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Updated: May 5, 2026

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Ancestral covariance and the Bulmer effect.

G M Tallis1

  • 1Department of Statistics, University of Adelaide, 5001, Adelaide, SA, Australia.

TAG. Theoretical and Applied Genetics. Theoretische Und Angewandte Genetik
|November 19, 2013
PubMed
Summary
This summary is machine-generated.

This study develops a method to track genetic variance reduction across generations due to selection. It provides a formula to quantify these changes and extends the analysis to multiple traits, offering insights into genetic selection processes.

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Area of Science:

  • Quantitative Genetics
  • Animal Breeding
  • Statistical Genetics

Background:

  • Selection is a fundamental process in quantitative genetics.
  • Understanding the impact of selection on genetic variance and covariance is crucial for breeding programs.
  • Previous models have limitations in assessing long-term selection effects across multiple generations and traits.

Purpose of the Study:

  • To develop a framework for analyzing the effects of selection on genetic variance and covariance over multiple generations.
  • To derive Bulmer's general recursion formula for the reduction in genetic variance due to selection.
  • To extend these findings to multivariate selection scenarios and explore connections with ancestral regression.

Main Methods:

  • Generation-by-generation pedigree analysis.
  • Assessment of covariances in subsequent generations.
  • Derivation of recursive formulas for genetic variance reduction.
  • Application of ancestral regression concepts.

Main Results:

  • A general recursion formula for the reduction in genetic variance due to selection (Bulmer's formula) was obtained.
  • The study successfully extended the analysis to assess the effect of selecting one or more characters on the genetic covariance matrix.
  • Ancestral regression provided a novel perspective on the selection process.

Conclusions:

  • The developed methods accurately quantify the impact of selection on genetic variance and covariance over generations.
  • The findings are applicable to both univariate and multivariate selection scenarios in quantitative genetics.
  • Ancestral regression offers a valuable tool for understanding selection dynamics and justifying mating models.