| Quantitative traits whose phenotypic values change with time are called dynamic quantitative traits. Mapping and determining the underlying variants is an important problem in genetic study. Genetic analyses of dynamic traits are usually conducted in one of two ways. One is to treat phenotypic values collected at different time points as repeated measurements of the same traits, which are analyzed in the framework of multivariate theory. Alternatively, a growth curve may be fit to the phenotypes at multiple time points, and inferences can be made through the parameters of the growth trajectories. The latter has been used in quantitative trait loci (QTL) mapping for developmental traits. Fitting the dynamic trait model using the logistic growth curve applies only to the particular s-shaped growth trajectory. In general, a dynamic trait may show a trajectory in any shape, e.g., linear, quadratic, cubic, exponential, and so on. We demonstrated that one can fit dynamic traits with the B-splines, which are sufficiently general for any shape of trajectory by selecting various orders of the B-splines.; In this work, we took a Bayesian approach implemented via the Markov Chain Monte Carlo (MCMC) algorithm to estimate the positions and effects of multiple QTLS. The entire genome was divided into a finite number of regions. QTL effects at all regions were evaluated simultaneously. With this method, regions with no actual QTL will have negligible estimated QTL effects. The method was demonstrated with simulated data as well as data collected from published experiments on trees. The simulation results show that the proposed techniques have high power of QTL detection and high precision of the parameter estimation. |
