Bistability in two-locus models with selection, mutation, and recombination

Journal of Mathematical Biology

Volumn 62, Issue 5, 2011, Pages 763-788

  Park, Su Chan ^a,b   Krug, Joachim ^b  

^a The Catholic University of Korea   (South Korea)

^b UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Bistability; Evolution of recombination; Landau theory; Reciprocal sign epistasis

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; EVOLUTION; GENE FREQUENCY; GENETIC EPISTASIS; GENETIC RECOMBINATION; GENETIC SELECTION; GENOTYPE; HAPLOIDY; METHODOLOGY; MUTATION; PHYSIOLOGY; POPULATION GENETICS; PROBABILITY; REPRODUCTIVE FITNESS; STATISTICAL DISTRIBUTION; STATISTICAL MODEL;

ALGORITHMS; BIOLOGICAL EVOLUTION; EPISTASIS, GENETIC; GENE FREQUENCY; GENETIC FITNESS; GENETICS, POPULATION; GENOTYPE; HAPLOIDY; MODELS, GENETIC; MODELS, STATISTICAL; MUTATION; PROBABILITY; RECOMBINATION, GENETIC; SELECTION, GENETIC; STATISTICAL DISTRIBUTIONS;

EID: 79953788919     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-010-0352-x     Document Type: Article

References (27)

1. Bodmer WF, Felsenstein J (1967) Linkage and selection: theoretical analysis of the deterministic two locus random mating model. Genetics 57: 237-265.
2. Boerlijst MC, Bonhoeffer S, Nowak MA (1996) Viral quasi-species and recombination. Proc R Soc Lond Ser B 263: 1577-1584.
3. Bonhoeffer S, Chappey C, Parkin NT, Whitcomb JM, Petropoulos CJ (2004) Evidence for positive epistasis in HIV-1. Science 306: 1547-1550.
4. Bürger R (1989) Linkage and the maintenance of heritable variation by mutation-selection balance. Genetics 121: 175-184.
5. Bürger R (2000) The mathematical theory of selection, recombination and mutation. Wiley, Chichester.
6. Crow JF, Kimura M (1965) Evolution in sexual and asexual populations. Am Nat 99: 439-450.
7. de Visser JAGM, Elena SF (2007) The evolution of sex: empirical insights into the roles of epistasis and drift. Nat Rev Genet 8: 139-149.
8. de Visser JAGM, Hoekstra RH, van den Ende H (1997) Test of interaction between genetic markers that affect fitness in Aspergillus niger. Evolution 51: 1499-1505.
9. de Visser JAGM, Park SC, Krug J (2009) Exploring the effect of sex on empirical fitness landscapes. Am Nat 174: S15-S30.
10. Elena SF, Lenski RE (1997) Test of synergistic interactions among deleterious mutations in bacteria. Nature 390: 395-398.
11. Eshel I, Feldman MW (1970) On the evolutionary effect of recombination. Theor Popul Biol 1: 88-100.
12. Feldman MW (1971) Equilibrium studies of two locus haploid populations with recombination. Theor Popul Biol 2: 299-318.
13. Higgs PG (1998) Compensatory neutral mutations and the evolution of RNA. Genetica 102/103: 91-101.
14. Jacobi MN, Nordahl M (2006) Quasispecies and recombination. Theor Popul Biol 70: 479-485.
15. Jain K (2010) Time to fixation in the presence of recombination. Theor Popul Biol 77: 23-31.
16. Karlin S, McGregor J (1971) On mutation selection balance for two-locus haploid and diploid populations. Theor Popul Biol 2: 60-70.
17. Kimura M (1956) A model for a genetic system which leads to closer linkage by natural selection. Evolution 10: 278-287.
18. Kondrashov AS (1988) Deleterious mutations and the evolution of sexual reproduction. Nature 336: 435-440.
19. Kouyos RD, Silander OK, Bonhoeffer S (2007) Epistasis between deleterious mutations and the evolution of recombination. Trends Ecol Evol 22: 308-315.
20. Otto SP (2009) The evolutionary enigma of sex. Am Nat 174: S1-S14.
21. Plischke M, Bergersen B (2006) Equilibrium statistical physics. World Scientific, Singapore.
22. Poelwijk FJ, Kiviet DJ, Weinreich DM, Tans SJ (2007) Empirical fitness landscapes reveal accessible evolutionary paths. Nature 445: 383-386.
23. Rutschman DA (1994) Dynamics of the two-locus haploid model. Theor Popul Biol 45: 167-176.
24. Stephan W (1996) The rate of compensatory mutation. Genetics 144: 419-426.
25. Weinreich DM, Chao L (2005) Rapid evolutionary escape by large populations from local fitness peaks is likely in nature. Evolution 59: 1175-1182.
26. Weinreich DM, Watson RA, Chao L (2005) Perspective: sign epistasis and genetic constraints on evolutionary trajectories. Evolution 59: 1165-1174.
27. Wright AH, Rowe JE, Stephens CR, Poli R (2003) Bistability in a gene pool GA with mutation. In: DeJong K, Poli R, Rowe J (eds) Foundations of genetic algorithms (FOGA-7). Morgan Kaufmann, San Francisco, pp 63-80.