Tourrette Elise, Martin Olivier C
INRAE, CNRS, AgroParisTech, GQE-Le Moulon, Université Paris-Saclay, Gif-sur-Yvette 91190, France.
INRAE, INPT, ENVT, GenPhySE, Université de Toulouse, Castanet-Tolosan 31326, France.
PNAS Nexus. 2024 Jul 26;3(8):pgae314. doi: 10.1093/pnasnexus/pgae314. eCollection 2024 Aug.
During the founding of the field of quantitative genetics, Fisher formulated in 1918 his "infinitesimal model" that provided a novel mathematical framework to describe the Mendelian transmission of quantitative traits. If the infinitely many genes in that model are assumed to segregate independently during reproduction, corresponding to having no linkage, directional selection asymptotically leads to a constant genetic gain at each generation. In reality, genes are subject to strong linkage because they lie on chromosomes and thus segregate in a correlated way. Various approximations have been used in the past to study that more realistic case of the infinitesimal model with the expectation that the asymptotic gain per generation is modestly decreased. To treat this system even in the strong linkage limit, we take the genes to lie on continuous chromosomes. Surprisingly, the consequences of genetic linkage are in fact rather singular, changing the of the long-term gain per generation: the asymptotic gain vanishes rather than being simply decreased. Nevertheless, the per-generation gain tends to zero sufficiently slowly for the total gain, accumulated over generations, to be unbounded.
在数量遗传学领域创立期间，费希尔于1918年提出了他的“无穷小模型”，该模型提供了一个新颖的数学框架来描述数量性状的孟德尔遗传。如果假设该模型中无穷多个基因在繁殖过程中独立分离，即不存在连锁，定向选择会渐近地导致每一代有恒定的遗传增益。实际上，基因会受到强烈的连锁影响，因为它们位于染色体上，因此以相关的方式分离。过去曾使用各种近似方法来研究无穷小模型的这种更现实的情况，期望每代的渐近增益会适度降低。为了即使在强连锁极限情况下也能处理这个系统，我们假设基因位于连续的染色体上。令人惊讶的是，遗传连锁的后果实际上相当奇特，改变了每代长期增益的 ：渐近增益消失而不是简单地降低。然而，每代增益趋于零的速度足够慢，以至于经过多代积累的总增益是无界的。
