. Sélectionné, Ceci conforte donc la thèse selon laquelle l'effet Lansing permettrait aux populations de s'adapter plus rapidement

. Bibliographie,

A. Ackleh, S. Azmy, J. Cleveland, and H. R. Thieme, Population dynamics under selection and mutation : Long-time behavior for differential equations in measure spaces, Journal of Differential Equations, vol.261, issue.2, pp.1472-1505, 2016.

A. Ackleh and S. Hu, Comparison between stochastic and deterministic selectionmutation models, Mathematical Biosciences and Engineering, vol.4, issue.2, p.133, 2007.

J. André and B. Godelle, The evolution of mutation rate in finite asexual populations, Genetics, 2005.

R. C. Arslan, K. P. Willführ, E. M. Frans, K. J. Verweij, P. Bürkner et al., Older fathers' children have lower evolutionary fitness across four centuries and in four populations, Proc. R. Soc. B, vol.284, p.20171562, 1862.
DOI : 10.1098/rspb.2017.1562

URL : http://europepmc.org/articles/pmc5597845?pdf=render

V. Bansaye, B. Cloez, and P. Gabriel, Ergodic behavior of non-conservative semigroups via generalized doeblin's conditions, 2017.
DOI : 10.1007/s10440-019-00253-5

URL : http://arxiv.org/pdf/1710.05584

H. Berestycki, J. Coville, and H. H. Vo, On the definition and the properties of the principal eigenvalue of some nonlocal operators, Journal of Functional Analysis, vol.271, issue.10, pp.2701-2751, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01245634

S. Billiard, R. Ferrière, S. Méléard, and V. C. Tran, Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks, Journal of mathematical biology, vol.71, issue.5, pp.1211-1242, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00875991

O. Bonnefon, J. Coville, and G. Legendre, Concentration phenomenon in some non-local equation, Discrete Contin. Dyn. Syst. Ser. B, vol.22, issue.3, pp.763-781, 2017.
DOI : 10.3934/dcdsb.2017037

URL : https://hal.archives-ouvertes.fr/hal-01212846

F. E. Browder, On the spectral theory of elliptic differential operators. i. Mathematische Annalen, vol.142, pp.22-130, 1961.

R. L. Brown, What evolvability really is, The British Journal for the Philosophy of Science, vol.65, pp.549-572, 2014.
DOI : 10.1093/bjps/axt014

URL : https://philpapers.org/archive/BROWER.pdf

R. Bürger, Perturbations of positive semigroups and applications to population genetics, Mathematische Zeitschrift, vol.197, issue.2, pp.259-272, 1988.

L. Burlando, Monotonicity of spectral radius for positive operators on ordered banach spaces, Archiv der Mathematik, vol.56, issue.1, pp.49-57, 1991.

À. Calsina and J. M. Palmada, Steady states of a selection-mutation model for an age structured population, Journal of Mathematical Analysis and Applications, vol.400, issue.2, pp.386-395, 2013.

J. A. Cañizo, J. A. Carrillo, and S. Cuadrado, Measure solutions for some models in population dynamics, Acta applicandae mathematicae, vol.123, issue.1, pp.141-156, 2013.

H. Caswell, Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates, Demographic Research, vol.23, pp.531-548, 2010.

N. Champagnat, A microscopic interpretation for adaptive dynamics trait substitution sequence models. Stochastic processes and their applications, vol.116, pp.1127-1160, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00015130

N. Champagnat, R. Ferrière, and S. Méléard, Unifying evolutionary dynamics : from individual stochastic processes to macroscopic models, Theoretical population biology, vol.69, issue.3, pp.297-321, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00164784

N. Champagnat, R. Ferrière, and G. Ben-arous, The canonical equation of adaptive dynamics : a mathematical view, Selection, vol.2, issue.1-2, pp.73-83, 2002.
URL : https://hal.archives-ouvertes.fr/inria-00164767

N. Champagnat and S. Méléard, Polymorphic evolution sequence and evolutionary branching. Probability Theory and Related Fields, vol.151, pp.45-94, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00345399

B. Charlesworth, Evolution in age-structured populations, vol.2, 1994.

F. Clément, F. Robin, and R. Yvinec, Analysis and calibration of a linear model for structured cell populations with unidirectional motion : Application to the morphogenesis of ovarian follicles, 2017.

