This paper investigates surface adsorption and migration on GaAs surfaces theoretically based on the ab initio calculations. First, we calculate the Ga migration potential on GaAs(001)-(2 x 3) surfaces by the ab initio calculations. The calculated migration potential sensitively depends on the Ga coverage. At lower Ga coverages, the most favorable sites are located in the As-dimer region. Whereas, as the Ga coverage increases, favorable lattice sites move from the As-dimer region to the missing-dimer region. Next, we clarify the mechanism of the coverage dependence of migration potential by considering the surface atomic structure and the energy band structure at each Ga coverage. The calculated results show that surface distortion mainly determines the most favorable site at lower Ga coverages. However, after the surface distortions are relaxed at higher Ga coverages, favorable sites are determined by the electron counting model. In addition, to investigate the dynamical behavior of cation adatoms at finite temperatures, we perform Monte Carlo simulations based on the ab initio results. The simulations show that the dynamical behavior of cation adatoms also strongly depends on the Ga coverage. At the initial stage of growth, randomly impinged cation adatoms predominantly occupy the lattice sites in the As-dimer region. While, as the Ga coverage increases, favorable lattice sites change from the lattice sites in the As-dimer region to those in the missing-dimer region, reflecting the coverage dependence of migration potential obtained by the ab initio calculations.