Population ‐ and Quantitative‐Genetic Models of Selection Limits

Abstract

The author is very pleased to dedicate this paper to John Dudley for his contributions to both maize and quantitative genetics. John answered what must have seemed to be an endless number of trivial questions and I thank him for his patience. Torbert Rocheford and Irwin Goldman also provided valuable input on the Illinois selection lines, and Jean-Luc Jannink for many useful comments on a draft version of this paper. ContentsI. Introduction II. Let's Get Small: Response Under the Infinitesimal Model A. Basic Structure of the Infinitesimal Model B. Gametic Phase Disequilibrium and the Additive Genetic Variance C. The Bulmer Effect: Disequilibrium-Induced Changes in the Variances D. The Dynamics of d Under Truncation Selection E. Within and Between-Family Contributions to Additive Genetic Variance III. Modifications of the Basic Infinitesimal Model A. Drift and the Infinitesimal Model B. Robertson's Theory of Selection Limits Under Drift C. Joint Treatment of Drift and Disequilibrium D. The Expected Reduction in N e from Directional Selection E. Test's of Robertson's Model F. Gaussian Approximations Allowing for a Finite Number of Loci IV. Strictly Deterministic Models of Response A. Single-locus Models B. Single-locus Deterministic Limits

Allelic changes in bread wheat cultivars were associated with long-term wheat trait improvements

“…These phenotypic shifts are the consequences of the genetic modifications of plant genomes by selective breeding or specifically the impacts of directional selections on target genes (Allard 1999). Theoretically, intensive directional selection within a narrow range of plant germplasm can be predicted to eliminate rare alleles, increase favorable allele frequencies, reduce genetic diversity, and increase linkage disequilibrium (Robertson 1960;Zeng and Cockerham 1990;Hedrick 2000;Walsh 2005). However, how long-term selective breeding influences a plant genome remains poorly understood .…”

Is Continued Genetic Improvement of Livestock Sustainable?

“…The Illinois maize experiment (Dudley and Lambert 2004) has now continued for .100 generations (years) with N e under 30, yet there is a continuing near linear increase in percentage of oil in the kernel that can be explained only by mutational input (Walsh 2004). Although the low line has reached a real limit, it has almost no oil in its kernel.…”

Genome-based establishment of a high-yielding heterotic pattern for hybrid wheat breeding

“…Substantial maize yield increases were realized in the United States, with grain yield doubled in the past eight decades through hybrid breeding (13). Considering this, along with the role of mutations generating new variations (27), suggests that a heterotic group size of around 16 individuals guarantees a sustainable long-term selection gain in hybrid wheat breeding for Central Europe. Impending genetic vulnerability to evolving pests and diseases, which cannot be tackled with the latent genetic variation present within heterotic groups, can be counteracted with targeted introgressions of relevant major resistance genes into the heterotic groups.…”