B. Rizzi, L. Duloquin, J. Delile, and R. Doursat, Paul Bourgine and Nadine Peyriéas -This study has been presented under various forms at the conferences "The developmental biology of the sea urchin" XXI and XXIIStochastic physics in biology, This chapter) and at the Gordon Research Conference, 2012.

L. Abouchar, D. Mariela, C. R. Petkova, T. Steinhardt, and . Gregor, Precision and reproducibility of macroscopic developmental patterns. arXiv preprint arXiv:1309, Bibliography, vol.6273, 2013.

A. Adcock, E. Carlsson, and G. Carlsson, The ring of algebraic functions on persistence bar codes, Homology, Homotopy and Applications, vol.18, issue.1, 2012.
DOI : 10.4310/HHA.2016.v18.n1.a21

T. Aegerter-wilmsen, C. Alister, . Smith, J. Alix, . Christen et al., Exploring the effects of mechanical feedback on epithelial topology, Development, vol.137, issue.3, pp.499-506, 2010.
DOI : 10.1242/dev.041731

P. Alberch, Ontogenesis and Morphological Diversification, American Zoologist, vol.20, issue.4, pp.653-667, 1980.
DOI : 10.1093/icb/20.4.653

P. Alberch, S. J. Gould, F. George, . Oster, B. David et al., Size and shape in ontogeny and phylogeny, Paleobiology, vol.175, issue.03, pp.296-317, 1979.
DOI : 10.2307/2407703

R. Albert and A. Barabási, Statistical mechanics of complex networks, Reviews of Modern Physics, vol.74, issue.1, p.47, 2002.
DOI : 10.1103/RevModPhys.74.47

J. David and . Aldous, Exchangeability and related topics, 1985.

. Vg-allfrey, A. Faulkner, and . Mirsky, ACETYLATION AND METHYLATION OF HISTONES AND THEIR POSSIBLE ROLE IN THE REGULATION OF RNA SYNTHESIS, Proceedings of the National Academy of Sciences, vol.51, issue.5, p.786, 1964.
DOI : 10.1073/pnas.51.5.786

H. Shun-ichi-amari and . Nagaoka, Methods of information geometry, American Mathematical Soc, vol.191, 2007.

M. Lynne, . Angerer, C. Robert, and . Angerer, Animal?vegetal axis patterning mechanisms in the early sea urchin embryo, Developmental biology, vol.218, issue.1, pp.1-12, 2000.

M. Asano, I. Basieva, A. Khrennikov, M. Ohya, Y. Tanaka et al., A model of epigenetic evolution based on theory of open quantum systems, Systems and Synthetic Biology, vol.5, issue.3, pp.161-173, 2013.
DOI : 10.1007/s11693-013-9109-3

B. Ricardo, R. Azevedo, V. Lohaus, M. Braun, M. Gumbel et al., al. The simplicity of metazoan cell lineages, Nature, issue.7022, pp.433152-156, 2005.

F. Bailly and G. Longo, Randomness and determinism in the interplay between the continuum and the discrete, Mathematical Structures in Computer Science, vol.17, issue.02, pp.289-305, 2007.
DOI : 10.1017/S0960129507006007

F. Bailly and G. Longo, Mathematics and the natural sciences: the physical singularity of life, 2011.
DOI : 10.1142/p774

Z. Bao, I. John, T. Murray, . Boyle, . Siew-loon et al., Automated cell lineage tracing in Caenorhabditis elegans, Proceedings of the National Academy of Sciences, vol.103, issue.8, pp.2707-2712, 2006.
DOI : 10.1073/pnas.0511111103

I. Basieva, A. Khrennikov, M. Ohya, and I. Yamato, Quantum-like interference effect in gene expression: glucose-lactose destructive interference, Systems and Synthetic Biology, vol.3, issue.3, pp.59-68, 2011.
DOI : 10.1007/s11693-011-9081-8

M. Behrndt, G. Salbreux, P. Campinho, R. Hauschild, F. Oswald et al., Forces Driving Epithelial Spreading in Zebrafish Gastrulation, Science, vol.338, issue.6104, pp.338257-260, 2012.
DOI : 10.1126/science.1224143

I. Bengtsson and K. Zyczkowski, Geometry of quantum states: an introduction to quantum entanglement, 2006.
DOI : 10.1017/CBO9780511535048

D. George and . Birkhoff, Proof of the ergodic theorem, Proceedings of the National Academy of Sciences, vol.17, issue.12, pp.656-660, 1931.

M. Bitbol, Mécanique quantique: une introduction philosophique. Editions Flammarion, 1996.
DOI : 10.14375/NP.9782081214866

M. Bitbol, La mécanique quantique comme théorie des probabilités généralisées, Prévision et Probabilité dans les Sciences . Éditions Frontières, 1998.

M. Bitbol, Théorie quantique et sciences humaines, CNRS, 2009.
DOI : 10.4000/books.editionscnrs.7885

I. Bjedov, O. Tenaillon, B. Gerard, V. Souza, E. Denamur et al., Stress-Induced Mutagenesis in Bacteria, Science, vol.300, issue.5624, pp.3001404-1409, 2003.
DOI : 10.1126/science.1082240

J. Todd-blankenship, T. Stephanie, . Backovic, S. Justina, O. Sanny et al., Multicellular Rosette Formation Links Planar??Cell??Polarity to Tissue Morphogenesis, Developmental Cell, vol.11, issue.4, pp.459-470, 2006.
DOI : 10.1016/j.devcel.2006.09.007

S. Bohn, Y. Douady, and . Couder, Four sided domains in hierarchical space dividing patterns. Physical review letters, p.54503, 2005.