M. Costa, C. Hauzy, N. Loeuille, and S. Méléard, Stochastic eco-evolutionary model of a prey-predator community, Journal of mathematical biology, vol.72, issue.3, pp.573-622, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01023709

J. Coville, On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators, Journal of Differential Equations, vol.249, issue.11, pp.2921-2953, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00603471

J. Coville, Singular measure as principal eigenfunction of some nonlocal operators, Applied Mathematics Letters, vol.26, issue.8, pp.831-835, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00784899

J. Coville, J. Davila, and S. Martinéz, Pulsating fronts for nonlocal dispersion and kpp nonlinearity, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.30, pp.179-223, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00785039

E. Dambroise, L. Monnier, L. Ruisheng, H. Aguilaniu, J. S. Joly et al., Two phases of aging separated by the smurf transition as a public path to death, Scientific reports, vol.6, p.23523, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01304283

C. Darwin-;-london and J. Murray, The origin of species by means of natural selection, or, the preservation of favoured races in the struggle for life, p.1871

D. Dawson, Measure-valued markov processes. École d'été de probabilités de SaintFlour XXI-1991, pp.1-260, 1993.

L. Desvillettes, P. E. Jabin, S. Mischler, and G. Raoul, On selection dynamics for continuous structured populations, Communications in Mathematical Sciences, vol.6, issue.3, pp.729-747, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00363138

U. Dieckmann and R. Law, The dynamical theory of coevolution : a derivation from stochastic ecological processes, Journal of mathematical biology, vol.34, issue.5-6, pp.579-612, 1996.

J. W. Drake, A constant rate of spontaneous mutation in dna-based microbes, Proceedings of the National Academy of Sciences, vol.88, issue.16, pp.7160-7164, 1991.

S. N. Ethier and T. G. Kurtz, Markov processes : characterization and convergence, vol.282, 2009.

D. Fabian and T. Flatt, The evolution of aging, Nature Education Knowledge, vol.3, issue.9, 2011.

R. A. Fisher, The genetical theory of natural selection : a complete variorum edition, 1999.

N. Gao, Extensions of Perron-Frobenius theory, vol.17, pp.965-977, 2013.
DOI : 10.1007/s11117-012-0215-3

URL : http://arxiv.org/pdf/1208.3490.pdf

N. Gast and B. Gaujal, Markov chains with discontinuous drifts have differential inclusion limits. Performance Evaluation, vol.69, pp.623-642, 2012.
DOI : 10.1016/j.peva.2012.07.003

URL : https://hal.archives-ouvertes.fr/hal-00787999

Q. Griette, Singular measure traveling waves in an epidemiological model with continuous phenotypes, 2017.

M. E. Gurtin and R. C. Maccamy, Non-linear age-dependent population dynamics. Archive for Rational Mechanics and Analysis, vol.54, pp.281-300, 1974.
DOI : 10.1007/bf00250793

P. Gwiazda and E. Wiedemann, Generalized entropy method for the renewal equation with measure data, Commun. Math. Sci, vol.15, issue.2, pp.577-586, 2017.
DOI : 10.4310/cms.2017.v15.n2.a13

URL : http://arxiv.org/pdf/1604.07657

J. B. Haldane, New paths in genetics. New paths in genetics, 1941.

J. B. Haldane, New paths in genetics. George allen & Unwin, 1942.

W. D. Hamilton, The moulding of senescence by natural selection, Journal of theoretical biology, vol.12, issue.1, pp.12-45, 1966.

