Permanents
Project Leader
- Sylvie Méléard, Professeur, Ecole polytechnique, France.
Mathématiciens
- Vincent Bansaye, Professeur, Ecole polytechnique, France.
- Nicolas Champagnat, DR, INRIA Nancy - Grand est, France.
- Marie Doumic, DR, INRIA Paris, France.
- Sepideh Mirrahimi, DR, CNRS Montpellier, France.
- Chi Viet Tran, Professeur, Université Gustave Eiffel, France.
- Anita Winter, Professeur, Universität Duisburg - Essen, Allemagne.
Biologistes et Médecins
- Sylvain Billiard, Professeur, Université de Lille, France.
- Meriem El Karoui, Professeur, Université d'Edimbourg, Ecosse.
- Stéphane Giraudier, Professeur, Hôpital Saint - Louis, France.
- Raphaël Itzykson, Professeur, Hôpital Saint - Louis, France.
- Evelyne Lauret, CR, CNRS, INSERM, Institut Cochin, France.
Membres temporaires
- Clément Foucart (01/09/2023 - 31/08/2025) chercheur associé
- Pierre Gabriel (01/02/2023 – 30/07/2023) délégation
- Sarah Kaakai - Collaboratrice
- Jaime San Martin (3/05/2023 – 05/07/2023) Professeur invité
Evènements à destination du public
- Séminaire
- Ecole d’été
Evènements internes
- Groupe de travail
Références du projet
[1] V. Bansaye. Ancestral lineages and limit theorems for branching Markov chains in varying environment. J. Theoret. Probab. 32 (2019), no. 1, 249-281.
[2] M. Baar, L. Coquille, H. Mayer, M. Holzel, M. Rogava, T. Touting, A. Bovier. A stochastic model for immunotherapy of cancer. Sci. Rep. 6, (2016),24169.
[3] M. Baar, A. Bovier, N. Champagnat. From stochastic, individual-based models to the canonical equation of adaptive dynamics in one step. Ann. Appl. Probab. 27 (2017), no. 2, 1093-1170.
[4] M. Baar, A. Bovier. The polymorphic evolution sequence for populations with phenotypic plasticity. Electron. J. Probab. 23 (2018), No 72.
[5] Z. Baharoglu, D. Mazel. SOS, the formidable strategy of bacteria against aggressions. FEMS Microbiology Reviews, Volume 38, Issue 6, November 2014, Pages 1126- 1145, https://doi.org/10.1111/1574-6976.12077.
[6] J. Baker, P. Chigansky, P. Jagers, F.C. Klebaner. On the establishment of a mutant. J. Math. Biol. 80 (2020), no. 6, 1733-1757.
[7] G. Barles, B. Perthame, Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics. In D. Danielli (ed.), Recent Developments in Nonlinear Partial Diferential Equations, Contemp. Math. Series 439 (2007), 57-68.
[8] G. Barles, S. Mirrahimi, B. Perthame. Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result. Methods Appl. Anal., 16(3), (2009), 32-340.
[9] N. Berestycki. Recent progress in coalescent theory, Ensaios Matematicos 16, (2009), 1-193. [10] [10] S. Billiard, P. Collet, R. Ferriere, S. Meleard, V.C. Tran. The effect of competition and horizontal trait hesitance on invasion, fixation and polymorphism. J. Theoret. Biol. 411 (2016), 48-58.
[11] S. Billiard, C. Smadi, The interplay of two mutations in a population of varying size: a stochastic eco-evolutionary model for clonal interference, Stochastic Processes and their Applications, 127(3), (2017), 701-748.
[12] S. Billiard, P. Collet, R. Ferriere, S. Meleard, V.C. Tran. Stochastic dynamics for adaptation and evolution of microorganisms. European Congress of Mathematics Berlin 2016, V. Mehrmann and M. Skutella eds, pp. 525-550, EMS Publishing House, (2018).