S. Bohn, Y. Pauchard, and . Couder, Hierarchical crack pattern as formed by successive domain divisions., Physical Review E, vol.71, issue.4, p.46214, 2005.
DOI : 10.1103/PhysRevE.71.046214

F. Bosveld, I. Bonnet, B. Guirao, S. Tlili, Z. Wang et al., Mechanical Control of Morphogenesis by Fat/Dachsous/Four-Jointed Planar Cell Polarity Pathway, Science, vol.336, issue.6082, pp.336724-727, 2012.
DOI : 10.1126/science.1221071

Y. Bradford, T. Conlin, N. Dunn, D. Fashena, K. Frazer et al., ZFIN: enhancements and updates to the zebrafish model organism database, Nucleic Acids Research, vol.39, issue.Database, pp.822-829, 2011.
DOI : 10.1093/nar/gkq1077

I. Brigandt, From Developmental Constraint to Evolvability: How Concepts Figure in Explanation and Disciplinary Identity, Conceptual Change in Biology, pp.305-325, 2015.
DOI : 10.1007/978-94-017-9412-1_14

E. Briggs, M. Gary, and . Wessel, In the beginning??? Animal fertilization and sea urchin development, Developmental Biology, vol.300, issue.1, pp.15-26, 2006.
DOI : 10.1016/j.ydbio.2006.07.014

P. Bromiley, Products and convolutions of gaussian distributions, Medical School, vol.3, 2003.

M. Buiatti and G. Longo, Randomness and multilevel interactions in biology, Theory in Biosciences, vol.31, issue.7, pp.139-158, 2013.
DOI : 10.1007/s12064-013-0179-2

S. Cristian, . Calude, J. Michael, C. Dinneen, and . Shu, Computing a glimpse of randomness, Experimental Mathematics, vol.11, issue.3, pp.361-370, 2002.

C. Calude and G. Longo, Classical, quantum and biological randomness as relative incomputability
DOI : 10.1007/s11047-015-9533-2

URL : https://hal.archives-ouvertes.fr/hal-01380600/file/CaludeLongoRandom.pdf

Ö. Carlborg and C. S. Haley, Opinion: Epistasis: too often neglected in complex trait studies?, Nature Reviews Genetics, vol.138, issue.8, pp.618-625, 2004.
DOI : 10.1089/10665270260518272

G. Carlsson, Topology and data. Bulletin of the, pp.255-308, 2009.

G. Carlsson, Topological pattern recognition for point cloud data, Acta Numerica, vol.1, issue.5, pp.289-368
DOI : 10.1051/0004-6361/201116485

G. Carlsson and A. Zomorodian, The Theory of Multidimensional Persistence, Discrete & Computational Geometry, vol.33, issue.2, pp.71-93, 2009.
DOI : 10.1007/s00454-009-9176-0

G. Casella, L. Roger, and . Berger, Statistical Inference., Biometrics, vol.49, issue.1, 1990.
DOI : 10.2307/2532634

P. Carbayo and . Bourgine, A digital framework to build, visualize and analyze a gene expression atlas with cellular resolution in zebrafish early embryogenesis
URL : https://hal.archives-ouvertes.fr/hal-01054811

H. Hannah, M. Chang, M. Hemberg, . Barahona, E. Donald et al., Transcriptome-wide noise controls lineage choice in mammalian progenitor cells, Nature, issue.7194, pp.453544-547, 2008.

Y. Chen and A. F. Schier, erratum: The zebrafish Nodal signal Squint functions as a morphogen, Nature, vol.411, issue.6846, pp.411607-610, 2001.
DOI : 10.1038/35087633

Y. Shih, C. , and H. Teicher, Probability theory: independence, interchangeability , martingales, 2003.

D. Cohen-steiner, H. Edelsbrunner, and D. Morozov, Vines and vineyards by updating persistence in linear time, Proceedings of the twenty-second annual symposium on Computational geometry , SCG '06, pp.119-126, 2006.
DOI : 10.1145/1137856.1137877

L. Da, F. Costa, A. Francisco, and . Rodrigues, Gonzalo Travieso, and Paulino Ribeiro Villas Boas. Characterization of complex networks: A survey of measurements, Advances in Physics, vol.56, issue.1, pp.167-242, 2007.

C. Darwin, On the origins of species by means of natural selection, 1859.
DOI : 10.5962/bhl.title.24329

E. Davidson and . Cameron, Specification of cell fate in the sea urchin embryo: summary and some proposed mechanisms, Development, vol.125, issue.17, pp.3269-90, 1998.

H. Eric and . Davidson, Lineage-specific gene expression and the regulative capacities of the sea urchin embryo: a proposed mechanism, Development, vol.105, issue.3, pp.421-445, 1989.

H. Eric and . Davidson, Gene activity in early development, 2012.

H. Eric, J. P. Davidson, P. Rast, A. Oliveri, C. Ransick et al., Cesar Arenas-Mena, et al. A genomic regulatory network for development, Science, issue.5560, pp.2951669-1678, 2002.

