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A Multi-Type Λ-Coalescent

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Book cover Branching Processes and Their Applications

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 219))

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Abstract

This paper discusses multi-type Λ–coalescent processes which arise naturally from Λ–Fleming–Viot processes as dual processes back in time. Mutation and selection may be modelled as happening at random in the population, or in families at birth. The paper is a review of models developed in [4, 7].

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References

  1. Berestycki, N.: Recent progress in coalescent theory. Ensaios Matematicos 16, 1–193 (2009)

    MathSciNet  MATH  Google Scholar 

  2. Bertoin, J., Le Gall, J.-F.: Stochastic flows associated to coalescent processes III: limit theorems. Ill. J. Math. 50, 147–181 (2006)

    MathSciNet  MATH  Google Scholar 

  3. Birkner, B., Blath, J.: Measure-valued diffusions, general coalescents and population genetic inference. In: Trends in Stochastic Analysis, Chap. 12 Cambridge University Press, Cambridge (2009)

    Google Scholar 

  4. Birkner, M., Etheridge, A., Griffiths, R., Miller, L.: A multi-type Λ-coalescent with mutation and selection. In preparation (2016)

    Google Scholar 

  5. Donnelly, P.J., Kurtz, T.G.: Particle representations for measure-valued population models. Ann. Probab. 24, 166–205 (1999)

    MathSciNet  MATH  Google Scholar 

  6. Etheridge, A.: Some mathematical models from population genetics. In: École d’Été de Probabilitités de Saint-Flour XXXIX-2009. Springer, Heidelberg (2012)

    Google Scholar 

  7. Etheridge, A.M., Griffiths, R.C., Taylor, J.E.: A coalescent dual process in a moran model with genic selection, and the lambda coalescent limit. Theor. Popul. Biol. 78, 77–92 (2010)

    Article  MATH  Google Scholar 

  8. Griffiths R.C.: The Lambda-Fleming-Viot process and a connection with Wright-Fisher diffusion. Adv. Appl. Probab. 46, 1009–1035 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pitman, J.: Coalescents with multiple collisions. Ann. Probab. 27, 1870–1902 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Pitman, J.: Combinatorial stochastic processes. In: École d’Été de Probabilitités de Saint-Flour XXXII-2002. Springer, Heidelberg (2006)

    Google Scholar 

  11. Sagitov, S.: The general coalescent with asynchronous mergers of ancestral lines. J. Appl. Probab. 36, 1116–1125 (1999)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Oxford, 1 South Parks Road, Oxford, UK

    Robert C. Griffiths

Authors
  1. Robert C. Griffiths
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Corresponding author

Correspondence to Robert C. Griffiths .

Editor information

Editors and Affiliations

  1. Departamento de Matemáticas Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

    Inés M. del Puerto

  2. Departamento de Matemáticas Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

    Miguel González

  3. Departamento de Matemáticas Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

    Cristina Gutiérrez

  4. Departamento de Matemáticas Centro Universitario de Plasencia, Universidad de Extremadura, Plasencia, Spain

    Rodrigo Martínez

  5. Departamento de Matemáticas Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

    Carmen Minuesa

  6. Departamento de Matemáticas Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

    Manuel Molina

  7. Departamento de Matemáticas Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain

    Manuel Mota

  8. Departamento de Matemáticas Facultad de Veterinaria, Universidad de Extremadura, Cáceres, Spain

    Alfonso Ramos

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Griffiths, R.C. (2016). A Multi-Type Λ-Coalescent. In: del Puerto, I., et al. Branching Processes and Their Applications. Lecture Notes in Statistics(), vol 219. Springer, Cham. https://doi.org/10.1007/978-3-319-31641-3_2

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