A quantitative model of carcinogenesis based on methods from population biology and game theory demonstrates normal cells in vivo occupy a ridge-shaped maximum in a well-defined tissue fitness landscape, a novel configuration that allows cooperative coexistence of multiple cellular populations. This state, although necessary for development of functioning multicellular organisms, is subject to invasion by fitter, mutant phenotypes permitting somatic evolution of cancer. The model demonstrates carcinogenesis is an emergent phenomenon requiring a sequence of evolutionary steps as cellular proliferation follows successful adaptation to varying environmental constraints. In the initial development of preneoplastic lesions, cellular proliferation is controlled exclusively by interactions with other cells, the extracellular matrix, and soluble or insoluble growth factors so that gain of function mutations in oncogenes, loss of function mutations in tumor suppressor genes, and disruption of normal senescence pathways will permit clonal expansion. This provides explicit selection mechanisms for the mutations depicted in the classical Fearon-Vogelstein model of colorectal carcinogenesis. The model demonstrates neoplastic cellular proliferation can also be promoted by alterations in the somatic landscape that reduce inhibitory signals produced by the normal cells and extracellular matrix. This is consistent with experimental evidence for a strong microenvironmental influence in tumorigenesis independent of genomic changes in the neoplastic populations. However, we find that these changes alone produce only self-limited neoplastic growth because cellular crowding alters system dynamics so that proliferation is dependent on substrate availability. Consequent cellular competition for critical nutrients results in Darwinian selection pressures favoring phenotypes that increase substrate delivery (e.g., angiogenesis) or uptake (e.g., amplify membrane transporters). These previously unknown substrate dynamics in the later stages of carcinogenesis provide a mechanism for evolution of cellular properties typically found in invasive cancers including the angiogenic and glycolytic phenotypes.