V. Debat and P. David, Mapping phenotypes: canalization, plasticity and developmental stability, Trends in Ecology & Evolution, vol.16, issue.10, pp.555-561, 2001.
DOI : 10.1016/S0169-5347(01)02266-2

J. Delile, R. Doursat, and N. Peyriéras, Computational Modeling and Simulation of Animal Early Embryogenesis with the MecaGen Platform, Computational Systems Biology, pp.359-405
DOI : 10.1016/B978-0-12-405926-9.00016-2

J. Delile, H. Matthieu, N. Peyriéras, and R. Doursat, Mecagen: A cell-based computational model of embryogenesis coupling mechanical behavior and gene regulation. submitted, 2015.

W. Denk, H. James, . Strickler, W. Watt, and . Webb, Two-photon laser scanning fluorescence microscopy, Science, vol.248, issue.4951, pp.73-76, 1990.
DOI : 10.1126/science.2321027

P. Diaconis and D. Freedman, Finite exchangeable sequences. The Annals of Probability, pp.745-764, 1980.

O. Julien, R. Dubuis, T. Samanta, and . Gregor, Accurate measurements of dynamics and reproducibility in small genetic networks, Molecular systems biology, vol.9, issue.1, p.2013

R. E. , L. Duncan, H. Arthur, and . Whiteley, The echinoid mitotic gradient: effect of cell size on the micromere cleavage cycle. Molecular reproduction and development, pp.10-11868, 2011.

F. Duveau and M. Félix, Role of Pleiotropy in the Evolution of a Cryptic Developmental Variation in Caenorhabditis elegans, PLoS Biology, vol.125, issue.1, p.1001230, 2012.
DOI : 10.1371/journal.pbio.1001230.s012

URL : https://hal.archives-ouvertes.fr/hal-00665102

H. Edelsbrunner and J. Harer, Computational topology: an introduction, 2010.
DOI : 10.1090/mbk/069

H. Edelsbrunner, C. Heisenberg, M. Kerber, and G. Krens, The medusa of spatial sorting: topological construction. arXiv preprint arXiv:1207, 2012.

A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Physical review, p.47777, 1935.

B. Michael, . Elowitz, J. Arnold, . Levine, D. Eric et al., Stochastic gene expression in a single cell, Science, vol.297, issue.5584, pp.1183-1186, 2002.

G. Susan and . Ernst, A century of sea urchin development, American zoologist, vol.37, issue.3, pp.250-259, 1997.

M. Luis, L. Escudero, A. Costa, J. Kicheva, M. Briscoe et al., Epithelial organisation revealed by a network of cellular contacts, Nature communications, vol.2, p.526, 2011.

T. Evans, T. Eric, J. Rosenthal, D. Youngblom, T. Distel et al., Cyclin: A protein specified by maternal mRNA in sea urchin eggs that is destroyed at each cleavage division, Cell, vol.33, issue.2, pp.389-396, 1983.
DOI : 10.1016/0092-8674(83)90420-8

D. Fabrèges, Phenotypic variation and resilience in sea urchin morphogenesis

B. Feldman, A. Michael, . Gates, S. Elizabeth, . Egan et al., Zebrafish organizer development and germ-layer formation require nodal-related signals, Nature, issue.6698, pp.395181-185, 1998.

L. Figard, H. Xu, G. Hernan, I. Garcia, A. M. Golding et al., The Plasma Membrane Flattens Out to Fuel Cell-Surface Growth during Drosophila Cellularization, Developmental Cell, vol.27, issue.6, pp.648-655, 2013.
DOI : 10.1016/j.devcel.2013.11.006

V. Fleury, Clarifying tetrapod embryogenesis, a physicist's point of view, The European Physical Journal Applied Physics, vol.45, issue.3, p.30101, 2009.
DOI : 10.1051/epjap/2009033

V. Fleury, Clarifying tetrapod embryogenesis by a dorso-ventral analysis of the tissue flows during early stages of chicken development, Biosystems, vol.109, issue.3, pp.460-474, 2012.
DOI : 10.1016/j.biosystems.2012.04.003

G. Forgacs, A. Stuart, and . Newman, Biological physics of the developing embryo, 2005.
DOI : 10.1017/CBO9780511755576

R. Frigg, J. Berkovitz, and F. Kronz, The ergodic hierarchy

E. Zalta, Stanford encyclopedia of philosophy, Proceedings of the first ACM/IEEE-CS joint conference on Digital libraries , JCDL '01, 2014.
DOI : 10.1145/379437.379789

S. Galatolo, M. Hoyrup, and C. Rojas, Effective symbolic dynamics, random points, statistical behavior, complexity and entropy, Information and Computation, vol.208, issue.1, pp.23-41, 2010.
DOI : 10.1016/j.ic.2009.05.001

URL : https://hal.archives-ouvertes.fr/inria-00517382

N. Geard, S. Bullock, R. Lohaus, B. Ricardo, J. Azevedo et al., Developmental motifs reveal complex structure in cell lineages, Complexity, vol.11, issue.4, pp.48-57, 2011.
DOI : 10.1002/cplx.20341

C. Matthew, . Gibson, B. Ankit, R. Patel, N. Nagpal et al., The emergence of geometric order in proliferating metazoan epithelia, Nature, vol.442, issue.7106, pp.1038-1041, 2006.