[13] J. Blath, T. Paul, A. Tobias. A stochastic adaptive dynamics model for bacterial populations with mutation, dormancy ad transfer. arXiv:2105.09228 (2021).
[14] C. Bonnet, S. Meleard Large fluctuations in multi-scale modeling for rest erythropoiesis, in revision for J. Math. Biol..
[15] V. Calvez, S. Figueroa Iglesias, H. Hivert, S. Meleard, A. Melnykova, S. Nordmann. Horizontal gene transfer: numerical comparison between stochastic and deterministic approaches. To appear in ESAIM Proceedings (CEMRACS 2018).
[16] P. Cattiaux, P. Collet, A. Lambert, S. Martinez, S. Meleard, J. San Martin. Quasi-stationarity distributions and diffusion models in population dynamics, Ann. Probab. 37 (2009), no. 5, 1926-1969.
[17] N. Champagnat. A microscopic interpretation for adaptive dynamics trait substitution sequence models. Stoch. Process. Their Appl. 116 (2006), 1127-1160.
[18] N. Champagnat, S. Meleard. Polymorphic evolution sequence and evolutionary branching. Probab. Theory Related Fields 151 (2011), no. 1-2, 45-94.
[19] N. Champagnat, S. Meleard, V.C. Tran. Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer, to appear in Ann. Appl. Probability (2020).
[20] J.R. Chazottes, P. Collet, S. Meleard. Sharp asymptotics for the quasi-stationary distribution of birth-and-death processes. Probab. Theory Related Fields 164 (2016), no. 1-2, 285-332.
[21] J.R. Chazottes, P. Collet, S. Meleard. On time scales and quasi-stationary distributions for multitype birth-and-death processes. Ann. of IHP, Vol. 55, No. 4, 2249-2294 (2019).
[22] J.R. Chazottes, P. Collet, S. Martinez, S. Meleard. Quasi-stationary distributions and resilience: what to get from a sample? J. Ec. polytech. Math. 7 (2020), 943-980.
[23] K.L. Chung, J.B. Walsh. To reverse a Markov process. Acta Mathematica 123, (1969), 225-251.
[24] B. Cloez, P. Gabriel. On an irreducibility type condition for the ergodicity of nonconservative semigroups. Comptes Rendus. Mathematique 358, 6 (2020), 733-742.
[25] P. Collet, S. Meleard, J.A.J. Metz. rigorous model study of the adaptive dynamics of Mendelian diploids. J. Math. Biol. 67 (2013), no. 3, 569-607.
[26] M. Costa, C. Etchegaray, S. Mirrahimi. Survival criterion for a population subject to selection and mutations; Application to temporally piecewise constant environments, Nonlinear Analysis: Real World Applications, Vol. 59, (2021), 103239.
[27] L. Desvillettes, P. E. Jabin, S. Mischler, G. Raoul. On mutation-selection dynamics for continuous structured populations. Commun. Math. Sci. 6(3), (2008), 729-747.
[28] U. Dieckmann, R. Law. The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol. 34 (1996), 579-612.
[29] O. Diekmann. A beginner's guide to adaptive dynamics. In Mathematical modelling of population dynamics, volume 63 of Banach Center Publ., Polish Acad. Sci. (2004), 47-86.
[30] O. Diekmann, P. E. Jabin, S. Mischler, B. Perthame. The dynamics of adaptation: An illuminating example and a Hamilton-Jacobi approach. Theor. Popul. Biol. 67 (2005), 257-271.
[31] D. Donnelly, T.G. Kurtz. Genealogical processes for Fleming-Viot models with selection and recombination. Ann. Appl. Probab. 9(4), (1999), 1091-1148.
[32] M. Doumic, M. Homann, N. Krell, L. Robert. Statistical estimation of a growth-fragmentation model observed on a genealogical tree. Bernoulli 21 (2015), no. 3, 1760-1799.
[33] M.B. Elowitz, A.J. Levine, E.D. Siggia, P.S. Swain, Stochastic Gene Expression in a Single Cell. Science 297, (2002), no. 5584, 1183-1186.
