A tight coupling between metabolic rate, efficacy of oxygen supply and the temperature sensitivities of marine animals predicts a variety of geographical niches that better aligns with the distributions of species than models of either temperature or oxygen alone. Climate and physiology shape biogeography, yet the range limits of species can rarely be ascribed to the quantitative traits of organisms(1-3). Here we evaluate whether the geographical range boundaries of species coincide with ecophysiological limits to acquisition of aerobic energy(4)for a global cross-section of the biodiversity of marine animals. We observe a tight correlation between the metabolic rate and the efficacy of oxygen supply, and between the temperature sensitivities of these traits, which suggests that marine animals are under strong selection for the tolerance of low O-2(hypoxia)(5). The breadth of the resulting physiological tolerances of marine animals predicts a variety of geographical niches-from the tropics to high latitudes and from shallow to deep water-which better align with species distributions than do models based on either temperature or oxygen alone. For all studied species, thermal and hypoxic limits are substantially reduced by the energetic demands of ecological activity, a trait that varies similarly among marine and terrestrial taxa. Active temperature-dependent hypoxia thus links the biogeography of diverse marine species to fundamental energetic requirements that are shared across the animal kingdom.