15. Hardy–Weinberg Equilibrium: A Nonparametric Compositional Approach

  1. Vera Pawlowsky-Glahn3 and
  2. Antonella Buccianti4
  1. Jan Graffelman1 and
  2. Juan José Egozcue2

Published Online: 28 JUL 2011

DOI: 10.1002/9781119976462.ch15

Compositional Data Analysis: Theory and Applications

Compositional Data Analysis: Theory and Applications

How to Cite

Graffelman, J. and Egozcue, J. J. (2011) Hardy–Weinberg Equilibrium: A Nonparametric Compositional Approach, in Compositional Data Analysis: Theory and Applications (eds V. Pawlowsky-Glahn and A. Buccianti), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119976462.ch15

Editor Information

  1. 3

    Department of Computer Science and Applied Mathematics, University of Girona, Spain

  2. 4

    Department of Earth Sciences, University of Florence, Italy

Author Information

  1. 1

    Department of Statistics and Operations Research, Technical University of Catalonia, Spain

  2. 2

    Department of Applied Mathematics III, Technical University of Catalonia, Spain

Publication History

  1. Published Online: 28 JUL 2011
  2. Published Print: 23 SEP 2011

ISBN Information

Print ISBN: 9780470711354

Online ISBN: 9781119976462

SEARCH

Keywords:

  • Hardy–Weinberg equilibrium - nonparametric compositional approach;
  • Hardy and Weinberg (1908), independently formulated - principle, that the genotypes at a bi-allelic locus, in proportions p2, 2pq and q2;
  • modern genetic studies - using single nucleotide polymorphisms (SNPs);
  • genetic data sets - most SNPs, being bi-allelic markers;
  • SNPs, grouped as per particular position - within gene;
  • classical tests for HWE - most important statistical tests for HWE;
  • compositional approach - Bruno de Finetti, that genotype frequencies for bi-allelic locus, being represented in ternary plot;
  • Euclidean distance in ilr coordinates - corresponding to the Aitchison distance;
  • bootstrap test, to empirical data set - result compared with those obtained by classical tests;
  • compositional considerations based on Aitchison's geometry - different equilibrium composition, affecting the inference made

Summary

This chapter contains sections titled:

  • Introduction

  • Genetic Data Sets

  • Classical Tests for HWE

  • A Compositional Approach

  • Example

  • Conclusion and Discussion

  • Acknowledgements

  • References