T. William, . Gibson, C. Matthew, and . Gibson, Cell topology, geometry, and morphogenesis in proliferating epithelia, Current topics in developmental biology, vol.89, pp.87-114, 2009.

T. William, . Gibson, H. James, B. Veldhuis, . Rubinstein et al., Control of the mitotic cleavage plane by local epithelial topology, Cell, vol.144, issue.3, pp.427-438, 2011.

S. Gilbert, Developmental Biology, 2000.

D. Gillies, Philosophical theories of probability, Routledge, 2000.

J. Wolfgang and V. Goethe, Versuch die Metamorphose der Pflanzen zu erklären, 1790.

S. J. Gould, Wonderful Life: The Burgess Shale and the Nature of History, 1989.

J. Stephen and . Gould, Ontogeny and phylogeny, 1977.

F. Graner, A. James, and . Glazier, Simulation of biological cell sorting using a two-dimensional extended potts model. Physical review letters, p.2013, 1992.

L. Jonathan, . Gross, W. Thomas, and . Tucker, Topological graph theory, 2001.

C. Guillot and T. Lecuit, Mechanics of Epithelial Tissue Homeostasis and Morphogenesis, Science, vol.340, issue.6137, pp.1185-1189, 2013.
DOI : 10.1126/science.1235249

P. Haffter, M. Granato, M. Brand, C. Mary, M. Mullins et al., The identification of genes with unique and essential functions in the development of the zebrafish, danio rerio, Development, vol.123, issue.1, pp.1-36, 1996.

J. Harthong, De l'intuition aux applications, Probabilités & statistiques Diderot éditeur, collection Arts et Sciences, 1996.

B. He, K. Doubrovinski, O. Polyakov, and E. Wieschaus, Apical constriction drives tissue-scale hydrodynamic flow to mediate cell elongation, Nature, vol.120, issue.7496, pp.392-396, 2014.
DOI : 10.1038/nature13070

T. Heams, Randomness in biology, Mathematical Structures in Computer Science, vol.52, issue.03, p.240308, 2014.
DOI : 10.1371/journal.pgen.1000049

URL : https://hal.archives-ouvertes.fr/hal-01194088

C. Heisenberg and Y. Bellaïche, Forces in Tissue Morphogenesis and Patterning, Cell, vol.153, issue.5, pp.948-962, 2013.
DOI : 10.1016/j.cell.2013.05.008

F. Helmchen and W. Denk, Deep tissue two-photon microscopy, Nature Methods, vol.63, issue.12, pp.932-940, 2005.
DOI : 10.1038/nmeth818

URL : http://hdl.handle.net/11858/00-001M-0000-0019-9B52-A

A. Hilfinger and J. Paulsson, Separating intrinsic from extrinsic fluctuations in dynamic biological systems, Proceedings of the National Academy of Sciences, vol.108, issue.29, pp.12167-12172, 2011.
DOI : 10.1073/pnas.1018832108

M. Ho, An exercise in rational taxonomy, Journal of Theoretical Biology, vol.147, issue.1, pp.43-57, 1990.
DOI : 10.1016/S0022-5193(05)80251-6

M. Ho, A. Matheson, T. Peter, . Saunders, C. Brian et al., Ether-induced segmentation disturbances in drosophila melanogaster. Roux's archives of developmental biology, pp.511-521, 1987.

M. Ho, T. Peter, and . Saunders, Rational taxonomy and the natural system, Acta Biotheoretica, vol.25, issue.suppl, pp.289-304, 1993.
DOI : 10.1007/BF00709367

H. Robert, H. John, and E. Sulston, Isolation and genetic characterization of celllineage mutants of the nematode caenorhabditis elegans, Genetics, vol.96, issue.2, pp.435-454, 1980.

S. Huang, Non-genetic heterogeneity of cells in development: more than just noise, Development, vol.136, issue.23, pp.3853-3862, 2009.
DOI : 10.1242/dev.035139

S. Huang, The molecular and mathematical basis of Waddington's epigenetic landscape: A framework for post-Darwinian biology?, BioEssays, vol.24, issue.2, pp.149-157, 2012.
DOI : 10.1002/bies.201100031

D. Huh and J. Paulsson, Random partitioning of molecules at cell division, Proceedings of the National Academy of Sciences, pp.15004-15009, 2011.
DOI : 10.1073/pnas.1013171108

J. Huxley, Evolution. the modern synthesis. Evolution. The Modern Synthesis, 1942.

N. Irie and S. Kuratani, Comparative transcriptome analysis reveals vertebrate phylotypic period during organogenesis, Nature Communications, vol.2, p.248, 2011.
DOI : 10.1038/nprot.2007.324

S. Ishihara, . Sugimura, . Cox, . Bonnet, F. Bellaïche et al., Comparative study of non-invasive force and stress inference methods in tissue, The European Physical Journal E, vol.150, issue.4, pp.1-13, 2013.
DOI : 10.1140/epje/i2013-13045-8

S. Ishihara and K. Sugimura, Bayesian inference of force dynamics during morphogenesis, Journal of Theoretical Biology, vol.313, pp.201-211, 2012.
DOI : 10.1016/j.jtbi.2012.08.017

E. Jablonka, J. Marion, and . Lamb, The Changing Concept of Epigenetics, Annals of the New York Academy of Sciences, vol.401, issue.Suppl. 1, pp.82-96, 2002.
DOI : 10.1111/j.1749-6632.2002.tb04913.x

F. Jacob and J. Monod, Genetic regulatory mechanisms in the synthesis of proteins, Journal of Molecular Biology, vol.3, issue.3, pp.318-356, 1961.
DOI : 10.1016/S0022-2836(61)80072-7

R. William and . Jeffery, Cavefish as a model system in evolutionary developmental biology, Developmental biology, vol.231, issue.1, pp.1-12, 2001.