[34] A.M. Etheridge, T.G. Kurtz. Genealogical constructions of population models. Ann. Probab. 47 (2019), no. 4, 1827-1910.
[35] S; Ethier, T. Kurtz. Markov Processes: characterization and Convergence. John Wiley & Sons, Inc., 1986.
[36] A. Gupta, J.A.J. Metz, V.C. Tran. A new proof for the convergence of an individual based model to the trait substitution sequence. Acta Appl. Math. 131 (2014), 1-27.
[37] S. Figueroa Iglesias, S. Mirrahimi, Long time evolutionary dynamics of phenotypically structured populations in time-periodic environments, SIAM J. Math. Anal., Vol. 50.5 (2018) pp. 5537-5568.
[38] S. Figueroa Iglesias, S. Mirrahimi. Selection and mutation in a shifting and fluctuating environment, accepted in Comm. Math. Sci., (2021).
[39] N. Fournier, S. Meleard. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14 (2004), 1880-1919.
[40] S.C. Harris, M.I. Roberts. The many-to-few lemma and multiple spines. Ann. Inst. Henri Poincare Probab. Stat. 53 (2017), no. 1, 226-242.
[41] S.C. Harris, S. Johnston and M.I. Roberts. The coalescent structure of continuous-time Galton-Watson trees. Ann. Appl. Probab. Vol. 30, No 3.1368-1414, 2020.
[42] M. Holzel, A. Bovier, T. Tuting. Plasticity of tumour and immune cells: a source of heterogeneity and a cause of therapy resistance? Nat.Rev. Cancer 13, (2013), 365-376.
[43] P.-E.Jabin. Small populations corrections for selection-mutation models. Netw. Heterog. Media, 7(4), (2012), 805-836.
[44] J.F.C. Kingman. The coalescent. Stochastic Processes and Their Applications 13 (1982), 235-248.
[45] F. Knauer, T. Stiehl, A. Marciniak-Czochra. Oscillations in a white blood cell production model with multiple differentiation stages. J Math Biol 80, (2020), 575-600.
[46] A. Marguet. Uniform sampling in a structured branching population, Bernoulli, 25, 4A (2019), 2649-2695.
[47] S. Meleard, D. Villemonais. Quasi-stationary distributions and population processes. Probab. Surv. 9 (2012), 340-410.
[48] S. Meleard, V.C. Tran. Nonlinear historical superprocess approximations for population models with past dependence. Electron. J. Probab. 17 (2012), no. 47, 1-32.
[49] S. Meleard, V.C. Tran. Trait substitution sequence process and canonical equation for age structured populations. J. Math. Biol. 58 (2009), no. 6, 881-921.
[50] J.A.J. Metz, V.C. Tran. Daphnias: from the individual based model to the large population equation. J. Math. Biol. 66 (2013), no. 4-5, 915-933.
[51] J. A. J. Metz, S. A. H. Geritz, G. Meszena, F. J. A. Jacobs, J. S. van Heerwaarden. Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. In Stochastic and spatial structures of dynamical systems (Amsterdam, 1995), Konink. Nederl. Akad.Wetensch. Verh. Afd. Natuurk. Eerste Reeks, 45, 183-231, North-Holland, Amsterdam, 1996.
[52] S. Mirrahimi, G. Barles, B. Perthame, P. E. Souganidis. A singular Hamilton-Jacobi equation modeling the tail problem. SIAM J. Math. Anal., (2012), 44(6), 4297-4319.
[53] N.V. Mon Pere, T. Lenaerts, J.M.D.S. Pacheco, D. Dingli. Multistage feedback-driven compartmental dynamics of hematopoiesis. IScience 24, (2021), 102326.
[54] M. Nagasawa. Time reversion of Markov processes. Nagoya Math. J. 24, (1964), 117-204.
[55] S.H. Orkin, LM.I. Zon. hematopoiesis: an evolving paradigm from stem cell biology. Cell 132, (2008), 631-644.
