IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v123y2013i4p1368-1414.html
   My bibliography  Save this article

Splitting trees with neutral Poissonian mutations II: Largest and oldest families

Author

Listed:
  • Champagnat, Nicolas
  • Lambert, Amaury

Abstract

We consider a supercritical branching population, where individuals have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant rate. We assume that individuals independently experience neutral mutations, at constant rate θ during their lifetimes, under the infinite-alleles assumption: each mutation instantaneously confers a brand new type, called allele or haplotype, to its carrier. The type carried by a mother at the time when she gives birth is transmitted to the newborn.

Suggested Citation

  • Champagnat, Nicolas & Lambert, Amaury, 2013. "Splitting trees with neutral Poissonian mutations II: Largest and oldest families," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1368-1414.
  • Handle: RePEc:eee:spapps:v:123:y:2013:i:4:p:1368-1414
    DOI: 10.1016/j.spa.2012.11.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912002530
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2012.11.013?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. Champagnat, Nicolas & Lambert, Amaury, 2012. "Splitting trees with neutral Poissonian mutations I: Small families," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1003-1033.
    2. Pardis C. Sabeti & David E. Reich & John M. Higgins & Haninah Z. P. Levine & Daniel J. Richter & Stephen F. Schaffner & Stacey B. Gabriel & Jill V. Platko & Nick J. Patterson & Gavin J. McDonald & Han, 2002. "Detecting recent positive selection in the human genome from haplotype structure," Nature, Nature, vol. 419(6909), pages 832-837, October.
    3. Geiger, Jochen, 1996. "Size-biased and conditioned random splitting trees," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 187-207, December.
    4. Jagers, Peter & Nerman, Olle, 1984. "Limit theorems for sums determined by branching and other exponentially growing processes," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 47-71, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Henry, Benoit, 2021. "Approximation of the allelic frequency spectrum in general supercritical branching populations," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 192-225.

    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. Champagnat, Nicolas & Lambert, Amaury, 2012. "Splitting trees with neutral Poissonian mutations I: Small families," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1003-1033.
    2. Bing Guo & Victor Borda & Roland Laboulaye & Michele D. Spring & Mariusz Wojnarski & Brian A. Vesely & Joana C. Silva & Norman C. Waters & Timothy D. O’Connor & Shannon Takala-Harrison, 2024. "Strong positive selection biases identity-by-descent-based inferences of recent demography and population structure in Plasmodium falciparum," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    3. Yupeng Sang & Zhiqin Long & Xuming Dan & Jiajun Feng & Tingting Shi & Changfu Jia & Xinxin Zhang & Qiang Lai & Guanglei Yang & Hongying Zhang & Xiaoting Xu & Huanhuan Liu & Yuanzhong Jiang & Pär K. In, 2022. "Genomic insights into local adaptation and future climate-induced vulnerability of a keystone forest tree in East Asia," Nature Communications, Nature, vol. 13(1), pages 1-14, December.
    4. Rafajlović, M. & Klassmann, A. & Eriksson, A. & Wiehe, T. & Mehlig, B., 2014. "Demography-adjusted tests of neutrality based on genome-wide SNP data," Theoretical Population Biology, Elsevier, vol. 95(C), pages 1-12.
    5. Chen, Hua & Hey, Jody & Slatkin, Montgomery, 2015. "A hidden Markov model for investigating recent positive selection through haplotype structure," Theoretical Population Biology, Elsevier, vol. 99(C), pages 18-30.
    6. Xinkai Tong & Dong Chen & Jianchao Hu & Shiyao Lin & Ziqi Ling & Huashui Ai & Zhiyan Zhang & Lusheng Huang, 2023. "Accurate haplotype construction and detection of selection signatures enabled by high quality pig genome sequences," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    7. Cécile Delaporte, 2015. "Lévy Processes with Marked Jumps I: Limit Theorems," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1468-1499, December.
    8. Henry, Benoit, 2021. "Approximation of the allelic frequency spectrum in general supercritical branching populations," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 192-225.
    9. Wiuf, Carsten, 2018. "Some properties of the conditioned reconstructed process with Bernoulli sampling," Theoretical Population Biology, Elsevier, vol. 122(C), pages 36-45.

    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:spapps:v:123:y:2013:i:4:p:1368-1414. 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: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.