It is said that the stonefish (Synanceia) is able to stay out of the water for up to 24 hours. I wonder how they get oxygen from the air. Could someone explain this?
Two things to add the the answer from @Chris.
We are used to the idea that fish extract oxygen from water using gills. When such a fish is transferred into air we imagine that it can no longer breathe. However fish do in fact obtain a significant proportion of their oxygen through their skin. Furthermore, as long as the gills remain moist it should be possible to obtain some oxygen by direct diffusion from the air into the layer of water surrounding the gills.
According to Rombough PJ (1998) Partitioning of oxygen uptake between the gills and skin in fish larvae: a novel method for estimating cutaneous oxygen uptake. J Expt. Biol. 201: 1763 - 1769
Adults of water-breathing fish typically obtain 10–20 % of their oxygen across the skin, but values as high as 30 % have been reported (Feder and Burggren, 1985).
The cited paper is: Feder, M.E. and Burggren WW (1985) Cutaneous gas exchange in vertebrates: design, patterns, control and implications. Biol. Rev. 60: 1-45. Table 1 of this paper presents measurements for the contribution of cutaneous respiration for a number of species including, for example, the European plaice (Pleuronectes platessa) which apparently can obtain 27 % of its oxygen through its skin.
There are, of course many fish, which are designated as air-breathing e.g. the European eel (Anguilla vulgaris). Table 2 of Feder & Burggren presents data acomparing the contribution of skin and gills for various air-breathing fish in water and in air. In the eel this goes from (skin/gills) 12%/88% in water to 33%/67% in air at 15 °C.
I don't know if stone-fish are designated as 'air-breathing' but it is clear that as long as they are in a moist environment many fish can obtain significant amounts of oxygen from the surrounding air. @Chris suggests that the fish may "turn down their metabolism" under these circumstances. The very fact that the fish is no longer swimming presumably reduces oxygen requirement considerably.
I have been trying to find an answer to this question, but until now, no one seems to have really analyzed why this is possible. The only hint I found comes from this paper:
At periods of low water, stone-fish are often left partially exposed by the retreating tide. At such times they may be surrounded only by a small quantity of water which fills the depression in which each lies and the main mass of water may be a considerable distance away. They can survive long periods (at least 24 hours) out of water providing their surroundings are kept moist.
Obviously the fish only needs minimal moisture to get enough oxygen. I would further speculate that the fish turns down its metabolism during this time to minimize the need for oxygen. This paper is widely cited as a source for this survival time, but there seems to be no follow up on it. What is widely analyzed is the toxin of the stonefish.