Tumor is characterized by extensive heterogeneity with respect to its microenvironment and its genetic composition. We extend a previously developed monoclonal continuous spatial model of tumor growth to account for polyclonal cell populations and investigate the interplay between a more proliferative and a more invasive phenotype under different conditions. The model simulations demonstrate a transition from the dominance of the proliferative to the dominance of the invasive phenotype resembling malignant tumor progression and show a time period where both subpopulations are abundant. As the dominant phenotype switches from proliferative to invasive, the geometry of tumor changes from a compact and almost spherical shape to a more diffusive and fingered morphology with the proliferative phenotype to be restricted in the tumor bulk and the invasive to dominate at tumor edges. Different micro-environmental conditions and different phenotypic properties can promote or inhibit invasion demonstrating their mutual importance. The model provides a computational framework to investigate tumor heterogeneity and the constant interplay between the environment and the specific characteristics of phenotypes that should be taken into account for the prediction of tumor evolution, morphology and effective treatment.