O. Johnson, Information theory and the central limit theorem, World Scientific, vol.8, 2004.
DOI : 10.1142/p341

T. Alex, . Kalinka, M. Karolina, . Varga, T. Dave et al., Gene expression divergence recapitulates the developmental hourglass model, Nature, issue.7325, pp.468811-814, 2010.

I. Kant, Critique of judgment, 1790.

A. Stuart and . Kauffman, The origins of order: Self-organization and selection in evolution, 1993.

B. Benjamin, Q. Kaufmann, . Yang, T. Jerome, A. Mettetal et al., Heritable stochastic switching revealed by single-cell genealogy, PLoS biology, vol.5, issue.9, p.239, 2007.

B. Douglas, . Kell, G. Stephen, and . Oliver, Here is the evidence, now what is the hypothesis? the complementary roles of inductive and hypothesis-driven science in the post-genomic era, Bioessays, vol.26, issue.1, pp.99-105, 2004.

O. Kempthorne, An introduction to genetic statistics, 1957.

N. Kern, . Weaire, . Martin, S. Hutzler, and . Cox, Two-dimensional viscous froth model for foam dynamics, Physical Review E, vol.70, issue.4, p.41411, 2004.
DOI : 10.1103/PhysRevE.70.041411

M. Kimmel and D. E. Axelrod, Branching Processes in Biology, Interdisciplinary Applied Mathematics, vol.19, 2002.

C. Peter and K. , Evolution and development of shape: integrating quantitative approaches, Nature Reviews Genetics, vol.11, issue.9, pp.623-635, 2010.

A. Kolmogorov, Grundbegriffe der Wahrscheilichkeitsrechnung, 1933.

S. Kondo and T. Miura, Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation, Science, vol.329, issue.5999, pp.1616-1620, 2010.
DOI : 10.1126/science.1179047

Z. Krivá, K. Mikula, N. Peyriéras, B. Rizzi, A. Sarti et al., 3D early embryogenesis image filtering by nonlinear partial differential equations, Medical Image Analysis, vol.14, issue.4, pp.510-526, 2010.
DOI : 10.1016/j.media.2010.03.003

J. Kupiec, L'origine des individus. Fayard, 2008.

J. Kupiec and P. Sonigo, Ni Dieu ni gène, pour une autre théorie de l'hérédité. Seuil, 2000.

B. Lim, N. Samper, H. Lu, C. Rushlow, G. Jiménez et al., Kinetics of gene derepression by ERK signaling, Proceedings of the National Academy of Sciences, pp.10330-10335, 2013.
DOI : 10.1073/pnas.1303635110

E. Limpert, A. Werner, M. Stahel, and . Abbt, Log-normal Distributions across the Sciences: Keys and Clues, BioScience, vol.51, issue.5, pp.341-352, 2001.
DOI : 10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2

B. Lombardot, Description intégrative des cinématiques de la structure embryonnaire: morphogenèse précoce du poisson zébré, 2010.

G. Longo and . Laplace, jeu de l'imitation" aléas, déterminisme et programmes dans le test de turing, Intellectica, vol.35, issue.2, pp.131-161, 2002.

G. Longo, Mathematical infinity "in prospettiva" and spaces of possibilities, Visible, a Semiotics Journal, vol.9, 2011.

G. Longo and M. Montévil, From physics to biology by extending criticality and symmetry breakings, Progress in biophysics and molecular biology, p.106, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01192902

G. Longo and M. Montévil, Perspectives on Organisms: Biological Time, Symmetries and Singularities, 2013.
DOI : 10.1007/978-3-642-35938-5

URL : https://hal.archives-ouvertes.fr/hal-01349797

G. Longo, M. Montévil, and S. Kauffman, No entailing laws, but enablement in the evolution of the biosphere, Proceedings of the fourteenth international conference on Genetic and evolutionary computation conference companion, GECCO Companion '12, pp.1379-1392, 2012.
DOI : 10.1145/2330784.2330946

R. Losick and C. Desplan, Stochasticity and Cell Fate, Science, vol.320, issue.5872, pp.65-68, 2008.
DOI : 10.1126/science.1147888

E. Salvador, M. Luria, and . Delbrück, Mutations of bacteria from virus sensitivity to virus resistance, Genetics, vol.28, issue.6, p.491, 1943.

M. Lynch, S. John, and . Conery, The Origins of Genome Complexity, Science, vol.302, issue.5649, pp.1401-1404, 2003.
DOI : 10.1126/science.1089370

A. Marinucci, Tra ordine e caos: metodi e linguaggi tra fisica, matematica e filosofia, Aracne, 2011.

P. Martin-löf, The definition of random sequences, Information and Control, vol.9, issue.6, pp.602-619, 1966.
DOI : 10.1016/S0019-9958(66)80018-9

E. Mayr, Animal species and evolution. Animal species and their evolution, 1963.
DOI : 10.4159/harvard.9780674865327

R. David and . Mcclay, Evolutionary crossroads in developmental biology: sea urchins, Development, vol.138, issue.13, pp.2639-2648, 2011.

