The hidden geometry of breeding constraints.

Thousands of years of breeding and agronomic change have pushed genetic change into increasingly narrow corridors. The approach has worked effectively, but gains are slowing and much genetic variance expected from heritability estimates is not readily found. We propose that breeding constraints, the practical demands that make crops useful, force genetic exploration onto curved, lower-dimensional surfaces within the larger landscape of possibility. In crops, these constraints arise jointly from genetic choices and management decisions about fertilizer, sowing density, weed and pest control, irrigation and harvest logistics, which together define the range of environments in which genotypes are routinely grown. These constraints may hide certain classes of gene interactions from breeding programmes, creating an additive appearance where the underlying biology may remain epistatic. Selection moves by additive steps, but on a curved, constrained surface: the speed looks additive, but the long-term path follows the geometry of the constraints. This framework particularly applies to major crop species subjected to intensive directional selection over many generations for stable agricultural requirements, the context where constraint-based filtering of genetic variance is most pronounced. When selection has had less opportunity to impose its effects and gene interactions are weak, this geometric filtering may be less consequential. But when epistatic effects shape fitness, constraints could hide substantial genetic potential behind these boundaries. This Perspective suggests potential escape routes from current plateaus: strategic wide crosses, transgene combinations and targeted edits that access genetic variance currently excluded by constraints.