IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v122y2018icp67-77.html
   My bibliography  Save this article

Wright–Fisher diffusion bridges

Author

Listed:
  • Griffiths, Robert C.
  • Jenkins, Paul A.
  • Spanò, Dario

Abstract

The trajectory of the frequency of an allele which begins at x at time 0 and is known to have frequency z at time T can be modelled by the bridge process of the Wright–Fisher diffusion. Bridges when x=z=0 are particularly interesting because they model the trajectory of the frequency of an allele which appears at a time, then is lost by random drift or mutation after a time T. The coalescent genealogy back in time of a population in a neutral Wright–Fisher diffusion process is well understood. In this paper we obtain a new interpretation of the coalescent genealogy of the population in a bridge from a time t∈(0,T). In a bridge with allele frequencies of 0 at times 0 and T the coalescence structure is that the population coalesces in two directions from t to 0 and t to T such that there is just one lineage of the allele under consideration at times 0 and T. The genealogy in Wright–Fisher diffusion bridges with selection is more complex than in the neutral model, but still with the property of the population branching and coalescing in two directions from time t∈(0,T). The density of the frequency of an allele at time t is expressed in a way that shows coalescence in the two directions. A new algorithm for exact simulation of a neutral Wright–Fisher bridge is derived. This follows from knowing the density of the frequency in a bridge and exact simulation from the Wright–Fisher diffusion. The genealogy of the neutral Wright–Fisher bridge is also modelled by branching Pólya urns, extending a representation in a Wright–Fisher diffusion. This is a new very interesting representation that relates Wright–Fisher bridges to classical urn models in a Bayesian setting.

Suggested Citation

  • Griffiths, Robert C. & Jenkins, Paul A. & Spanò, Dario, 2018. "Wright–Fisher diffusion bridges," Theoretical Population Biology, Elsevier, vol. 122(C), pages 67-77.
    • Handle: RePEc:eee:thpobi:v:122:y:2018:i:c:p:67-77
    DOI: 10.1016/j.tpb.2017.09.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580917300308
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2017.09.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Schraiber, Joshua G. & Griffiths, Robert C. & Evans, Steven N., 2013. "Analysis and rejection sampling of Wright–Fisher diffusion bridges," Theoretical Population Biology, Elsevier, vol. 89(C), pages 64-74.
    2. Etheridge, A.M. & Griffiths, R.C., 2009. "A coalescent dual process in a Moran model with genic selection," Theoretical Population Biology, Elsevier, vol. 75(4), pages 320-330.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Schraiber, Joshua G., 2014. "A path integral formulation of the Wright–Fisher process with genic selection," Theoretical Population Biology, Elsevier, vol. 92(C), pages 30-35.
    2. Vogl, Claus & Bergman, Juraj, 2015. "Inference of directional selection and mutation parameters assuming equilibrium," Theoretical Population Biology, Elsevier, vol. 106(C), pages 71-82.
    3. Vogl, Claus & Clemente, Florian, 2012. "The allele-frequency spectrum in a decoupled Moran model with mutation, drift, and directional selection, assuming small mutation rates," Theoretical Population Biology, Elsevier, vol. 81(3), pages 197-209.
    4. Desai, Michael M. & Nicolaisen, Lauren E. & Walczak, Aleksandra M. & Plotkin, Joshua B., 2012. "The structure of allelic diversity in the presence of purifying selection," Theoretical Population Biology, Elsevier, vol. 81(2), pages 144-157.
    5. Burden, Conrad J. & Tang, Yurong, 2017. "Rate matrix estimation from site frequency data," Theoretical Population Biology, Elsevier, vol. 113(C), pages 23-33.
    6. Malaguti, Giulia & Singh, Param Priya & Isambert, Hervé, 2014. "On the retention of gene duplicates prone to dominant deleterious mutations," Theoretical Population Biology, Elsevier, vol. 93(C), pages 38-51.
    7. Frank Hollander & Shubhamoy Nandan, 2022. "Spatially Inhomogeneous Populations with Seed-Banks: I. Duality, Existence and Clustering," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1795-1841, September.
    8. Corujo, Josué, 2021. "Dynamics of a Fleming–Viot type particle system on the cycle graph," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 57-91.
    9. Der, Ricky & Epstein, Charles L. & Plotkin, Joshua B., 2011. "Generalized population models and the nature of genetic drift," Theoretical Population Biology, Elsevier, vol. 80(2), pages 80-99.
    10. Griffiths, Robert C. & Jenkins, Paul A. & Lessard, Sabin, 2016. "A coalescent dual process for a Wright–Fisher diffusion with recombination and its application to haplotype partitioning," Theoretical Population Biology, Elsevier, vol. 112(C), pages 126-138.
    11. Etheridge, Alison M. & Griffiths, Robert C. & Taylor, Jesse E., 2010. "A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit," Theoretical Population Biology, Elsevier, vol. 78(2), pages 77-92.
    12. Lenz, Ute & Kluth, Sandra & Baake, Ellen & Wakolbinger, Anton, 2015. "Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution," Theoretical Population Biology, Elsevier, vol. 103(C), pages 27-37.
    13. Vogl, Claus & Mikula, Lynette C. & Burden, Conrad J., 2020. "Maximum likelihood estimators for scaled mutation rates in an equilibrium mutation–drift model," Theoretical Population Biology, Elsevier, vol. 134(C), pages 106-118.
    14. Jüri Lember & Chris Watkins, 2022. "An Evolutionary Model that Satisfies Detailed Balance," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 1-37, March.
    15. Thierry E. Huillet, 2016. "Random walk Green kernels in the neutral Moran model conditioned on survivors at a random time to origin," Mathematical Population Studies, Taylor & Francis Journals, vol. 23(3), pages 164-200, July.
    16. Vogl, Claus & Mikula, Lynette Caitlin, 2021. "A nearly-neutral biallelic Moran model with biased mutation and linear and quadratic selection," Theoretical Population Biology, Elsevier, vol. 139(C), pages 1-17.
    17. Carinci, Gioia & Giardinà, Cristian & Giberti, Claudio & Redig, Frank, 2015. "Dualities in population genetics: A fresh look with new dualities," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 941-969.
    18. Schrempf, Dominik & Hobolth, Asger, 2017. "An alternative derivation of the stationary distribution of the multivariate neutral Wright–Fisher model for low mutation rates with a view to mutation rate estimation from site frequency data," Theoretical Population Biology, Elsevier, vol. 114(C), pages 88-94.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:thpobi:v:122:y:2018:i:c:p:67-77. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/intelligence .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.