A New Approache To QTL Interval Mapping For Dynamic Traits

Quantitative traits whose phenotypic values change with time are called dynamic traits. Genetic analyses of dynamic traits are usually conducted in the following approaches: (1) treating the phenotypic values at different time points as repeated measurements of the same trait and analyzing the traits under the framework of repeated measurements; (2) treating the phenotypes measured from different time points as different traits and analyzing the traits based on the theory of multivariate analysis; and (3) fitting a growth curve to the phenotypic values across time 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 dynamic traits by fitting the data to a logistic growth trajectory, which only applies to the particular s-shaped growth process. In general, a dynamic trait may show a trajectory in any shapes. We develop a mixed model methodology of QTL mapping for dynamic traits and a maximum likelihood method for parameter estimation and statistical tests. The expectation-maximization (EM) algorithm is applied to perform the parameter estimation. We embed polynomials and B-Spline curves into mixed model framework, respectively, to demonstrate that one can describe a dynamic trait with both sub-models, which are sufficiently general for fitting any shapes of the biological curves. Application of the method is demonstrated using both simulated data and real data collected from a pseudo backcross family of Populus (poplar) trees.