The nature of robustness in development.

A trait is robust to a genetic or environmental variable if its variation is weakly correlated with variation in that variable. The source of robustness lies in the fact that the developmental processes that give rise to complex traits are nonlinear. A consequence of this nonlinearity is that not all genes are equally correlated with the trait whose ontogeny they control. Here we explore how developmental mechanisms determine and alter the correlation structure between genes and the traits that they control. A formula is developed by which the correlation of a gene or environmental variable with a trait can be calculated if the mechanism that gives rise to the trait is known. The nature of robustness and the ways in which robustness can evolve are discussed in the context of the problems that arise in the analysis of inherently nonlinear systems.