Mapping quantitative trait loci for longitudinal traits in line crosses.

Quantitative traits whose phenotypic values change over time are called longitudinal traits. Genetic analyses of longitudinal traits can be conducted using any of the following approaches: (1) treating the phenotypic values at different time points as repeated measurements of the same trait and analyzing the trait under the repeated measurements framework, (2) treating the phenotypes measured from different time points as different traits and analyzing the traits jointly on the basis of the theory of multivariate analysis, and (3) fitting a growth curve to the phenotypic values across time points and analyzing the fitted parameters of the growth trajectory under the theory of multivariate analysis. The third approach has been used in QTL mapping for longitudinal traits by fitting the data to a logistic growth trajectory. This approach applies only to the particular S-shaped growth process. In practice, a longitudinal trait may show a trajectory of any shape. We demonstrate that one can describe a longitudinal trait with orthogonal polynomials, which are sufficiently general for fitting any shaped curve. We develop a mixed-model methodology for QTL mapping of longitudinal traits and a maximum-likelihood method for parameter estimation and statistical tests. The expectation-maximization (EM) algorithm is applied to search for the maximum-likelihood estimates of parameters. The method is verified with simulated data and demonstrated with experimental data from a pseudobackcross family of Populus (poplar) trees.