Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 13 (2008) > Paper 68 open journal systems 


The pattern of genetic hitchhiking under recurrent mutation

Joachim Hermisson, University of Vienna
Peter Pfaffelhuber, University of Freiburg


Abstract
Genetic hitchhiking describes evolution at a neutral locus that is linked to a selected locus. If a beneficial allele rises to fixation at the selected locus, a characteristic polymorphism pattern (so-called selective sweep) emerges at the neutral locus. The classical model assumes that fixation of the beneficial allele occurs from a single copy of this allele that arises by mutation. However, recent theory (Pennings and Hermisson, 2006a,b) has shown that recurrent beneficial mutation at biologically realistic rates can lead to markedly different polymorphism patterns, so-called soft selective sweeps. We extend an approach that has recently been developed for the classical hitchhiking model (Schweinsberg and Durrett, 2005; Etheridge et al., 2006) to study the recurrent mutation scenario. We show that the genealogy at the neutral locus can be approximated (to leading orders in the selection strength) by a marked Yule process with immigration. Using this formalism, we derive an improved analytical approximation for the expected heterozygosity at the neutral locus at the time of fixation of the beneficial allele.


Full text: PDF

Pages: 2069-2106

Published on: November 26, 2008
Bibliography
  1. Aldous, D. (1985). Exchangeability and related topics. In Ecole d'Ete St Flour 1983, pp. 1--198. Springer. Lecture Notes in Math. 1117. MR0883646
  2. Barton, N. (1998). The effect of hitch-hiking on neutral genealogies. Genetical Research, 72}, 123--133. Math. Review number not available.
  3. Barton, N., A. Etheridge, and A. Sturm (2004). Coalescence in a random background. Ann. of Appl. Probab., em 14, no. 2}, 754--785. MR2052901
  4. Bronstein, I. N. (1982). Taschenbuch der Mathematik. Teubner, 23rd edition.
  5. Eriksson, A., P. Fernström, B. Mehlig, and S. Sagitov (2008). An accurate model for genetic hitchhiking. Genetics, em 178, 439--451. Math. Review number not available.
  6. Etheridge, A., P. Pfaffelhuber, and A. Wakolbinger (2006). An approximate sampling formula under genetic hitchhiking. Ann. Appl. Probab. 16, 685--729. MR2244430
  7. Ethier, S. and T. Kurtz (1986). Markov Processes: Characterization and Convergence. Wiley.
  8. Evans, S. N. and N. O'Connell (1994). Weighted occupation time for branching particle systems and a representation for the supercritical superprocess. Canad. Math. Bull.. 37(2), 187--196. MR1275703
  9. Ewens, W. J. (2004). Mathematical Population Genetics. I. Theoretical introduction. Second edition. Springer.
  10. Fisher, R. A. (1930). The Genetical Theory of Natural Selection. Second edition. Oxford: Clarendon Press. MR1785121
  11. Harr, B., M. Kauer, and C. Schlötterer (2002). Hitchhiking mapping: a population-based fine-mapping strategy for adaptive mutations in Drosophila melanogaster. Proc. Natl. Acad. Sci. U.S.A. 99, 12949--12954. Math. Review number not available.
  12. Hermisson, J. and P. Pennings (2005). Soft sweeps: molecular population genetics of adaptation from standing genetic variation. Genetics. 169(4), 2335--2352. Math. Review number not available.
  13. Hudson, R. (1983). Properties of a neutral allele model with intragenic recombination. Theo. Pop. Biol. 23, 183--201. Math. Review number not available.
  14. Jensen, J. D., K. R. Thornton, C. D. Bustamante, and C. F. Aquadro (2007). On the utility of linkage disequilibrium as a statistic for identifying targets of positive selection in non-equilibrium populations. Genetics. 176, 2371--2379. Math. Review number not available.
  15. Jeong, S., M. Rebeiz, P. Andolfatto, T. Werner, J. True, and S. Carroll (2008). The evolution of gene regulation underlies a morphological difference between two {D}rosophila sister species. Cell. 132, 783--793. Math. Review number not available.
  16. Joyce, P. and S. Tavare (1987). Cycles, Permutations and the Structure of the Yule proess with immigration. Stoch. Proc. Appl. 25, 309--314. MR0915145
  17. Kaplan, N. L., R. R. Hudson, and C. H. Langley (1989). The 'Hitchhiking effect' revisited. Genetics. 123, 887--899. Math. Review number not available.
