Developmental quantitative genetic models of evolutionary change.

Discussions about evolutionary change in developmental processes or morphological structures are predicated on specific quantitative genetic models whose parameters predict whether evolutionary change can occur, its relative rate and direction, and if correlated change will occur in other related and unrelated structures. The appropriate genetic model should reflect the relevant genetical and developmental biology of the organisms, yet be simple enough in its parameters so that deductions can be made and hypotheses tested. As a consequence, the choice of the most appropriate genetic model for polygenically controlled traits is a complex tissue and the eventual choice of model is often a compromise between completeness of the model and computational expediency. Herein, we discuss several developmental quantitative genetic models for the evolution of development and morphology. The models range from the classical direct effects model to complex epigenetic models. Further, we demonstrate the algebraic equivalency of the Cowley and Atchley epigenetic model and Wagner's developmental mapping model. Finally, we propose a new multivariate model for continuous growth trajectories. The relative efficacy of these various models for understanding evolutionary change in developmental and morphological traits is discussed.