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Study the genetic variation using Eta functions

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Abstract

This paper studies the genetic variation within species using the Eta base functions. We consider the House of Cards Kingman’s model to study genetic variation. This model analyzes the balance between mutation and selection within species, while other forces that produce and maintain genetic variation cause only perturbations. Since this model is a nonlinear integral equation, we introduce a new numerical method for solving the nonlinear mixed Volterra–Fredholm integral equations. We find the best approximation of unknown functions to solve the integral equation using the Eta functions and collocation method. We derive the error bounds of the numerical method and solve some numerical examples to show the high accuracy of the new numerical technique. Using this numerical method, we study the behavior of the probability density of genes within species by considering three different cases of fitnesses for individuals.

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Acknowledgements

Somayeh Mashayekhi was supported by the National Science Foundation grant DBI 2109990. Salameh Sedaghat thanks CIMPA-ICTP Research in Paris Fellowships program. We thank two anonymous referees for giving us many suggestions that helped us to improve our manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Kennesaw State University, Marietta, GA, 30060, Georgia

    S. Mashayekhi

  2. Imam Khomeini International University-Buein Zahra Higher Education Center of Engineering and Technology, Qazvin, Iran

    S. Sedaghat

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  1. S. Mashayekhi
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  2. S. Sedaghat
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Correspondence to S. Mashayekhi.

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Communicated by Hui Liang.

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Mashayekhi, S., Sedaghat, S. Study the genetic variation using Eta functions. Comp. Appl. Math. 42, 95 (2023). https://doi.org/10.1007/s40314-023-02242-9

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  • DOI: https://doi.org/10.1007/s40314-023-02242-9

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