[56] E. Perkins. On the martingale problem for interactive measure-valued branching diffusions, Memoirs of the American Mathematical Society ed., vol. 115(549), American Mathematical Society, May 1995.
[57] B. Perthame. Transport Equations in Biology. Birkhauser 2007.
[58] B. Perthame, G. Barles. Dirac concentration in Lotka-Volterra parabolic PDEs. Indiana Univ. Math. J. (57(7), (2008), 3275-3301.
[59] B. Perthame, M. Gauduchon. Survival thresholds and mortality rates in adaptive dynamics: conciliating deterministic and stochastic simulations. Math. Med. Biol., 27(3), (2010),195-210.
[60] A. Raj, A. van Oudenaarden. Nature, Nurture, or Chance: Stochastic Gene Expression and Its Consequences. Cell 135 no. 2, (2008), 216-226.
[61] L. Roques, F. Patout, O. Bonnefon, G. Martin. Adaptation in general temporally changing environments. SIAM J. Appl. Math. 80 (2020), no. 6, 2420-2447.
[62] T. Stiehl, A.D. HO, A. Marciniak-Czochra. Assessing hematopoietic (stem)-cell behavior during regenerative pressure. Adv. Exp. Med. Biol. 844 (2014), 347-367.
[63] D. Waxman, S. Gavrilets. 20 Questions on Adaptive Dynamics. J. Evol. Biol. 18(5), (2005), 1139-1154.
En cours de recrutement
Membres Permanents
Project Leader
- Sylvie Méléard, Professeur, Ecole polytechnique, France.
Mathématiciens
- Vincent Bansaye, Professeur, Ecole polytechnique, France.
- Nicolas Champagnat, DR, INRIA Nancy - Grand est, France.
- Marie Doumic, DR, INRIA Paris, France.
- Sepideh Mirrahimi, DR, CNRS Montpellier, France.
- Chi Viet Tran, Professeur, Université Gustave Eiffel, France.
- Anita Winter, Professeur, Universität Duisburg - Essen, Allemagne.
Biologistes et Médecins
- Sylvain Billiard, Professeur, Université de Lille, France.
- Meriem El Karoui, Professeur, Université d'Edimbourg, Ecosse.
- Stéphane Giraudier, Professeur, Hôpital Saint - Louis, France.
- Raphaël Itzykson, Professeur, Hôpital Saint - Louis, France.
- Evelyne Lauret, CR, CNRS, INSERM, Institut Cochin, France.
Membres temporaires
- Clément Foucart (01/09/2023 - 31/08/2025) chercheur associé
- Pierre Gabriel (01/02/2023 – 30/07/2023) délégation
- Sarah Kaakai - Collaboratrice
- Jaime San Martin (3/05/2023 – 05/07/2023) Professeur invité
Evènements à destination du public
- Séminaire
- Ecole d’été
Evènements internes
- Groupe de travail
Références du projet
[1] V. Bansaye. Ancestral lineages and limit theorems for branching Markov chains in varying environment. J. Theoret. Probab. 32 (2019), no. 1, 249-281.
[2] M. Baar, L. Coquille, H. Mayer, M. Holzel, M. Rogava, T. Touting, A. Bovier. A stochastic model for immunotherapy of cancer. Sci. Rep. 6, (2016),24169.
[3] M. Baar, A. Bovier, N. Champagnat. From stochastic, individual-based models to the canonical equation of adaptive dynamics in one step. Ann. Appl. Probab. 27 (2017), no. 2, 1093-1170.
[4] M. Baar, A. Bovier. The polymorphic evolution sequence for populations with phenotypic plasticity. Electron. J. Probab. 23 (2018), No 72.
[5] Z. Baharoglu, D. Mazel. SOS, the formidable strategy of bacteria against aggressions. FEMS Microbiology Reviews, Volume 38, Issue 6, November 2014, Pages 1126- 1145, https://doi.org/10.1111/1574-6976.12077.
