标题： 数量遗传学的基因视角 显示英文标题

标题： The gene's eye-view of quantitative genetics

摘要： 对生物种群中连续性状演化的建模是进化生物学中最古老的问题之一，这导致了数量遗传学的诞生。 随着GWAS方法的最近发展，将性状分布的演化与许多位点等位基因频率的潜在演化联系起来变得至关重要，这些共同贡献于性状值。 大多数文章处理这个问题的方法是对性状分布做出假设，并使用Wright公式来模拟性状演化如何在每个单独位点上表现。 在这里，我们从系统的基因视角出发，从一个具有选择、漂变、重组和突变的显式有限位点模型开始，其中性状值是基因组的直接乘积。 我们在强重组的假设下让位点数量趋于无穷大，并用McKean-Vlasov SDE和相应的Fokker-Planck IPDE来描述给定位点的极限行为。 换句话说，典型位点的选择取决于其他位点的平均行为，这可以用焦点位点的定律来近似。 结果包括两个位点的独立性以及给定位点等位基因频率的显式平稳分布（在适应度函数的一些假设下）。 我们恢复了Wright公式和育种者方程作为特例。 显示英文摘要

摘要： Modelling the evolution of a continuous trait in a biological population is one of the oldest problems in evolutionary biology, which led to the birth of quantitative genetics. With the recent development of GWAS methods, it has become essential to link the evolution of the trait distribution to the underlying evolution of allelic frequencies at many loci, co-contributing to the trait value. The way most articles go about this is to make assumptions on the trait distribution, and use Wright's formula to model how the evolution of the trait translates on each individual locus. Here, we take a gene's eye-view of the system, starting from an explicit finite-loci model with selection, drift, recombination and mutation, in which the trait value is a direct product of the genome. We let the number of loci go to infinity under the assumption of strong recombination, and characterize the limit behavior of a given locus with a McKean-Vlasov SDE and the corresponding Fokker-Planck IPDE. In words, the selection on a typical locus depends on the mean behaviour of the other loci which can be approximated with the law of the focal locus. Results include the independence of two loci and explicit stationary distribution for allelic frequencies at a given locus (under some hypotheses on the fitness function). We recover Wright's formula and the breeder's equation as special cases.