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This answer says that breathing water is inefficient, and that may act as a limiter to the size of fish. I've heard this in a couple of other places as well, but cannot recall the sources. However, the Wikipedia page on allometry indicates that metabolic rate and oxygen consumption scale logarithmically with mass, which implies that the ratio of required oxygen to mass will be lower in larger animals than smaller ones. As such, I would think that the size of respiratory organs would shrink relative to the over-all size of the animal as it is scaled up. The answer linked above even says:

Gills grow in proportionate scales to body size, generally for every 100% increase in body size there is a 50-90% increase in gill size.

Which is entirely compatible with the (admittedly naive) application of allometric organ scaling. How, then, does access to oxygen limit fish growth?

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  • $\begingroup$ water contains drastically less oxygen, it is not about gills vs lung anatomy. air contains about 21% free oxygen, while water contains about 1% dissolved oxygen. $\endgroup$
    – John
    Commented Mar 30, 2021 at 3:25
  • $\begingroup$ I've heard this point made before, but I'm really struggling to understand it's relevance. If the issue is about the concentration of oxygen in the water, then I would think that should impede oxygen absorption rate only by a constant factor. This constant factor should already be accounted for by a constant factor increase to surface area for absorption. Then, when comparing larger fish to smaller fish, the difference should be in the logarithmic function of the mass increase. Is this incorrect? $\endgroup$
    – Charlim
    Commented Mar 30, 2021 at 3:45
  • $\begingroup$ this may help you understand, why is it harder to breath at high altitude, lower oxygen content due to lower air density. above a certain altitude the oxygen content is too low to survive on. If you are taking in less oxygen you are producing less metabolic energy. the mass of the organism has no effect on the oxygen content of what they are breathing, and the efficiency of a breathing mechanism cannot compensate for such a large difference. $\endgroup$
    – John
    Commented Mar 30, 2021 at 3:50
  • $\begingroup$ I'm afraid I still don't follow :s It's clear to me why breathing less dense air would prove problematic for animals in general, but it's not clear to me why that would put a cap on animal size. Surely, if there is enough oxygen at a given altitude for a small creature, then another animal with double the metabolic rate would simply need to breath twice as much air. I don't mean that they absorb oxygen more efficiently, perhaps their lungs are just twice as large, so twice as much oxygen can be inhaled, regardless of it's density. $\endgroup$
    – Charlim
    Commented Mar 30, 2021 at 4:50
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    $\begingroup$ you can only speed up breathing so much before it results in less oxygen uptake, gas exchange takes time. the other problem is water, bigger lungs means more water loss via breathing, soon you reach the point you can't replace the water as fast as you lose it, the same thing happens will gills in salt water. $\endgroup$
    – John
    Commented Mar 30, 2021 at 13:15

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