IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v148y2022icp28-39.html
   My bibliography  Save this article

A central limit theorem concerning uncertainty in estimates of individual admixture

Author

Listed:
  • Pfaffelhuber, Peter
  • Rohde, Angelika

Abstract

The concept of individual admixture (IA) assumes that the genome of individuals is composed of alleles inherited from K ancestral populations. Each copy of each allele has the same chance qk to originate from population k, and together with the allele frequencies p in all populations at all M markers, comprises the admixture model. Here, we assume a supervised scheme, i.e. allele frequencies p are given through a reference database of size N, and q is estimated via maximum likelihood for a single sample. We study laws of large numbers and central limit theorems describing effects of finiteness of both, M and N, on the estimate of q. We recall results for the effect of finite M, and provide a central limit theorem for the effect of finite N, introduce a new way to express the uncertainty in estimates in standard barplots, give simulation results, and discuss applications in forensic genetics.

Suggested Citation

  • Pfaffelhuber, Peter & Rohde, Angelika, 2022. "A central limit theorem concerning uncertainty in estimates of individual admixture," Theoretical Population Biology, Elsevier, vol. 148(C), pages 28-39.
    • Handle: RePEc:eee:thpobi:v:148:y:2022:i:c:p:28-39
    DOI: 10.1016/j.tpb.2022.09.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580922000661
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2022.09.003?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. Swapan Mallick & Heng Li & Mark Lipson & Iain Mathieson & Melissa Gymrek & Fernando Racimo & Mengyao Zhao & Niru Chennagiri & Susanne Nordenfelt & Arti Tandon & Pontus Skoglund & Iosif Lazaridis & Sri, 2016. "The Simons Genome Diversity Project: 300 genomes from 142 diverse populations," Nature, Nature, vol. 538(7624), pages 201-206, October.
    2. Oded Galor, 2007. "Discrete Dynamical Systems," Springer Books, Springer, edition 1, number 978-3-540-36776-5, December.
    3. Tvedebrink, Torben & Eriksen, Poul Svante & Mogensen, Helle Smidt & Morling, Niels, 2018. "Weight of the evidence of genetic investigations of ancestry informative markers," Theoretical Population Biology, Elsevier, vol. 120(C), pages 1-10.
    4. Daniel J. Lawson & Lucy van Dorp & Daniel Falush, 2018. "A tutorial on how not to over-interpret STRUCTURE and ADMIXTURE bar plots," Nature Communications, Nature, vol. 9(1), pages 1-11, December.
    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. Estavoyer, Maxime & François, Olivier, 2022. "Theoretical analysis of principal components in an umbrella model of intraspecific evolution," Theoretical Population Biology, Elsevier, vol. 148(C), pages 11-21.
    2. Strulik, Holger & Werner, Katharina, 2014. "Elite education, mass education, and the transition to modern growth," University of Göttingen Working Papers in Economics 205, University of Goettingen, Department of Economics.
    3. Carl-Johan Dalgaard & Holger Strulik, 2015. "The physiological foundations of the wealth of nations," Journal of Economic Growth, Springer, vol. 20(1), pages 37-73, March.
    4. Kai Yuan & Xumin Ni & Chang Liu & Yuwen Pan & Lian Deng & Rui Zhang & Yang Gao & Xueling Ge & Jiaojiao Liu & Xixian Ma & Haiyi Lou & Taoyang Wu & Shuhua Xu, 2021. "Refining models of archaic admixture in Eurasia with ArchaicSeeker 2.0," Nature Communications, Nature, vol. 12(1), pages 1-15, December.
    5. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    6. Solomon Sorin & Golo Natasa, 2013. "Minsky Financial Instability, Interscale Feedback, Percolation and Marshall–Walras Disequilibrium," Accounting, Economics, and Law: A Convivium, De Gruyter, vol. 3(3), pages 167-260, October.
    7. Battigalli, Pierpaolo & Panebianco, Fabrizio & Pin, Paolo, 2023. "Learning and selfconfirming equilibria in network games," Journal of Economic Theory, Elsevier, vol. 212(C).
    8. de Oliveira, Juliano A. & N. Ramos, Larissa C. & Leonel, Edson D., 2018. "Dynamics towards the steady state applied for the Smith-Slatkin mapping," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 119-122.
    9. Donal Smith, 2015. "Collateral Constraints and the Interest Rate," Discussion Papers 15/22, Department of Economics, University of York.
    10. Lindner, Ines & Strulik, Holger, 2014. "From tradition to modernity: Economic growth in a small world," Journal of Development Economics, Elsevier, vol. 109(C), pages 17-29.
    11. Kalin Hristov & Rossen Rozenov, 2009. "Financial Convergence in the New EU Member States," Working Paper / FINESS 1.2, DIW Berlin, German Institute for Economic Research.
    12. Heifetz, Aviad & Minelli, Enrico & Polemarchakis, Herakles, 2023. "Affective interdependence and welfare," The Warwick Economics Research Paper Series (TWERPS) 1450, University of Warwick, Department of Economics.
    13. Jin, Wen-Long, 2013. "Stability and bifurcation in network traffic flow: A Poincaré map approach," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 191-208.
    14. Chi-Chun Liu & David Witonsky & Anna Gosling & Ju Hyeon Lee & Harald Ringbauer & Richard Hagan & Nisha Patel & Raphaela Stahl & John Novembre & Mark Aldenderfer & Christina Warinner & Anna Di Rienzo &, 2022. "Ancient genomes from the Himalayas illuminate the genetic history of Tibetans and their Tibeto-Burman speaking neighbors," Nature Communications, Nature, vol. 13(1), pages 1-14, December.
    15. Andreas Irmen, 2017. "Capital‐ And Labor‐Saving Technical Change In An Aging Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(1), pages 261-285, February.
    16. Yingyan Yu & Zhen Zhang & Xiaorui Dong & Ruixin Yang & Zhongqu Duan & Zhen Xiang & Jun Li & Guichao Li & Fazhe Yan & Hongzhang Xue & Du Jiao & Jinyuan Lu & Huimin Lu & Wenmin Zhang & Yangzhen Wei & Sh, 2022. "Pangenomic analysis of Chinese gastric cancer," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    17. Josselin Thuilliez & Nouhoum Touré, 2024. "Opinions and vaccination during an epidemic," Post-Print hal-04490900, HAL.
    18. Kuhle, Wolfgang, 2021. "Equilibrium with computationally constrained agents," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 77-92.
    19. Luis Alcalá & Fernando Tohmé & Carlos Dabús, 2019. "Strategic Growth with Recursive Preferences: Decreasing Marginal Impatience," Dynamic Games and Applications, Springer, vol. 9(2), pages 314-365, June.
    20. Iong, Ka-Kit & Irmen, Andreas, 2021. "The supply of hours worked and fluctuations between growth regimes," Journal of Economic Theory, Elsevier, vol. 194(C).

    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:148:y:2022:i:c:p:28-39. 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.