In this work, the quantum dot (QD) formation of InAs on In_0.5Ga_0.5As/InP(001) has been studied theoretically using a hybrid approach. The surface energies were calculated using density functional theory. For elastic relaxation energies, continuum elasticity theory was applied. This hybrid method, as already shown in the literature, takes into account the atomic structure of the various facets of the QDs as well as the wetting layer. Our study deals with the aspect of shape evolution of InAs QDs on a ternary substrate. It shows how the island shape close to equilibrium evolves with varying volume in InAs/In_0.5Ga_0.5As/InP (001) epitaxy. Overall, our study indicates that for this system, there may exist two paths for island growth: one path involves an early energetic stabilization of flat, hut-shaped islands with high-index facets (that may persist due to kinetic limitations), whereas the other path involves islands with larger height-to-base ratios that develop low-index facets. At large volumes, the steeper but more compact islands tend to be energetically more favourable compared to the elongated shapes.