H. John and . Mcdonald, Handbook of biological statistics, 2009.

P. Michael, . Mckinley, C. David, . Bolton, B. Stanley et al., A protease-resistant protein is a structural component of the scrapie prion, Cell, vol.35, issue.1, pp.57-62, 1983.

A. Mcmahon, W. Supatto, E. Scott, A. Fraser, and . Stathopoulos, Dynamic Analyses of Drosophila Gastrulation Provide Insights into Collective Cell Migration, Science, vol.322, issue.5907
DOI : 10.1126/science.1167094

P. Andrew, . Mcmahon, N. Constantin, . Flytzanis, R. Barbara et al., Introduction of cloned dna into sea urchin egg cytoplasm: replication and persistence during embryogenesis, Developmental biology, vol.108, issue.2, pp.420-430, 1985.

G. Sean, . Megason, E. Scott, and . Fraser, Imaging in systems biology, Cell, vol.130, issue.5, pp.784-795, 2007.

G. Mendel, Versuche über Pflanzenhybriden, 1866.
DOI : 10.1007/978-3-663-19714-0

F. Merlin and . Le, hasard évolutionnaire" de toute mutation génétique, ou la vision consensuelle de la synthèse moderne. Bulletin d'Histoire et d'épistémologie des sciences de la vie, pp.79-108, 2011.

M. Morange, Histoire de la biologie moléculaire

G. Eric and . Moss, Heterochronic genes and the nature of developmental time, Current Biology, vol.17, issue.11, pp.425-434, 2007.

E. Munch, Applications of Persistent Homology to Time Varying Systems, 2013.

D. James and . Murray, Mathematical biology i: An introduction, 2002.

A. Nakamasu, G. Takahashi, A. Kanbe, and S. Kondo, Interactions between zebrafish pigment cells responsible for the generation of Turing patterns, Proceedings of the National Academy of Sciences, pp.8429-8434, 2009.
DOI : 10.1073/pnas.0808622106

E. Mark, . Newman, H. Steven, . Strogatz, J. Duncan et al., Random graphs with arbitrary degree distributions and their applications, Physical Review E, vol.64, issue.2, p.26118, 2001.

F. Nielsen and R. Nock, Sided and symmetrized bregman centroids. Information Theory, IEEE Transactions on, vol.55, issue.6, pp.2882-2904, 2009.
DOI : 10.1109/tit.2009.2018176

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.2671

A. Novick and M. Weiner, ENZYME INDUCTION AS AN ALL-OR-NONE PHENOMENON, Proceedings of the National Academy of Sciences, vol.43, issue.7, p.553, 1957.
DOI : 10.1073/pnas.43.7.553

C. Nüsslein-volhard and E. Wieschaus, Mutations affecting segment number and polarity in Drosophila, Nature, vol.52, issue.5785, pp.795-801, 1980.
DOI : 10.1038/287795a0

I. Okamoto, A. P. Otte, D. David-allis, E. Reinberg, and . Heard, Epigenetic Dynamics of Imprinted X Inactivation During Early Mouse Development, Science, vol.303, issue.5658, pp.644-649, 2004.
DOI : 10.1126/science.1092727

N. Olivier, M. A. Luengo-oroz, L. Duloquin, E. Faure, T. Savy et al., Cell Lineage Reconstruction of Early Zebrafish Embryos Using Label-Free Nonlinear Microscopy, Science, vol.329, issue.5994, pp.329967-971, 2010.
DOI : 10.1126/science.1189428

URL : https://hal.archives-ouvertes.fr/hal-00519834

S. Osher, A. James, and . Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

M. Osterfield, X. Du, T. Schüpbach, E. Wieschaus, Y. Stanislav et al., Three-Dimensional Epithelial Morphogenesis in the Developing Drosophila Egg, Developmental Cell, vol.24, issue.4, pp.400-410, 2013.
DOI : 10.1016/j.devcel.2013.01.017

P. Pantazis and W. Supatto, Advances in whole-embryo imaging: a quantitative transition is underway, Nature Reviews Molecular Cell Biology, vol.459, issue.5, pp.327-339, 2014.
DOI : 10.1038/nrm3786

URL : https://hal.archives-ouvertes.fr/hal-00998245

B. Ankit, . Patel, T. William, . Gibson, C. Matthew et al., Modeling and inferring cleavage patterns in proliferating epithelia, PLoS computational biology, vol.5, issue.6, p.1000412, 2009.

J. Paulsson, Summing up the noise in gene networks, Nature, vol.427, issue.6973, pp.415-418, 2004.
DOI : 10.1038/nature02257

W. Pei and B. Feldman, Identification of common and unique modifiers of zebrafish midline bifurcation and cyclopia, Developmental Biology, vol.326, issue.1, pp.201-211, 2009.
DOI : 10.1016/j.ydbio.2008.11.008

W. Pei, . Williams, D. Matthew, . Clark, L. Derek et al., Environmental and genetic modifiers of squint penetrance during zebrafish embryogenesis, Developmental Biology, vol.308, issue.2, pp.368-378, 2007.
DOI : 10.1016/j.ydbio.2007.05.026

S. Isabelle, E. Peter, E. H. Faure, and . Davidson, Predictive computation of genomic logic processing functions in embryonic development, Proceedings of the National Academy of Sciences, pp.16434-16442, 2012.