[6] J. Baker, P. Chigansky, P. Jagers, F.C. Klebaner. On the establishment of a mutant. J. Math. Biol. 80 (2020), no. 6, 1733-1757.
[7] G. Barles, B. Perthame, Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics. In D. Danielli (ed.), Recent Developments in Nonlinear Partial Diferential Equations, Contemp. Math. Series 439 (2007), 57-68.
[8] G. Barles, S. Mirrahimi, B. Perthame. Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result. Methods Appl. Anal., 16(3), (2009), 32-340.
[9] N. Berestycki. Recent progress in coalescent theory, Ensaios Matematicos 16, (2009), 1-193. [10] [10] S. Billiard, P. Collet, R. Ferriere, S. Meleard, V.C. Tran. The effect of competition and horizontal trait hesitance on invasion, fixation and polymorphism. J. Theoret. Biol. 411 (2016), 48-58.
[11] S. Billiard, C. Smadi, The interplay of two mutations in a population of varying size: a stochastic eco-evolutionary model for clonal interference, Stochastic Processes and their Applications, 127(3), (2017), 701-748.
[12] S. Billiard, P. Collet, R. Ferriere, S. Meleard, V.C. Tran. Stochastic dynamics for adaptation and evolution of microorganisms. European Congress of Mathematics Berlin 2016, V. Mehrmann and M. Skutella eds, pp. 525-550, EMS Publishing House, (2018).
[13] J. Blath, T. Paul, A. Tobias. A stochastic adaptive dynamics model for bacterial populations with mutation, dormancy ad transfer. arXiv:2105.09228 (2021).
[14] C. Bonnet, S. Meleard Large fluctuations in multi-scale modeling for rest erythropoiesis, in revision for J. Math. Biol..
[15] V. Calvez, S. Figueroa Iglesias, H. Hivert, S. Meleard, A. Melnykova, S. Nordmann. Horizontal gene transfer: numerical comparison between stochastic and deterministic approaches. To appear in ESAIM Proceedings (CEMRACS 2018).
[16] P. Cattiaux, P. Collet, A. Lambert, S. Martinez, S. Meleard, J. San Martin. Quasi-stationarity distributions and diffusion models in population dynamics, Ann. Probab. 37 (2009), no. 5, 1926-1969.
[17] N. Champagnat. A microscopic interpretation for adaptive dynamics trait substitution sequence models. Stoch. Process. Their Appl. 116 (2006), 1127-1160.
[18] N. Champagnat, S. Meleard. Polymorphic evolution sequence and evolutionary branching. Probab. Theory Related Fields 151 (2011), no. 1-2, 45-94.
[19] N. Champagnat, S. Meleard, V.C. Tran. Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer, to appear in Ann. Appl. Probability (2020).
[20] J.R. Chazottes, P. Collet, S. Meleard. Sharp asymptotics for the quasi-stationary distribution of birth-and-death processes. Probab. Theory Related Fields 164 (2016), no. 1-2, 285-332.
[21] J.R. Chazottes, P. Collet, S. Meleard. On time scales and quasi-stationary distributions for multitype birth-and-death processes. Ann. of IHP, Vol. 55, No. 4, 2249-2294 (2019).
[22] J.R. Chazottes, P. Collet, S. Martinez, S. Meleard. Quasi-stationary distributions and resilience: what to get from a sample? J. Ec. polytech. Math. 7 (2020), 943-980.
[23] K.L. Chung, J.B. Walsh. To reverse a Markov process. Acta Mathematica 123, (1969), 225-251.
[24] B. Cloez, P. Gabriel. On an irreducibility type condition for the ergodicity of nonconservative semigroups. Comptes Rendus. Mathematique 358, 6 (2020), 733-742.
[25] P. Collet, S. Meleard, J.A.J. Metz. rigorous model study of the adaptive dynamics of Mendelian diploids. J. Math. Biol. 67 (2013), no. 3, 569-607.
