  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 nature 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.
