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A path integral approach for allele frequency dynamics under polygenic selection.

Nathan W Anderson1, Lloyd Kirk1, Joshua G Schraiber2

  • 1Department of Integrative Biology, University of Wisconsin-Madison, Madison, WI 53706, USA.

Genetics
|November 12, 2024
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Summary

This study extends path integral methods to predict allele frequency changes under selection in evolve-and-resequence experiments. The new analytic expressions help identify genetic architectures of complex polygenic traits.

Keywords:
diffusion approximationevolve and resequencepolygenic selectiontransition density

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Area of Science:

  • Quantitative genetics
  • Evolutionary biology
  • Population genetics

Background:

  • Polygenic traits pose challenges for genetic architecture studies and phenotype prediction.
  • Evolve-and-resequence (E&R) experiments identify trait loci via allele frequency changes (AFCs) under selection.
  • Distinguishing selection from genetic drift in AFCs is difficult, especially for complex traits.

Purpose of the Study:

  • To extend path integral methods for predicting AFCs under selection in quantitative genetics.
  • To derive analytic expressions for allele transition probabilities under stabilizing and adaptive selection.
  • To improve the design of E&R experiments for uncovering polygenic architectures.

Main Methods:

  • Applied the perturbation approximation, a path integral method, to quantitative genetics selection scenarios.
  • Derived analytic expressions for allele transition probabilities.
  • Utilized these expressions to analyze AFCs for selection detection and E&R experimental design.

Main Results:

  • Developed novel analytic expressions for allele frequency dynamics under stabilizing and adaptive selection.
  • Provided a framework to better distinguish selection from drift in E&R experiments.
  • Characterized optimal E&R experimental designs for studying polygenic traits.

Conclusions:

  • The extended path integral approach enhances the analysis of E&R experiments for complex traits.
  • This work provides tools to better understand the genetic basis of adaptation and trait evolution.
  • Improved experimental designs will facilitate the discovery of genetic architectures underlying polygenic traits.