Population ecology mathematical models examine tumors not as an isolated collection of transformed individuals but as part of a dynamic society of interacting malignant and normal cells. This approach investigates the mechanisms by which a small clone of neoplastic cells is able to replace the much larger and previously stable population of normal cells, despite the numerical advantage of the latter and the inhibitory effects of the host response. The models define a sequence of different stable equilibria with critical mathematical parameters which control the outcome of different stages of the neoplasm-host competition--parameters which can be correlated with cellular physiologic properties. When neoplasm is viewed as a network of interacting tumor and normal populations, a unifying hypothesis can be developed that allows the diverse but inconsistent properties of transformed cells to be understood according to their specific contributions to tumorigenesis within this network. It predicts general sequences of genetic changes necessary for tumor survival and invasion and demonstrates that apparently disparate properties found in different tumor models can be functionally equivalent. The paper proposes novel modes of therapy requiring classification and treatment of tumors according to the strategies they employ, rather than the traditional criteria of cell type and organ of origin.