M. Iannelli and F. Milner, The Basic Approach to Age-Structured Population Dynamics : Models, Methods and Numerics, 2017.

P. Jagers and F. C. Klebaner, Population-size-dependent and age-dependent branching processes, Stochastic Processes and their Applications, vol.87, pp.235-254, 2000.
DOI : 10.1016/s0304-4149(99)00111-8

URL : https://doi.org/10.1016/s0304-4149(99)00111-8

O. R. Jones, A. Scheuerlein, R. Salguero-gómez, C. G. Camarda, R. Schaible et al., Diversity of ageing across the tree of life, Nature, vol.505, issue.7482, p.169, 2014.

T. Kato, Perturbation theory for linear operators, vol.132, 2013.

M. Kimura, On the evolutionary adjustment of spontaneous mutation rates, Genetics Research, vol.9, issue.1, pp.23-34, 1967.

T. B. Kirkwood and S. N. Austad, Why do we age ?, Nature, vol.408, issue.6809, p.233, 2000.

T. B. Kirkwood and T. Cremer, Cytogerontology since 1881 : a reappraisal of august weismann and a review of modern progress, Human genetics, vol.60, issue.2, pp.101-121, 1982.

M. Kirschner, J. Gerhart, and . Evolvability, Proceedings of the National Academy of Sciences, vol.95, pp.8420-8427, 1998.

F. D. Klironomos, J. Berg, and S. Collins, How epigenetic mutations can affect genetic evolution : model and mechanism, Bioessays, vol.35, issue.6, pp.571-578, 2013.
DOI : 10.1002/bies.201200169

M. G. Krein and M. A. Rutman, Linear operators leaving invariant a cone in a banach space, Uspekhi Matematicheskikh Nauk, vol.3, issue.1, pp.3-95, 1948.

J. Kristensen and F. Rindler, Relaxation of signed integral functionals in bv, Calculus of Variations and Partial Differential Equations, vol.37, pp.29-62, 2010.

M. Kunze, Non-smooth dynamical systems, vol.1744, 2000.

A. I. Lansing, A transmissible, cumulative, and reversible factor in aging, Journal of Gerontology, vol.2, issue.3, pp.228-239, 1947.

A. I. Lansing, A nongenic factor in the longevity of rotifers, Annals of the New York Academy of Sciences, vol.57, issue.1, pp.455-464, 1954.

H. Leman, Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence, Stochastics and Partial Differential Equations : Analysis and Computations, vol.4, pp.791-826, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01194574

H. Leman, S. Méléard, and S. Mirrahimi, Influence of a spatial structure on the long time behavior of a competitive lotka-volterra type system, Discrete Contin. Dyn. Syst. Ser. B, vol.20, issue.2, pp.469-493, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00924459

M. Lynch, Evolution of the mutation rate, Trends in Genetics, vol.26, issue.8, pp.345-352, 2010.

T. R. Malthus, An essay on the principle of population : or, A view of its past and present effects on human happiness, 1888.

L. Markus, Asymptotically autonomous differential systems, Contributions to the theory of nonlinear oscillations, vol.3, pp.17-29, 1956.

P. B. Medawar, An unsolved problem of biology, 1952.

S. Méléard and V. C. Tran, Trait substitution sequence process and canonical equation for age-structured populations, Journal of mathematical biology, vol.58, issue.6, pp.881-921, 2009.

J. A. Metz and O. Diekmann, The dynamics of physiologically structured populations, vol.68, 2014.

J. A. Metz, S. A. Geritz, G. Meszéna, F. A. Jacobs, and J. S. Van-heerwaarden, Adaptive dynamics : a geometrical study of the consequences of nearly faithful reproduction. Stochastic and Spatial Structures of Dynamical Systems, pp.183-231, 1996.

J. A. Metz, R. M. Nisbet, and S. A. Geritz, How should we define 'fitness' for general ecological scenarios ?, Trends in Ecology & Evolution, vol.7, issue.6, pp.198-202, 1992.