[26] M. Costa, C. Etchegaray, S. Mirrahimi. Survival criterion for a population subject to selection and mutations; Application to temporally piecewise constant environments, Nonlinear Analysis: Real World Applications, Vol. 59, (2021), 103239.
[27] L. Desvillettes, P. E. Jabin, S. Mischler, G. Raoul. On mutation-selection dynamics for continuous structured populations. Commun. Math. Sci. 6(3), (2008), 729-747.
[28] U. Dieckmann, R. Law. The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol. 34 (1996), 579-612.
[29] O. Diekmann. A beginner's guide to adaptive dynamics. In Mathematical modelling of population dynamics, volume 63 of Banach Center Publ., Polish Acad. Sci. (2004), 47-86.
[30] O. Diekmann, P. E. Jabin, S. Mischler, B. Perthame. The dynamics of adaptation: An illuminating example and a Hamilton-Jacobi approach. Theor. Popul. Biol. 67 (2005), 257-271.
[31] D. Donnelly, T.G. Kurtz. Genealogical processes for Fleming-Viot models with selection and recombination. Ann. Appl. Probab. 9(4), (1999), 1091-1148.
[32] M. Doumic, M. Homann, N. Krell, L. Robert. Statistical estimation of a growth-fragmentation model observed on a genealogical tree. Bernoulli 21 (2015), no. 3, 1760-1799.
[33] M.B. Elowitz, A.J. Levine, E.D. Siggia, P.S. Swain, Stochastic Gene Expression in a Single Cell. Science 297, (2002), no. 5584, 1183-1186.
[34] A.M. Etheridge, T.G. Kurtz. Genealogical constructions of population models. Ann. Probab. 47 (2019), no. 4, 1827-1910.
[35] S; Ethier, T. Kurtz. Markov Processes: characterization and Convergence. John Wiley & Sons, Inc., 1986.
[36] A. Gupta, J.A.J. Metz, V.C. Tran. A new proof for the convergence of an individual based model to the trait substitution sequence. Acta Appl. Math. 131 (2014), 1-27.
[37] S. Figueroa Iglesias, S. Mirrahimi, Long time evolutionary dynamics of phenotypically structured populations in time-periodic environments, SIAM J. Math. Anal., Vol. 50.5 (2018) pp. 5537-5568.
[38] S. Figueroa Iglesias, S. Mirrahimi. Selection and mutation in a shifting and fluctuating environment, accepted in Comm. Math. Sci., (2021).
[39] N. Fournier, S. Meleard. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14 (2004), 1880-1919.
[40] S.C. Harris, M.I. Roberts. The many-to-few lemma and multiple spines. Ann. Inst. Henri Poincare Probab. Stat. 53 (2017), no. 1, 226-242.
[41] S.C. Harris, S. Johnston and M.I. Roberts. The coalescent structure of continuous-time Galton-Watson trees. Ann. Appl. Probab. Vol. 30, No 3.1368-1414, 2020.
[42] M. Holzel, A. Bovier, T. Tuting. Plasticity of tumour and immune cells: a source of heterogeneity and a cause of therapy resistance? Nat.Rev. Cancer 13, (2013), 365-376.
[43] P.-E.Jabin. Small populations corrections for selection-mutation models. Netw. Heterog. Media, 7(4), (2012), 805-836.
[44] J.F.C. Kingman. The coalescent. Stochastic Processes and Their Applications 13 (1982), 235-248.
[45] F. Knauer, T. Stiehl, A. Marciniak-Czochra. Oscillations in a white blood cell production model with multiple differentiation stages. J Math Biol 80, (2020), 575-600.
[46] A. Marguet. Uniform sampling in a structured branching population, Bernoulli, 25, 4A (2019), 2649-2695.
[47] S. Meleard, D. Villemonais. Quasi-stationary distributions and population processes. Probab. Surv. 9 (2012), 340-410.
[48] S. Meleard, V.C. Tran. Nonlinear historical superprocess approximations for population models with past dependence. Electron. J. Probab. 17 (2012), no. 47, 1-32.
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