The genotype-phenotype relationships are a central focus of modern genetics. While deletion analyses have uncovered many regulatory genes of specific traits, it remains largely unknown how these regulators execute their commands through downstream genes, or executors. Here, we wish to know the number of executors for each trait, their relationships with the regulators and the role natural selection may play in shaping the regulator-executor-phenotype architecture. By analyzing ~500 morphological traits of the yeast Saccharomyces cerevisiae we found that a trait is often controlled directly by a large number of executors, the expressions of which are affected by regulators. By recruiting a set of “coordinating” regulators, natural selection helps organize the large number of executors into a small number of co-expression modules. This way, the individual executors can be readily recognized by observational approaches that examine the statistical association between gene activity and trait. When the trait is subject to little or no selection, however, the executors are controlled only by “non-coordinating” regulators that evolve passively and do not build the executors’ co-expression. As a result, none of the executors remain a statistically tractable relationship with the trait. Thus, natural selection by governing some traits strongly (such as fertility) and others weakly (such as aging-related phenotypes) profoundly influences the genotype-phenotype relationships as well as their tractability.