In other words, does it take more effort for fish to swim in very deep water than in shallow water.
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It’s less dense because it’s warmer, but if you’re asking if it’s less dense due to the lower pressure, the effect is negligible. Liquids are not compressible. As far as how much effort it takes to swim in more or less dense air it’s probably a wash. The reason why you can’t swim through air is because it’s not dense; you need something to push off against. Each stroke through water gives you hundreds of times more thrust than each stroke through air. Just look how large airplane propellers have to be compared to boat propellers. [Mythbusters](https://www.youtube.com/watch?v=cG8AuhDvh4o) did an episode on this
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