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Tumor growth, which plays a central role in cancer evolution, depends on boththe internal features of the cells, such as their ability for unlimitedduplication, and the external conditions, e.g., supply of nutrients, as well asthe dynamic interactions between the two. A stem cell theory of cancer hasrecently been developed that suggests the existence of a subpopulation ofself-renewing tumor cells which is responsible for tumorigenesis, and is ableto initiate metastatic spreading. The question of abundance of the cancer stemcells (CSCs) and its relation to tumor malignancy has, however, remained anunsolved problem and has been a subject of recent debates. In this paper, wepropose a novel model beyond the standard stochastic models of tumordevelopment, in order to explore the effect of the density of the CSCs andoxygen on the tumor's invasive behavior. The model identifies natural selectionas the underlying process for complex morphology of tumors, which has beenobserved experimentally, and indicates that their invasive behavior depends on{\it both} the number of the CSCs and the oxygen density in themicroenvironment. The interplay between the external and internal conditionsmay pave the way for a new cancer therapy.

Role of the Interplay Between the Internal and External Conditions in Invasive Behavior of Tumors