A. Petit, E. Legué, and J. Nicolas, Methods in clonal analysis and applications, Reproduction Nutrition Development, vol.45, issue.3, pp.321-339, 2005.
DOI : 10.1051/rnd:2005024

URL : https://hal.archives-ouvertes.fr/hal-00900564

A. Petryk, D. Graf, and R. Marcucio, Holoprosencephaly: signaling interactions between the brain and the face, the environment and the genes, and the phenotypic variability in animal models and humans, Wiley Interdisciplinary Reviews: Developmental Biology, vol.143, issue.suppl, pp.17-32, 2015.
DOI : 10.1002/wdev.161

C. Patrick and . Phillips, Epistasis?the essential role of gene interactions in the structure and evolution of genetic systems, Nature Reviews Genetics, vol.9, issue.11, pp.855-867, 2008.

N. Pippenger and K. Schleich, Topological characteristics of random triangulated surfaces. Random Structures & Algorithms, pp.247-288, 2006.

J. Piveteau, Le débat entre cuvier et geoffroy saint-hilaire sur l'unité de plan et de composition. Revue d'histoire des sciences et de leurs applications, pp.343-363, 1950.

H. Poincaré, Science and Method, 2013.

H. Poincaré, Sur le problème des trois corps et les équations de la dynamique, Acta mathematica, vol.13, issue.1, pp.3-270, 1890.

R. Purcell, Life at low Reynolds number, American Journal of Physics, 1977.

C. Rao, Information and the Accuracy Attainable in the Estimation of Statistical Parameters, Bulletin of the Calcutta Mathematical Society, vol.37, issue.3, pp.81-91, 1945.
DOI : 10.1007/978-1-4612-0919-5_16

A. Raj, A. Scott, E. Rifkin, A. Andersen, and . Van-oudenaarden, Variability in gene expression underlies incomplete penetrance, Nature, vol.460, issue.7283, pp.913-918, 2010.
DOI : 10.1038/nature08781

J. Oliver, . Rando, J. Kevin, and . Verstrepen, Timescales of genetic and epigenetic inheritance, Cell, vol.128, issue.4, pp.655-668, 2007.

M. Regulski, K. Harding, R. Kostriken, F. Karch, M. Levine et al., Homeo box genes of the Antennapedia and Bithorax Complexes of Drosophila, Cell, vol.43, issue.1, pp.71-80, 1985.
DOI : 10.1016/0092-8674(85)90013-3

B. Rizzi and N. Peyriéras, Towards 3D in silico modeling of the sea urchin embryonic development, Journal of Chemical Biology, vol.6, issue.10, pp.17-28
DOI : 10.1007/s12154-013-0101-x

URL : https://hal.archives-ouvertes.fr/hal-01054767

B. Rizzi, *. , P. Villoutreix, J. Delile, *. et al., René Doursat, and Nadine Peyriéras. Predicting sea urchin's normal development from a small cohort of digital embryos, 2015.

D. Romaschoff, Über die variabilität in der manifestierung eines erblichen merkmales (abdomen abnormalis) bei drosophila funebris f, Journal für Psychologie und Neurologie, vol.31, pp.323-325, 1925.

R. Rosen, A quantum-theoretic approach to genetic problems. The bulletin of mathematical biophysics, pp.227-255, 1960.

W. Roux, Über die Entwicklungsmechanik der Organismen, 1890.

P. Sahlin and H. Jönsson, A Modeling Study on How Cell Division Affects Properties of Epithelial Tissues Under Isotropic Growth, PLoS ONE, vol.106, issue.7, p.11750, 2010.
DOI : 10.1371/journal.pone.0011750.t002

D. Sánchez-gutiérrez, A. Sáez, A. Pascual, M. Luis, and . Escudero, Topological Progression in Proliferating Epithelia Is Driven by a Unique Variation in Polygon Distribution, PLoS ONE, vol.139, issue.11, p.79227, 2013.
DOI : 10.1371/journal.pone.0079227.s004

A. Sebastian, M. Sandersius, . Chuai, J. Cornelis, T. J. Weijer et al., Correlating cell behavior with tissue topology in embryonic epithelia, PloS one, vol.6, issue.4, p.18081, 2011.

O. Sandler, S. Pearl-mizrahi, N. Weiss, O. Agam, I. Simon et al., Lineage correlations of single cell division time as a probe of cell-cycle dynamics, Nature, vol.105, issue.7544, pp.519468-471, 2015.
DOI : 10.1038/nature14318

A. Sarti, R. Malladi, and J. A. Sethian, Subjective surfaces: A method for completing missing boundaries, Proceedings of the National Academy of Sciences, pp.6258-6263, 2000.
DOI : 10.1073/pnas.110135797

S. Schneider, H. Steinbeisser, M. Rachel, P. Warga, and . Hausen, ??-catenin translocation into nuclei demarcates the dorsalizing centers in frog and fish embryos, Mechanisms of Development, vol.57, issue.2, pp.191-198, 1996.
DOI : 10.1016/0925-4773(96)00546-1

E. Schrödinger, What is life, 1944.

G. Shafer and V. Vovk, The Sources of Kolmogorov???s Grundbegriffe, Statistical Science, vol.21, issue.1, pp.70-98, 2006.
DOI : 10.1214/088342305000000467

I. Shmulevich, R. Edward, S. Dougherty, W. Kim, and . Zhang, Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks, Bioinformatics, vol.18, issue.2, pp.261-274, 2002.
DOI : 10.1093/bioinformatics/18.2.261

J. Maynard-smith, R. Burian, S. Kauffman, P. Alberch, J. Campbell et al., Developmental constraints and evolution: a perspective from the mountain lake conference on development and evolution, Quarterly Review of Biology, pp.265-287, 1985.

