Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T17:16:32.603Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  17 March 2017

Rebekka Brink-Spalink  and
Charline Smadi
Rebekka Brink-Spalink*
Affiliation:
Georg-August-Universität Göttingen
Charline Smadi*
Affiliation:
LISC and University of Oxford
*
* 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: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

Birth-and-death processcoalescentcouplingeco-evolutiongenetic hitchhikingselective sweep

MSC classification

Primary: 92D25: Population dynamics (general) 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J27: Continuous-time Markov processes on discrete state spaces 92D15: Problems related to evolution
Secondary: 60F15: Strong theorems
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 1 , March 2017 , pp. 279 - 326
Copyright
Copyright © Applied Probability Trust 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Barton, N. H. (1998).The effect of hitch-hiking on neutral genealogies.Genet. Res. 72,123–133.Google Scholar
[2] Brink-Spalink, R. (2014).Stochastic models in population genetics: the impact of selection and recombination.Doctoral Thesis, Georg-August University.Google Scholar
[3] Champagnat, N. (2006).A microscopic interpretation for adaptive dynamics trait substitution sequence models.Stoch. Process. Appl. 116,1127–1160.CrossRefGoogle Scholar
[4] Champagnat, N. and Méléard, S. (2011).Polymorphic evolution sequence and evolutionary branching.Prob. Theory Relat. Fields 151,45–94.CrossRefGoogle Scholar
[5] Champagnat, N.,Jabin, P.-E. and Méléard, S. (2014).Adaptation in a stochastic multi-resources chemostat model.J. Math. Pures Appl. 101,755–788.Google Scholar
[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. 67,569–607.CrossRefGoogle ScholarPubMed
[7] Coron, C. (2016).Slow-fast stochastic diffusion dynamics and quasi-stationarity for diploid populations with varying size.J. Math. Biol. 72,171–202.Google Scholar
[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.15–18.Google Scholar
[9] Durrett, R. and Schweinsberg, J. (2004).Approximating selective sweeps.Theoret. Pop. Biol. 66,129–138.Google Scholar
[10] Etheridge, A.,Pfaffelhuber, P. and Wakolbinger, A. (2006).An approximate sampling formula under genetic hitchhiking.Ann. Appl. Prob. 16,685–729.Google Scholar
[11] Ethier, S. N. and Kurtz, T. G. (1986).Markov Processes: Characterization and Convergence.John Wiley,New York.Google Scholar
[12] Fournier, N. and Méléard, S. (2004).A microscopic probabilistic description of a locally regulated population and macroscopic approximations.Ann. App. Prob. 14,1880–1919.Google Scholar
[13] Kaplan, N. L.,Hudson, R. R. and Langley, C. H. (1989).The `hitchhiking effect' revisited.Genetics 123,887–899.Google Scholar
[14] Leocard, S. (2009).Selective sweep and the size of the hitchhiking set.Adv. Appl. Prob. 41,731–764.Google Scholar
[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.183–231.Google Scholar
[16] Ohta, T. and Kimura, M. (1975).The effect of selected linked locus on heterozygosity of neutral alleles (the hitch-hiking effect).Genet. Res. 25,313–325.Google Scholar
[17] Pfaffelhuber, P. and Studeny, A. (2007).Approximating genealogies for partially linked neutral loci under a selective sweep.J. Math. Biol. 55,299–330.Google Scholar
[18] Schweinsberg, J. and Durrett, R. (2005).Random partitions approximating the coalescence of lineages during a selective sweep.Ann. Appl. Prob. 15,1591–1651.CrossRefGoogle Scholar
[19] Smadi, C. (2015).An eco-evolutionary approach of adaptation and recombination in a large population of varying size.Stoch. Process. Appl. 125,2054–2095.Google Scholar
[20] Smith, J. M. and Haigh, J. (1974).The hitch-hiking effect of a favourable gene.Genet. Res. 23,23–35.Google Scholar
[21] Stephan, W.,Song, Y. S. and Langley, C. H. (2006).The hitchhiking effect on linkage disequilibrium between linked neutral loci.Genetics 172,2647–2663.Google Scholar
[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. 41,237–254.Google Scholar