  18. Kim, Y. and W. Stephan (2002). Detecting a local signature of genetic hitchhiking along a recombining chromosome. Genetics. 160, 765--777. Math. Review number not available.
  19. Kingman, J. F. C. (1982). The coalescent. Stoch. Proc. Appl. 13, 235--248. MR0671034
  20. Maynard Smith, J. and J. Haigh (1974). The hitch-hiking effect of a favorable gene. Genetic Research. 23, 23--35. Math. Review number not available.
  21. McVean, G. A. (2007). The structure of linkage disequilibrium around a selective sweep. Genetics. 175, 1395--1406. Math. Review number not available.
  22. Nair, S., D. Nash, D. Sudimack, A. Jaidee, M. Barends, A. Uhlemann, S. Krishna, F. Nosten, and T. Anderson (2007). Recurrent gene amplification and soft selective sweeps during evolution of multidrug resistance in malaria parasites. Mol. Biol. Evol. 24, 562--573. Math. Review number not available.
  23. Nielsen, R., S. Williamson, Y. Kim, M. Hubisz, A. Clark, and C. Bustamante (2005). Genomic scans for selective sweeps using SNP data. Genome Research. 15, 1566--1575. Math. Review number not available.
  24. O'Connell, N. (1993). Yule Process Approximation for the Skeleton of a Branching Process. J. Appl. Prob. 30, 725--729. MR1232747
  25. Ometto, L., S. Glinka, D. D. Lorenzo, and W. Stephan (2005). Inferring the effects of demography and selection on Drosophila melanogaster populations from a chromosome-wide scan of DNA variation. Mol. Biol. Evol.. 22, 2119--2130. Math. Review number not available.
  26. Pennings, P. and J. Hermisson (2006a). Soft sweeps II--molecular population genetics of adaptation from recurrent mutation or migration}. Mol. Biol. Evol. 23(5), 1076--1084. Math. Review number not available.
  27. Pennings, P. and J. Hermisson (2006b). Soft Sweeps III - The signature of positive selection from recurrent mutation. PLoS Genetics. 2(e186). Math. Review number not available.
  28. Pfaffelhuber, P., B. Haubold, and A. Wakolbinger (2006). Approximate genealogies under genetic hitchhiking. Genetics. 174, 1995--2008. Math. Review number not available.
  29. Pfaffelhuber, P., A. Lehnert, and W. Stephan (2008). Linkage disequilibrium under genetic hitchhiking in finite populations. Genetics. 179, 527--537. Math. Review number not available.
  30. Pfaffelhuber, P. and A. Studeny (2007). Approximating genealogies for partially linked neutral loci under a selective sweep. J. Math. Biol. 55, 299--330. MR2336065
  31. Przeworski, M., G. Coop, and J. D. Wall (2005). The signature of positive selection on standing genetic variation. Evolution. 59, 2312--2323. Math. Review number not available.
  32. Schlenke, T. A. and D. J. Begun (2004). Strong selective sweep associated with a transposon insertion in {D}rosophila simulans}. Proc. Natl. Acad. Sci. U.S.A. 101, 1626--1631. Math. Review number not available.
  33. Schweinsberg, J. and R. Durrett (2005). Random partitions approximating the coalescence of lineages during a selective sweep. Ann. Appl. Probab. 15, 1591--1651. MR2152239
  34. Stephan, W., T. H. E. Wiehe, and M. W. Lenz (1992). The effect of Strongly Selected Substitutions on Neutral Polymorphism: Analytical Results Based on Diffusion Theory. Theo. Pop. Biol. 41, 237--254. Math. Review number not available.
  35. Taylor, J. E. (2007). The common ancestor process for a Wright-Fisher diffusion. Elec. J. Prob. 12, 808--847. MR2318411
  36. Tishkoff, S., F. Reed, A. Ranciaro, B. Voight, C. Babbitt, J. Silverman, K. Powell, H. Mortensen, J. Hirbo, M. Osman, M. Ibrahim, S. Omar, G. Lema, T. Nyambo, J. Ghori, S. Bumpstead, J. Pritchard, G. Wray, and P. Deloukas (2007). Convergent adaptation of human lactase persistence in Africa and Europe. Nat. Genet. 39, 31--40. Math. Review number not available.
  37. van Herwaarden, O. and N. van der Wal (2002). Extinction time and age of an allele in a large finite population. Theo. Pop. Biol. 61, 311--318.
  38. Williamson, S. H., R. Hernandez, A. Fledel-Alon, L. Zhu, R. Nielsen, and C. D. Bustamante (2005). Simultaneous inference of selection and population growth from patterns of variation in the human genome. Proc. Natl. Acad. Sci. U.S.A. 102, 7882--7887. Math. Review number not available.
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489