A Lie symmetry approach to migration and gene frequency

Abstract

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.