2 is as part of a complex series of chemical equilibria.
Oxygen behaves as a nearly ideal gas, whose concentration is controlled by Henry's Law and currents, the currents determining how well mixed it is, and among other things the depth profile. For those who forgot, Henry's Law says that the concentration of gas well mixed into a liquid, C, is proportional to the partial pressure of the gas above the liquid, p,
where k(T) is a function of the temperature and the molecular identity of the gas. For the purpose of this post, all one needs to know is that as temperature increases k(T) decreases, so the concentration of the gas in the liquid decreases also. The van't Hoff equation can be used to calculate k(T).
In Science Deutsch, Ferrel, Seibel, Poertner and Huey, work out the consequences of a warming ocean on the ability of fish to breathe.
Warming of the oceans and consequent loss of dissolved oxygen (O2) will alter marine ecosystems, but a mechanistic framework to predict the impact of multiple stressors on viable habitat is lacking. Here, we integrate physiological, climatic, and biogeographic data to calibrate and then map a key metabolic index—the ratio of O2 supply to resting metabolic O2 demand—across geographic ranges of several marine ectotherms. These species differ in thermal and hypoxic tolerances, but their contemporary distributions are all bounded at the equatorward edge by a minimum metabolic index of ~2 to 5, indicative of a critical energetic requirement for organismal activity. The combined effects of warming and O2 loss this century are projected to reduce the upper ocean’s metabolic index by ~20% globally and by ~50% in northern high-latitude regions, forcing poleward and vertical contraction of metabolically viable habitats and species ranges.There is an editor's summary which puts this a bit more forcefully
It is well known that climate change will warm ocean waters, but dissolved oxygen levels also decrease as water warms. Deutsch et al. combined data on metabolism, temperature, and demographics to determine the impact of marine deoxygenation on a variety of fish and crustacean species (see the Perspective by Kleypas). Predicted climate and oxygen conditions can be expected to contract the distribution of marine fish poleward, as equatorward waters become too low in oxygen to support their energy needs. Furthermore, even the more-poleward waters will have reduced oxygen levels.Deutsch and co. looked at how the oxygen content would shift populations of cod, seabream, eelpout and rock crab. They define a metabolic index Φ as the ratio of the available partial pressure of oxygen to the oxygen needed by a resting sea critter. When Φ = 1, about all a fish can do is float. OTOH, for Φ < 1 the fish has to go somewhere else to be able to survive. The figure below shows how this shifts under RCP 8.5 in 100 years from the generic 2000 to 2100.