Additive Channels in Curved Fitness Landscapes

Abstract

Additive models of inheritance predict the short-term response to selection remarkably well, even when the underlying biology involves widespread dominance and gene-gene interaction. We argue that this success reflects a property of how fitness varies with the additive genetic component of a trait, not a property of the molecular architecture beneath. We make this quantitative through an additivity index, [A]g, that measures the fraction of local log-fitness variance captured by a linear approximation, with the remainder attributable to local curvature of the fitness surface. Under Gaussian/quadratic assumptions, [A]g equals the squared correlation between the linear approximation and local log-fitness, so 1- [A]g is the fraction of local log-fitness variance not captured by a purely linear predictor. We call regions of breeding-value space where [A]g is high additive channels and develop a coupled selection-inheritance framework that identifies when populations enter, persist in, and leave them. The framework predicts that stable, well-adapted populations can be those for which additive prediction is least informative for directional-response prediction. Article summaryGene interactions are common, yet additive genetic models often predict short-term evolution. We propose that additivity is a local property of where populations sit in breeding-value space on a curved fitness landscape, not a global property of the biology beneath. We define an index, [A]g, that compares slope variance to curvature variance and identifies populations in additive channels for which linear prediction performs well. The framework predicts that elite breeding pools enter such channels under sustained selection, while natural populations near a fitness optimum may leave them because the directional signal collapses.