I was thinking about the question why only birds have hollow and therefore lightweight bones. The birds bones are strong enough to support them in any way so why don't other animals also have this bone structure? Wouldn't it be an advantage to be lighter which needs less energy, less time to find food and so on?

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Bird bones are not necessarily lighter overall than for example mammal bones of similar size; they may be almost hollow, but they are also made of significantly denser material, which can make them stronger but heavier per unit bone. This may be one reason why there's no pressure on other land vertebrates to evolve hollow bones; or put differently: thi smay be one reason why bird ancestors found hollow bones advantageous, as they would otherwise be too heavy (this assumes that the denser material evolved before the hollowness).

They characteristic to make bones hollow probably originated in birds' ancestors at some point in the Triassic Period (about 230 million years ago). At this time in earth's history the atmosphere apparently contained much less oxygen than today (dropping below 15% after the Permian/Triassic Mass Extinction; as opposed to today's 21%). The group of dinosaurs that bird belong to, the Sauriscia, evolved at around this time, and all of them had hollow bones to some extent (including the giant sauropods). One theory is that as the air sacs that filled these hollows are a part of the lung system, the extra surface area allowed them to get more oxygen out of the depleted air. This came in handy later when oxygen levels rose and they could afford to use the extra oxygen for the very oxygen-intensive activity of flying.

After having said all that though, beware that these may simply be "Just So" Stories.

Pterosaurs also have the same hollow-bones system in common with the saurischian dinosaurs and it's certainly linked to the air-sac system and their respective breathing mechanisms. Quite why it originally evolved is certainly contentious, but the two are intricately linked and it's not a case of 'just' lightening the bones. Remember than big mammal bones are hollow already as they contain bone marrow which grows your red blood cells.

There are other ways of doing this too - if you ever get hold of a fresh bat skeleton you'll see that the bones are actually mostly sort of rubbery and flexible. So by cutting down on the crystalline (and very dense) part of the bones and maximising the collagen (which is lighter and more flexible) the bats reach a compromise where they have enough bone for support, but it's lighter than that of other mammals.