Whole-genome search of genes is an essential approach to dissecting complex traits, but a marginal one-single-nucleotide polymorphism (SNP)/one-phenotype regression analysis widely used in current genome-wide association studies fails to estimate the net and cumulative effects of SNPs and reveal the developmental pattern of interplay between genes and traits. Here we describe a computational framework, which we refer to as two-side high-dimensional genome-wide association studies (2HiGWAS), to associate an ultrahigh dimension of SNPs with a high dimension of developmental trajectories measured across time and space. The model is implemented with a dual dimension-reduction procedure for both predictors and responses to select a sparse but full set of significant loci from an extremely large pool of SNPs and estimate their net time-varying effects on trait development. The model can not only help geneticists to precisely identify an entire set of genes underlying complex traits but also allow them to elucidate a global picture of how genes control developmental and dynamic processes of trait formation. We investigated the statistical properties of the model via extensive simulation studies. With the increasing availability of GWAS in various organisms, 2HiGWAS will have important implications for genetic studies of developmental compelx traits. 