The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. Barton, N.H., Depaulis, F., and Etheridge, A.M. (2002). Neutral evolution in spatially continuous populations. Theor. Pop. Biol., 61:31--48.
  2. Barton, N.H., Kelleher, J., and Etheridge, A.M. (2009). A new model for large-scale population dynamics: quantifying phylogeography. Preprint.
  3. Berestycki, N., Etheridge, A.M., and Hutzenthaler, M. (2009). Survival, extinction and ergodicity in a spatially continuous population model. Markov Process. Related Fields, 15:265--288. MR2554364
  4. Bertoin, J. (1996). Lévy Processes. Cambridge University Press. MR1406564 (98e:60117)
  5. Bertoin, J. and Le Gall, J.-F. (2003). Stochastic flows associated to coalescent processes. Probab. Theory Related Fields, 126:261--288. MR1990057 (2004f:60080)
  6. Bhattacharya, R.N. (1977). Refinements of the multidimensional central limit theorem and applications. Ann. Probab., 5:1--27. MR0436273 (55 #9220)
  7. Billingsley, P. (1995). Probability and Measure. Wiley. MR1324786 (95k:60001)
  8. Birkner, M., Blath, J., Capaldo, M., Etheridge, A.M., M\"ohle, M., Schweinsberg, J., and Wakolbinger, A. (2005). Alpha-stable branching and Beta-coalescents. Electron. J. Probab., 10:303--325. MR2120246 (2006c:60100)
  9. Cox, J.T. (1989). Coalescing random walks and voter model consensus times on the torus in Z^d. Ann. Probab., 17:1333--1366. MR1048930 (91d:60250)
  10. Cox, J.T. and Durrett, R. (2002). The stepping stone model: new formulas expose old myths. Ann. Appl. Probab., 12:1348--1377. MR1936596 (2003j:60138)
  11. Cox, J.T. and Griffeath, D. (1986). Diffusive clustering in the two-dimensional voter model. Ann. Probab., 14:347--370. MR0832014 (87j:60146)
  12. Cox, J.T. and Griffeath, D. (1990). Mean field asymptotics for the planar stepping stone model. Proc. London Math. Soc., 61:189--208. MR1051103 (92b:60098)
  13. Donnelly, P.J. and Kurtz, T.G. (1999). Particle representations for measure-valued population models. Ann. Probab., 27:166--205. MR1681126 (2000f:60108)
  14. Eller, E., Hawks, J., and Relethford, J.H. (2004). Local extinction and recolonization, species effective population size, and modern human origins. Human Biology, 76(5):689--709.
  15. Etheridge, A.M. (2008). Drift, draft and structure: some mathematical models of evolution. Banach Center Publ., 80:121--144. MR2433141 (2009m:60237)
  16. Ethier, S.N. and Kurtz, T.G. (1986). Markov processes: characterization and convergence. Wiley. MR0838085 (88a:60130)
  17. Evans, S.N. (1997). Coalescing Markov labelled partitions and a continuous sites genetics model with infinitely many types. Ann. Inst. H. Poincaré Probab. Statist., 33:339--358. MR1457055 (98m:60126)
  18. Felsenstein, J. (1975). A pain in the torus: some difficulties with the model of isolation by distance. Amer. Nat., 109:359--368.
  19. Kimura, M. (1953). Stepping stone model of population. Ann. Rep. Nat. Inst. Genetics Japan, 3:62--63.
  20. Kingman, J.F.C. (1982). The coalescent. Stochastic Process. Appl., 13:235--248. MR0671034 (84a:60079)
  21. Limic, V. and Sturm, A. (2006). The spatial Lambda-coalescent. Electron. J. Probab., 11(15):363--393. MR2223040 (2007b:60183)
  22. Malécot, G. (1948). Les Mathématiques de l'hérédité. Masson et Cie, Paris. MR0027490 (10,314c)
  23. Möhle, M. and Sagitov, S. (2001). A classification of coalescent processes for haploid exchangeable population models. Ann. Probab., 29:1547--1562. MR1880231 (2003b:60134)
  24. Pitman, J. (1999). Coalescents with multiple collisions. Ann. Probab., 27:1870--1902. MR1742892 (2001h:60016)
  25. Ridler-Rowe, C.J. (1966). On first hitting times of some recurrent two-dimensional random walks. Z. Wahrsch. verw. Geb., 5:187--201. MR0199901 (33 #8041)
  26. Rogers, L.C.G. and Williams, D. (1987). Diffusions, Markov processes, and martingales: Itô calculus. Wiley. MR1780932 (2001g:60189)
  27. Sagitov, S. (1999). The general coalescent with asynchronous mergers of ancestral lines. J. Appl. Probab., 26:1116--1125. MR1742154 (2001f:92019)
  28. Sawyer, S. and Fleischmann, J. (1979). The maximal geographical range of a mutant allele considered as a subtype of a Brownian branching random field. Proc. Natl. Acad. Sci. USA, 76(2):872--875.
  29. Schweinsberg, J. (2000). Coalescents with simultaneous multiple collisions. Electron. J. Probab., 5:1--50. MR1781024 (2002g:60113)
  30. Wilkins, J.F. (2004). A separation of timescales approach to the coalescent in a continuous population. Genetics, 168:2227--2244.
  31. Wilkins, J.F. and Wakeley, J. (2002). The coalescent in a continuous, finite, linear population. Genetics, 161:873--888.
  32. Wright, S. (1931). Evolution in Mendelian populations. Genetics, 16:97--159.
  33. Wright, S. (1943). Isolation by distance. Genetics, 28:114--138.
  34. Zähle, I., Cox, J.T., and Durrett, R. (2005). The stepping stone model II: genealogies and the infinite sites model. Ann. Appl. Probab., 15:671--699. MR2114986 (2006d:60157)


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.