How does the genetic architecture of quantitative traits evolve over time? Answering this question is crucial for many applied fields such as human genetics and plant or animal breeding. In the last decades, high-throughput genome techniques have been used to better understand links between genetic information and quantitative traits. Recently, high-throughput phenotyping methods are also being used to provide huge information at a phenotypic scale. In particular, these methods allow traits to be measured over time, and this, for a large number of individuals. Combining both information might provide evidence on how genetic architecture evolves over time. However, such data raise new statistical challenges related to, among others, high dimensionality, time dependencies, time varying effects. In this work, we propose a Bayesian varying coefficient model allowing, in a single step, the identification of genetic markers involved in the variability of phenotypic traits and the estimation of their dynamic effects. We evaluate the use of spike-and-slab priors for the variable selection with either P-spline interpolation or non-functional techniques to model the dynamic effects. Numerical results are shown on simulations and on a functional mapping study performed on an Arabidopsis thaliana (L. Heynh) data which motivated these developments.