Study the genetic variation using Eta functions
Study the genetic variation using Eta functions
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DOI：
10.1007/s40314-023-02242-9
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发表时间：
2023-02
影响因子：
2.6
通讯作者：
Somayeh Mashayekhi;S. Sedaghat
中科院分区：
文献类型：
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作者：
Somayeh Mashayekhi;S. Sedaghat
本文利用Eta碱基函数研究了物种内的遗传变异。我们考虑用金曼的《纸牌屋》模型来研究遗传变异。这个模型分析了物种内部突变和选择之间的平衡，而产生和维持遗传变异的其他力量只会造成扰动。由于该模型是一个非线性积分方程，我们引入了一种新的数值方法来求解非线性混合Volterra-Fredholm型积分方程组。利用Eta函数和配置法求解积分方程解的未知函数的最佳逼近。给出了数值方法的误差界，并通过数值算例说明了新方法的高精度。使用这种数值方法，我们通过考虑三种不同的个体适合度情况，研究了物种内基因的概率密度行为。
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.