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Genealogies of two linked neutral loci after a selective sweep in a large population of stochastically varying size

  • Rebekka Brink-Spalink (a1) and Charline Smadi (a2)

We study the impact of a hard selective sweep on the genealogy of partially linked neutral loci in the vicinity of the positively selected allele. We consider a sexual population of stochastically varying size and, focusing on two neighboring loci, derive an approximate formula for the neutral genealogy of a sample of individuals taken at the end of the sweep. Individuals are characterized by ecological parameters depending on their genetic type, and governing their growth rate and interactions with other individuals (competition). As a consequence, the `fitness' of an individual depends on the population state and is not an intrinsic characteristic of individuals. We provide a deep insight into the dynamics of the mutant and wild-type populations during the different stages of a selective sweep.

Corresponding author
* Postal address: Institute for Mathematical Stochastics, Georg-August-Universität Göttingen, Goldschmidtstr. 7, 37077 Göttingen, Germany.
** Current address: Institut des Systèmes Complexes Paris Île-de-France, 113 rue Nationale, 75013 Paris, France. Email address:
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[1] Barton, N. H. (1998).The effect of hitch-hiking on neutral genealogies.Genet. Res. 72,123133.
[2] Brink-Spalink, R. (2014).Stochastic models in population genetics: the impact of selection and recombination.Doctoral Thesis, Georg-August University.
[3] Champagnat, N. (2006).A microscopic interpretation for adaptive dynamics trait substitution sequence models.Stoch. Process. Appl. 116,11271160.
[4] Champagnat, N. and Méléard, S. (2011).Polymorphic evolution sequence and evolutionary branching.Prob. Theory Relat. Fields 151,4594.
[5] Champagnat, N.,Jabin, P.-E. and Méléard, S. (2014).Adaptation in a stochastic multi-resources chemostat model.J. Math. Pures Appl. 101,755788.
[6] Collet, P.,Méléard, S. and Metz, J. A. J. (2013).A rigorous model study of the adaptive dynamics of Mendelian diploids.J. Math. Biol. 67,569607.
[7] Coron, C. (2016).Slow-fast stochastic diffusion dynamics and quasi-stationarity for diploid populations with varying size.J. Math. Biol. 72,171202.
[8] Diniz, M. A. and Polpo, A. (2014).A simple proof for the multinomial version of the representation theorem.In The Contribution of Young Researchers to Bayesian Statistics(Springer Proc. Math. Statist. 63).Springer,Cham,pp.1518.
[9] Durrett, R. and Schweinsberg, J. (2004).Approximating selective sweeps.Theoret. Pop. Biol. 66,129138.
[10] Etheridge, A.,Pfaffelhuber, P. and Wakolbinger, A. (2006).An approximate sampling formula under genetic hitchhiking.Ann. Appl. Prob. 16,685729.
[11] Ethier, S. N. and Kurtz, T. G. (1986).Markov Processes: Characterization and Convergence.John Wiley,New York.
[12] Fournier, N. and Méléard, S. (2004).A microscopic probabilistic description of a locally regulated population and macroscopic approximations.Ann. App. Prob. 14,18801919.
[13] Kaplan, N. L.,Hudson, R. R. and Langley, C. H. (1989).The `hitchhiking effect' revisited.Genetics 123,887899.
[14] Leocard, S. (2009).Selective sweep and the size of the hitchhiking set.Adv. Appl. Prob. 41,731764.
[15] Metz, J. A. J. et al. (1996).Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction.In Stochastic and Spatial Structures of Dynamical Systems,North-Holland,Amsterdam,pp.183231.
[16] Ohta, T. and Kimura, M. (1975).The effect of selected linked locus on heterozygosity of neutral alleles (the hitch-hiking effect).Genet. Res. 25,313325.
[17] Pfaffelhuber, P. and Studeny, A. (2007).Approximating genealogies for partially linked neutral loci under a selective sweep.J. Math. Biol. 55,299330.
[18] Schweinsberg, J. and Durrett, R. (2005).Random partitions approximating the coalescence of lineages during a selective sweep.Ann. Appl. Prob. 15,15911651.
[19] Smadi, C. (2015).An eco-evolutionary approach of adaptation and recombination in a large population of varying size.Stoch. Process. Appl. 125,20542095.
[20] Smith, J. M. and Haigh, J. (1974).The hitch-hiking effect of a favourable gene.Genet. Res. 23,2335.
[21] Stephan, W.,Song, Y. S. and Langley, C. H. (2006).The hitchhiking effect on linkage disequilibrium between linked neutral loci.Genetics 172,26472663.
[22] Stephan, W.,Wiehe, T. H. E. and Lenz, M. W. (1992).The effect of strongly selected substitutions on neutral polymorphism: analytical results based on diffusion theory.Theoret. Pop. Biol. 41,237254.
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Advances in Applied Probability
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