  Tumor growth, which plays a central role in cancer evolution, depends on both
the internal features of the cells, such as their ability for unlimited
duplication, and the external conditions, e.g., supply of nutrients, as well as
the dynamic interactions between the two. A stem cell theory of cancer has
recently been developed that suggests the existence of a subpopulation of
self-renewing tumor cells which is responsible for tumorigenesis, and is able
to initiate metastatic spreading. The question of abundance of the cancer stem
cells (CSCs) and its relation to tumor malignancy has, however, remained an
unsolved problem and has been a subject of recent debates. In this paper, we
propose a novel model beyond the standard stochastic models of tumor
development, in order to explore the effect of the density of the CSCs and
oxygen on the tumor's invasive behavior. The model identifies natural selection
as the underlying process for complex morphology of tumors, which has been
observed experimentally, and indicates that their invasive behavior depends on
{\it both} the number of the CSCs and the oxygen density in the
microenvironment. The interplay between the external and internal conditions
may pave the way for a new cancer therapy.