T. Sousbie, The persistent cosmic web and its filamentary structure - I. Theory and implementation, Monthly Notices of the Royal Astronomical Society, vol.414, issue.1, pp.350-383, 2011.
DOI : 10.1111/j.1365-2966.2011.18394.x

W. Frank and . Stearns, One hundred years of pleiotropy: a retrospective, Genetics, vol.186, issue.3, pp.767-773, 2010.

E. John, H. Sulston, and . Horvitz, Post-embryonic cell lineages of the nematode, caenorhabditis elegans, Developmental biology, vol.56, issue.1, pp.110-156, 1977.

S. Peter, . Swain, B. Michael, E. D. Elowitz, and . Siggia, Intrinsic and extrinsic contributions to stochasticity in gene expression, Proceedings of the National Academy of Sciences, pp.12795-12800, 2002.

N. Timoféeff-ressovsky, Über den einfluss des genotypus auf das phänotypen auftreten eines einzelnes gens, Journal für Psychologie und Neurologie, vol.31, pp.305-310, 1925.

G. Trichas, M. Aaron, N. Smith, V. White, T. Wilkins et al., Multi-Cellular Rosettes in the Mouse Visceral Endoderm Facilitate the Ordered Migration of Anterior Visceral Endoderm Cells, PLoS Biology, vol.226, issue.2, p.1001256, 2012.
DOI : 10.1371/journal.pbio.1001256.s009

V. Thai, W. Truong, . Supatto, S. David, . Koos et al., Deep and fast live imaging with two-photon scanned light-sheet microscopy, Nature methods, vol.8, issue.9, pp.757-760, 2011.

A. Mathison and T. , The chemical basis of morphogenesis, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, vol.237, issue.641, pp.37-72, 1952.

F. Varenne, La reconstruction phénoménologique par simulation : vers une épaisseur du simulat, Formes, systèmes et milieux techniques, pp.107-123

P. Villoutreix, Random triangulated surfaces with arbitrary degree distribution reveal embryonic epithelial organization, Algebraic Topology -Methods, p.2014

P. Villoutreix, Vers une modélisation multi-échelle de la variabilité biologique?, Modéliser & Simuler. Epistémologie et pratique de la modélisation et de la simulation Editions matériologiques, pp.643-664, 2014.

P. Villoutreix, Biological diversity and quantum formalism: Entanglement of genotype-phenotype relations, preparation, 2015.

P. Villoutreix, G. Carlsson, and N. Peyriéras, Topological analysis of epithelia uncovers high-order structures in spatial distribution of cells, 2015.

P. Villoutreix, B. Rizzi, J. Delile, L. Duloquin, E. Faure et al., A probabilistic modeling of the cell lineage highlights interindividual variability in paracentrotus lividus early development, The Developmental Biology of the Sea Urchin XXII, 2014.

C. Baer, Über Entwicklungsgeschichte der Thiere Beobachtung und Reflexion, pp.1828-1837, 1828.
DOI : 10.5962/bhl.title.112232

URL : http://dspace.library.uu.nl:8080/handle/1874/268325

C. Waddington, The strategy of the genes, Allen and Unwin, 1957.

Y. Wang, Z. Khan, M. Kaschube, and E. F. Wieschaus, Differential positioning of adherens junctions is associated with initiation of epithelial folding, Nature, vol.15, issue.7394, pp.484390-393, 2012.
DOI : 10.1038/nature10938

G. Webster, C. Brian, and . Goodwin, The origin of species: a structuralist approach, Journal of Social and Biological Systems, vol.5, issue.1, pp.15-47, 1982.
DOI : 10.1016/S0140-1750(82)91390-2

F. Xiong, W. Ma, W. Tom, . Hiscock, R. Kishore et al., Interplay of Cell Shape and Division Orientation Promotes Robust Morphogenesis of Developing Epithelia, Cell, vol.159, issue.2, pp.415-427, 2014.
DOI : 10.1016/j.cell.2014.09.007

F. Xiong, A. R. Tentner, P. Huang, A. Gelas, R. Kishore et al., Specified Neural Progenitors Sort to Form Sharp Domains after Noisy Shh Signaling, Cell, vol.153, issue.3, pp.550-561, 2013.
DOI : 10.1016/j.cell.2013.03.023

A. Jennifer and . Zallen, Planar polarity and tissue morphogenesis, Cell, vol.129, issue.6, pp.1051-1063, 2007.

C. Zanella, M. Campana, B. Rizzi, C. Melani, G. Sanguinetti et al., Cells Segmentation From 3-D Confocal Images of Early Zebrafish Embryogenesis, IEEE Transactions on Image Processing, vol.19, issue.3, pp.770-781, 2010.
DOI : 10.1109/TIP.2009.2033629

URL : https://hal.archives-ouvertes.fr/hal-00444516

A. Zomorodian and G. Carlsson, Computing persistent homology