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<p>This paper examines a genetic frequency model, governed by a second-order differential equation that includes a migration mean and variance parameters. Such a model is critical for understanding how gene flow affects genetic variation across migrating populations. We prove how to reduce the equation to a solvable expression, and thereafter apply Lie symmetries to obtain exact solutions. Finally, a case study of the CCR5-<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1357_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\triangle\)</EquationSource> </InlineEquation>32 mutant gene which provides resistance to HIV, is discussed.</p>

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A Lie symmetry approach to migration and gene frequency

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月20日

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  • Sameerah Jamal

摘要

This paper examines a genetic frequency model, governed by a second-order differential equation that includes a migration mean and variance parameters. Such a model is critical for understanding how gene flow affects genetic variation across migrating populations. We prove how to reduce the equation to a solvable expression, and thereafter apply Lie symmetries to obtain exact solutions. Finally, a case study of the CCR5- \(\triangle\) 32 mutant gene which provides resistance to HIV, is discussed.