J. C. Noguera, N. B. Metcalfe, and P. Monaghan, Experimental demonstration that offspring fathered by old males have shorter telomeres and reduced lifespans, Proc. R. Soc. B, vol.285, p.20180268, 1874.

S. Nordmann, B. Perthame, and C. Taing, Dynamics of concentration in a population model structured by age and a phenotypical trait, Acta Applicandae Mathematicae, pp.1-29, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01493068

B. Perthame, Transport equations in biology, 2006.

N. K. Priest, B. Mackowiak, and D. E. Promislow, The role of parental age effects on the evolution of aging, Evolution, vol.56, issue.5, pp.927-935, 2002.

J. Prüß, Equilibrium solutions of age-specific population dynamics of several species, Journal of Mathematical Biology, vol.11, issue.1, pp.65-84, 1981.

M. Rera, S. Bahadorani, J. Cho, C. L. Koehler, M. Ulgherait et al., Modulation of longevity and tissue homeostasis by the drosophila pgc-1 homolog, Cell metabolism, vol.14, issue.5, pp.623-634, 2011.

M. Rera, R. I. Clark, and D. W. Walker, Intestinal barrier dysfunction links metabolic and inflammatory markers of aging to death in drosophila, Proceedings of the National Academy of Sciences, vol.109, issue.52, pp.21528-21533, 2012.

M. Rera, C. Vallot, and C. Lefrançois, The smurf transition : new insights on ageing from end-of-life studies in animal models, Current opinion in oncology, vol.30, issue.1, pp.38-44, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01981182

T. Roget, On the long-time behaviour of age and trait structured population dynamics, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01643361

H. H. Schaefer and M. P. Wolff, Graduate texts in mathematics. Topological Vector Space, 1971.

R. J. Schmitz, M. D. Schultz, M. G. Lewsey, R. C. O'malley, M. A. Urich et al., Transgenerational epigenetic instability is a source of novel methylation variants, Science, vol.334, issue.6054, pp.369-373, 2011.

J. Schroeder, S. Nakagawa, M. Rees, M. Mannarelli, and T. Burke, Reduced fitness in progeny from old parents in a natural population, Proceedings of the National Academy of Sciences, p.201422715, 2015.

F. R. Sharpe and A. J. Lotka, L. a problem in age-distribution. The London, Edinburgh, and Dublin Philosophical Magazine and, Journal of Science, vol.21, issue.124, pp.435-438, 1911.

H. R. Thieme, Asymptotically autonomous differential equations in the plane, The Rocky Mountain Journal of Mathematics, pp.351-380, 1994.

V. C. Tran, Modèles particulaires stochastiques pour des problèmes d'évolution adaptative et pour l'approximation de solutions statistiques, 2006.

V. C. Tran, Large population limit and time behaviour of a stochastic particle model describing an age-structured population, ESAIM : Probability and Statistics, vol.12, pp.345-386, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00122191

H. Tricoire and M. Rera, A new, discontinuous 2 phases of aging model : lessons from drosophila melanogaster, PloS one, vol.10, issue.11, p.141920, 2015.

T. Tully and A. Lambert, The evolution of postreproductive life span as an insurance against indeterminacy, Evolution, vol.65, issue.10, pp.3013-3020, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00857606

C. Villani, Topics in optimal transportation, Number, vol.58, 2003.

H. and V. Foerster, Some remarks on changing populations, The Kinetics of Cellular Proliferation, pp.382-407, 1959.

G. F. Webb, Theory of nonlinear age-dependent population dynamics, 1985.

A. Weismann, The origin of the markings of caterpillars. Studies in the theory of descent, Searle Rivington, pp.161-389, 1881.

A. Weismann, E. Poulton, S. Bagnall, S. Schönland, A. E. Shipley et al., Essays upon heredity and kindred biological problems, pp.1891-1892