Constraints on the evolution of function‐valued traits: a study of growth in Tribolium castaneum

Growth trajectories often impact individual fitness. They are continuous by nature and so are amenable to analysis using a function‐valued (FV) trait framework to reveal their underlying genetic architecture. Previous studies have found high levels of standing additive genetic (co)variance for growth trajectories despite the expectation that growth should be responding to frequent strong directional selection. In this study, the FV framework is used to estimate the additive genetic covariance function for growth trajectories in larval Tribolium castaneum to address questions about standing additive genetic (co)variance and possible evolutionary constraints on growth and to predict responses to four plausible selection regimes. Results show that additive genetic (co)variance is high at the early ages, but decreases towards later ages in the larval period. A selection gradient function of the same size and in the same direction of the first eigenfunction of the G‐function should give the maximal response. However, evolutionary constraints may be acting to keep this maximal response from being realized, through either conflicting effects on survivability and fecundity of larger body size, few evolutionary directions having sufficient additive variance for a response, genetic trade‐offs with other traits or physiological regulatory mechanisms. More light may be shed on these constraints through the development of more sophisticated statistical approaches and implementation of additional empirical studies to explicitly test for specific types of constraints.