Department of Mathematics, Uppsala University, Uppsala, Sweden.
Department of Ecology and Genetics, Uppsala University, Uppsala, Sweden; Laboratory of Biometry and Evolutionary Biology, University of Lyon 1, UMR CNRS 5558, Villeurbanne, France.
Theor Popul Biol. 2024 Oct;159:13-24. doi: 10.1016/j.tpb.2024.07.004. Epub 2024 Jul 15.
We introduce a multi-allele Wright-Fisher model with mutation and selection such that allele frequencies at a single locus are traced by the path of a hybrid jump-diffusion process. The state space of the process is given by the vertices and edges of a topological graph, i.e. edges are unit intervals. Vertices represent monomorphic population states and positions on the edges mark the biallelic proportions of ancestral and derived alleles during polymorphic segments. In this setting, mutations can only occur at monomorphic loci. We derive the stationary distribution in mutation-selection-drift equilibrium and obtain the expected allele frequency spectrum under large population size scaling. For the extended model with multiple independent loci we derive rigorous upper bounds for a wide class of associated measures of genetic variation. Within this framework we present mathematically precise arguments to conclude that the presence of directional selection reduces the magnitude of genetic variation, as constrained by the bounds for neutral evolution.
我们介绍了一个具有突变和选择的多等位 Wright-Fisher 模型，使得单个基因座上的等位基因频率由杂种跳跃扩散过程的路径追踪。该过程的状态空间由拓扑图的顶点和边给出，即边是单位区间。顶点表示单态种群状态，边的位置标记多态段中祖先和衍生等位基因的二倍体比例。在这种情况下，突变只能发生在单态基因座上。我们推导出在突变-选择-漂变平衡下的平稳分布，并在大种群规模缩放下获得预期的等位基因频率谱。对于具有多个独立基因座的扩展模型，我们为广泛的遗传变异相关度量的一类推导了严格的上界。在这个框架内，我们提出了数学上精确的论点，以得出存在定向选择会减小遗传变异的幅度，这是由中性进化的界限定的。
