The genetic analysis of age-dependent traits: Modeling the character process

The extension of classical quantitative genetics to deal with function-valu ed characters (also called infinite-dimensional characters) such as growth curves, mortality curves, and reaction norms, was begun by Kirkpatrick and coworkers. In this theory, the analogs of variance components for single tr aits are covariance functions for function-valued traits. In the approach p resented here, we employ a variety of parametric models for covariance func tions that have a number of desirable properties: the functions (1) are pos itive definite, (2) can be estimated using procedures like those currently used for single traits, (3) have a small number of parameters, and (4) allo w simple hypotheses to be easily tested. The methods are illustrated using data from a large experiment that examined the effects of spontaneous mutat ions on age-specific mortality rates in Drosophila melanogaster. Our method s are shown to work better than a standard multivariate analysis, which ass umes the character value at each age is a distinct character. Advantages ov er existing methods that model covariance functions as a series of orthogon al polynomials are discussed.