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Tumors experience temporal and spatial fluctuations in oxygenation. Hypoxia inducible transcription factors (HIF-α) respond to low levels of oxygen and induce re-supply oxygen. HIF-α stabilization is typically facultative, induced by hypoxia and reduced by normoxia. In some cancers, HIF-α stabilization becomes constitutive under normoxia. We develop a mathematical model that predicts how fluctuating oxygenation affects HIF-α stabilization and impacts net cell proliferation by balancing the base growth rate, the proliferative cost of HIF-α expression, and the mortality from not expressing HIF-α during hypoxia. We compare optimal net cell proliferation rate between facultative and constitutive HIF-α regulation in environments with different oxygen profiles. We find that that facultative HIF-α regulation promotes greater net cell proliferation than constitutive regulation with stochastic or slow periodicity in oxygenation. However, cell fitness is nearly identical for both HIF-α regulation strategies under rapid periodic oxygenation fluctuations. The model thus indicates that cells constitutively expressing HIF-α may be at a selective advantage when the cost of expression is low. In cancer, this condition is known as pseudohypoxia or the "Warburg Effect". We conclude that rapid and regular cycling of oxygenation levels selects for pseudohypoxia, and that this is consistent with the ecological theory of optimal defense.

Tumors are not static masses of cells but dynamic ecosystems where cancer cells experience constant turnover and evolve fitness-enhancing phenotypes. Selection for different phenotypes may vary with (1) the tumor niche (edge or core), (2) cell turnover rates, (3) the nature of the tradeoff between traits, and (4) whether deaths occur in response to demographic or environmental stochasticity. Using a spatially-explicit agent-based model, we observe how two traits (proliferation rate and migration speed) evolve under different tradeoff conditions with different turnover rates. Migration rate is favored over proliferation at the tumor's edge and vice-versa for the interior. Increasing cell turnover rates slightly slows tumor growth but accelerates the rate of evolution for both proliferation and migration. The absence of a tradeoff favors ever higher values for proliferation and migration, while a convex tradeoff tends to favor proliferation, often promoting the coexistence of a generalist and specialist phenotype. A concave tradeoff favors migration at low death rates, but switches to proliferation at higher death rates. Mortality via demographic stochasticity favors proliferation, and environmental stochasticity favors migration. While all of these diverse factors contribute to the ecology, heterogeneity, and evolution of a tumor, their effects may be predictable and empirically accessible.