There was a good question and answer here: Does mermaid evolution come with buoyancy control?
But I would like to expand the question. I got off talking with a friend, it got me thinking about mermaid buoyancy. It came up that perhaps mermaids should exhibit some synergy or combination of the methods used by fish, sharks and dolphins. An interesting example was that, if a mermaid ascends too quickly, the gas from their swim bladder might empty out into their lungs or stomach, leading them to feel sick.
Reason for This
For plausible reasons this might be the case, I'll point first to the unusual nature of the mermaid granting the possibility of unusual biology. They are a naturally composite creature, so being a further composite biologically seems to build on that narrative.
More importantly, I'll point to the fact they're not exactly a whale, seal, shark or dolphin. Mermaids look pretty light, not like fat-laden sea creatures nor dense sharks. Their presumably muscular tails indicate they will not be as buoyant as humans. So it leaves the question of how they can best control/maintain the preferred buoyancy.
Advantages of Each?
There is the question of which advantages each biological method has, and how they may not mesh well or how they might mesh well.
Swim Bladders: As was mentioned in the other question post, swim bladders are good for saving up energy, if you're not spending much. Mermaids probably won't be spending just about all their time patrolling and hunting like sharks, so ways to preserve energy for low energy activities seem handy.
Large oily livers... I do not know enough about the biological implications of that to talk about pros and cons. It is intended to increase the buoyancy of the creature, not really to reach neutral buoyancy in the case of a shark. A mermaid probably can't afford to have an enormous, oily liver.
This could actually serve as a good reason for a combination. If a mermaid can't have a large enough liver for desired buoyancy, they need other factors involved. That is, assuming a small oily liver isn't much more trouble than it is worth.
Lungs and Swallowing Air: Sharks sometimes swallow air to help them counteract their density. Dolphins and seals apparently control their breath and lung capacity to aid in buoyancy control. The likelihood of these may depend on what mermaids breathe, air, water, or both. The Mermaids I'm thinking of can breathe both. If they still surface frequently, I don't see the problem with them utilizing this techniques for better buoyancy control, in what limited capacity a human-like creature can utilize them (when I tried to swallow air, it hurt).
A point of importance, is that whales apparently don't get much use out of this, because their lungs are too small relative to their great weight. They rely more on their blubber.
Synergy?
The most synergy I can see currently, is mermaids probably have mammal lungs capable of operating in the air, so they are free to use those lungs as divers and mammals do. Since their lungs will probably be pretty large, as humans' are, that makes them more useful for this purpose.
The other point, is simply the ineffectiveness of any one method for the diverse activities mermaids are likely to perform, as human-like creatures of the sea. Adaptability is one of humanity's real strong points, and I would hope the same to be true of mermaids both biologically and technologically.
Anyone with biological/marine knowledge who would like to weigh in?
