School of Applied Sciences, Huxley Building, University of Brighton, BN2 4GJ, Brighton, East Sussex, UK.
Centre for Computational Systems Biology, ISTBI, Fudan University, 220 Handan Road, 200433, Shanghai, People's Republic of China.
BMC Genomics. 2024 Aug 30;25(1):819. doi: 10.1186/s12864-024-10733-0.
Genes exist in a population in a variety of forms (alleles), as a consequence of multiple mutation events that have arisen over the course of time. In this work we consider a locus that is subject to either multiplicative or additive selection, and has n alleles, where n can take the values 2, 3, 4, . We focus on determining the probability of fixation of each of the n alleles. For alleles, analytical results, that are 'exact', under the diffusion approximation, can be found for the fixation probability. However generally there are no equally exact results for alleles. In the absence of such exact results, we proceed by finding results for the fixation probability, under the diffusion approximation, as a power series in scaled strengths of selection such as , where is the effective population size, while and are the selection coefficients associated with alleles i and j, respectively.
We determined the fixation probability when all terms up to second order in the are kept. The truncation of the power series requires that the cannot be indefinitely large. For magnitudes of the up to a value of approximately 1, numerical evidence suggests that the results work well. Additionally, results given for the particular case of alleles illustrate a general feature that holds for alleles, that the fixation probability of a particular allele depends on that allele's initial frequency, but generally, this fixation probability also depends on the initial frequencies of other alleles at the locus, as well as their selective effects.
We have analytically exposed the leading way the probability of fixation, at a locus with multiple alleles, is affected by selection. This result may offer important insights into CDCV traits that have extreme phenotypic variance due to numerous, low-penetrance susceptibility alleles.
由于在过去的时间里发生了多次突变事件，基因在人群中以多种形式（等位基因）存在。在这项工作中，我们考虑一个受乘法或加法选择影响的基因座，并且有 n 个等位基因，其中 n 可以取 2、3、4 等值。我们专注于确定 n 个等位基因中每个基因的固定概率。对于 2 个等位基因，可以找到在扩散近似下的“精确”固定概率的解析结果。然而，对于 3 个等位基因，一般没有同样精确的结果。在没有这种精确结果的情况下，我们通过在扩散近似下找到固定概率的结果来进行处理，该结果是关于选择强度的比例的幂级数，例如 ，其中 是有效种群大小，而 和 分别是与等位基因 i 和 j 相关的选择系数。
我们确定了保留到 次项的固定概率。幂级数的截断要求 不能无限大。对于 不超过约 1 的值，数值证据表明，结果表现良好。此外，对于 2 个等位基因的特殊情况给出的结果说明了一个普遍特征，即特定等位基因的固定概率取决于该等位基因的初始频率，但通常，该固定概率也取决于该基因座上其他等位基因的初始频率及其选择效应。
我们已经分析地揭示了具有多个等位基因的基因座中，固定概率受选择影响的主要方式。这一结果可能为由于众多低外显率易感等位基因而导致表型变异极大的 CDCV 特征提供重要的见解。
