Additive Channels in Curved Fitness Landscapes

Additive genetic models often predict evolutionary change reasonably well, even though fitness landscapes can be curved and gene interactions are common. This paper explores one possible explanation: populations may frequently reside in regions of genetic space where local curvature contributes relatively little to fitness variation, so that linear predictions remain adequate. We call such regions additive channels. We develop a diagnostic, the additivity index, that compares the extent to which genetic variance in fitness arises from the slope of the fitness surface versus its curvature. Under Gaussian assumptions, the additivity index equals the fraction of genetic variance in local log-fitness explained by the linear term, providing an analogue of the coefficient of determination for prediction accuracy. We connect this diagnostic to a dynamical framework in which selection reshapes genetic covariances within generations while recombination and mutation modify that structure across generations. This framework suggests conditions under which additive channels may persist and conditions under which populations may exit them. We discuss how these ideas relate to existing work on the maintenance of additive variance and the success of breeding programs, while acknowledging the limitations of our approach and the many questions that remain open.