Do bowfin surface breathe because their gills are less efficient at extracting O2 than more modern fishes?
There is a large spectrum of fish gill ‘efficiencies’; bowfin are not the worst or the best. My friend, Steve Katz, and I created a computer-generated model about this and found that air-breathing could enhance the efficiency of the gill, but whether this happens in ‘real life’ we can’t say with certainty. Another hypothesis (Colleen Farmer) is that air-breathing improves cardiac oxygen levels and is there to improve cardiac function. In other words, like an external coronary circulation. My own view is that air-breathing evolved to regulate buoyancy first, and then became important in low oxygen situations.