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References

  • Adler, Robert; Tribe, Roger. Uniqueness for a historical SDE with a singular interaction. J. Theoret. Probab. 11 (1998), no. 2, 515--533. MR1622584
  • Bansaye, Vincent; Delmas, Jean-François; Marsalle, Laurence; Tran, Viet Chi. Limit theorems for Markov processes indexed by continuous time Galton-Watson trees. Ann. Appl. Probab. 21 (2011), no. 6, 2263--2314. MR2895416
  • Barton, Nick H.; Etheridge, Alison M. The effect of selection on genealogies, Genetics 166 (2004), 1115--1131.
  • Barton, Nick H.; Etheridge, Alison M.; Véber, Amandine. A new model for evolution in a spatial continuum. Electron. J. Probab. 15 (2010), no. 7, 162--216. MR2594876
  • Berestycki, Nathanaël. Recent progress in coalescent theory. Ensaios Matemáticos [Mathematical Surveys], 16. Sociedade Brasileira de Matemática, Rio de Janeiro, 2009. 193 pp. ISBN: 978-85-85818-40-1 MR2574323
  • Billingsley, Patrick. Convergence of probability measures. John Wiley & Sons, Inc., New York-London-Sydney 1968 xii+253 pp. MR0233396
  • Billingsley, Patrick. Probability and measure. Third edition. Wiley Series in Probability and Mathematical Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1995. xiv+593 pp. ISBN: 0-471-00710-2 MR1324786
  • Bolker, Ben; Pacala, Stephen. Using moment equations to understand stochastically driven spatial pattern formation in ecological systems, Theoretical Population Biology 52 (1997), 179--197.
  • Bolker, Ben; Pacala, Stephen. Spatial moment equations for plant competition: Understanding spatial strategies and the advantages of short dispersal, The American Naturalist 153 (1999), 575--602.
  • Champagnat, Nicolas; Ferrière, Régis; Méléard, Sylvie. Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models via timescale separation, Theoretical Population Biology 69 (2006), 297--321.
  • Champagnat, Nicolas; Ferrière, Régis; Méléard, Sylvie. From individual stochastic processes to macroscopic models in adaptive evolution. Stoch. Models 24 (2008), suppl. 1, 2--44. MR2466448
  • Champagnat, Nicolas; Méléard, Sylvie. Polymorphic evolution sequence and evolutionary branching. Probab. Theory Related Fields 151 (2011), no. 1-2, 45--94. MR2834712
  • Dawson, Donald A. Measure-valued Markov processes. École d'Été de Probabilités de Saint-Flour XXI—1991, 1--260, Lecture Notes in Math., 1541, Springer, Berlin, 1993. MR1242575
  • Dawson, D. A. Geostochastic calculus. Canad. J. Statist. 6 (1978), no. 2, 143--168. MR0532855
  • Dawson, Donald A.; Perkins, Edwin A. Historical processes. Mem. Amer. Math. Soc. 93 (1991), no. 454, iv+179 pp. MR1079034
  • Depperschmidt, Andrej; Greven, Andreas; Pfaffelhuber, Peter. Tree-valued Fleming-Viot dynamics with mutation and selection, Annals of Applied Probability (2011), in press.
  • Dieckmann, Ulf; Doebeli, Michael. On the origin of species by sympatric speciation, Nature 400 (1999), 354--357.
  • Dieckmann, Ulf; Law, Richard. Relaxation projections and the method of moments, The Geometry of Ecological Interactions, Cambridge University Press, 2000, pp. 412--455.
  • Etheridge, Alison M. An introduction to superprocesses. University Lecture Series, 20. American Mathematical Society, Providence, RI, 2000. xii+187 pp. ISBN: 0-8218-2706-5 MR1779100
  • Etheridge, Alison; Pfaffelhuber, Peter; Wakolbinger, Anton. An approximate sampling formula under genetic hitchhiking. Ann. Appl. Probab. 16 (2006), no. 2, 685--729. MR2244430
  • Evans, Steven N.; Perkins, Edwin A. Measure-valued branching diffusions with singular interactions. Canad. J. Math. 46 (1994), no. 1, 120--168. MR1260341
  • Evans, Steven N.; Steinsaltz, David. Damage segregation at fissioning may increase growth rates: A superprocess model, Theoretical Population Biology 71 (2007), 473--490.
  • Fournier, Nicolas; Méléard, Sylvie. A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14 (2004), no. 4, 1880--1919. MR2099656
  • Greven, Andreas; Pfaffelhuber, Peter; Winter, Anita. Tree-valued resampling dynamics. martingale problems and applications, Probability Theory and Related Fields (2011), in press.
  • Jacod, Jean; Shiryaev, Albert N. Limit theorems for stochastic processes. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 288. Springer-Verlag, Berlin, 1987. xviii+601 pp. ISBN: 3-540-17882-1 MR0959133
  • Jagers, Peter. A general stochastic model for population development. Skand. Aktuarietidskr. 1969, 84--103. MR0431406
  • Jagers, Peter. Branching processes with biological applications. Wiley Series in Probability and Mathematical Statistics—Applied Probability and Statistics. Wiley-Interscience [John Wiley & Sons], London-New York-Sydney, 1975. xiii+268 pp. ISBN: 0-471-43652-6 MR0488341
  • Jagers, Peter; Nerman, Olle. The asymptotic composition of supercritical multi-type branching populations. Séminaire de Probabilités, XXX, 40--54, Lecture Notes in Math., 1626, Springer, Berlin, 1996. MR1459475
  • Jakubowski, Adam. On the Skorokhod topology. Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), no. 3, 263--285. MR0871083
  • Joffe, A.; Métivier, M. Weak convergence of sequences of semimartingales with applications to multitype branching processes. Adv. in Appl. Probab. 18 (1986), no. 1, 20--65. MR0827331
  • Kisdi, Eva. Evolutionary branching under asymmetric competition, J. Theor. Biol. 197 (1999), no. 2, 149--162.
  • Krone, Steve; Neuhauser, Claudia. Ancestral processes with selection, Theoretical Population Biology 51 (1997), 210--237.
  • Méléard, Sylvie; Tran, Viet Chi. Trait substitution sequence process and canonical equation for age-structured populations. J. Math. Biol. 58 (2009), no. 6, 881--921. MR2495555
  • Méléard, Sylvie; Tran, Viet Chi. Slow and fast scales for superprocess limits of age-structured populations. Stochastic Process. Appl. 122 (2012), no. 1, 250--276. MR2860449
  • Morlon, Hélène; Parsons, Todd L.; Plotkin, Joshua. Reconciling molecular phylogenies with the fossil record, Proceedings of the National Academy of Sciences 108 (2001), 16327--16332.
  • Perkins, Edwin. Conditional Dawson-Watanabe processes and Fleming-Viot processes, Seminar on Stochastic Processes 1991 (Birkhaüser, ed.), Progr. Probab., vol. 29, 1992, pp. 142--155.
  • Perkins, Edwin. On the martingale problem for interactive measure-valued branching diffusions. Mem. Amer. Math. Soc. 115 (1995), no. 549, vi+89 pp. MR1249422
  • Roughgarden, J.A. Theory of population genetics and evolutionary ecology: an introduction, Macmillan, New York, 1979.
  • Rudin, Walter. Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987. xiv+416 pp. ISBN: 0-07-054234-1 MR0924157
  • Tran, Viet Chi. Large population limit and time behaviour of a stochastic particle model describing an age-structured population. ESAIM Probab. Stat. 12 (2008), 345--386. MR2404035


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