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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.

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Predicting allele frequency changes under selection and drift is crucial for understanding complex traits. This study extends path integral methods to analyze selection on polygenic traits, aiding evolve-and-resequence experiments.

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Evolve and resequencediffusion approximationpolygenic selectiontransition density

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Area of Science:

  • Evolutionary genetics
  • Quantitative genetics
  • Population genetics

Background:

  • Many phenotypic traits are polygenic, complicating genetic architecture studies and phenotype prediction.
  • Evolve-and-resequence experiments identify trait loci via allele frequency changes under selection.
  • Distinguishing selection from genetic drift in allele frequency changes remains challenging, especially for complex traits.

Purpose of the Study:

  • To extend path integral methods for analyzing allele frequency dynamics under selection in quantitative genetics.
  • To derive analytic expressions for allele frequency transition probabilities under stabilizing and adaptive selection.
  • To improve the design and interpretation of evolve-and-resequence experiments for uncovering polygenic architectures.

Main Methods:

  • Application of the perturbation approximation, a path integral method, to quantitative genetic selection scenarios.
  • Derivation of analytic expressions for allele frequency transition probabilities.
  • Utilizing derived expressions to analyze selection detection and optimize experimental design.

Main Results:

  • Developed an extended path integral framework applicable to complex polygenic traits.
  • Derived analytic transition probabilities for alleles under stabilizing and rapid adaptive selection.
  • Provided a method to assess allele frequency changes for selection testing and experimental design.

Conclusions:

  • The extended path integral method offers a powerful tool for studying the genetic basis of complex traits.
  • The derived expressions facilitate the interpretation of evolve-and-resequence experiments.
  • This work enhances our ability to uncover genetic architectures of polygenic traits under selection.