Tyrannosaurs did have a sternum, however. It wasn’t an overly large sternum, but it did have a sternum. I don’t see how the sternum could be vestigial (i.e., without significant function). It is used in breathing as well as flight. You are probably talking about the absence of a keel rather than a sternum. I agree that the absence of a keel probably says that flight had faded away in the Tyrannosaur ancestor. Or maybe the ancestors of the Tyrannosaur didn’t fly at all. However, I am sure that the Tyrannosaur had to breath when running after pray.
The Tyrannosaur had no keel. However, it did have a sternum to which some ribs were attached. The arms were also attached to the sternum. So I conjecture that the sternum was mostly used for breathing. The arms may have also been used in breathing. Maybe the fused clavicle and forearm bones were used in pneumatic respiration.
I am not a professional biologist. I have not examined the issue of the small forearms closely. However, I have been reading about the pneumatic bones of arcosaurs. I know that the humerus of birds and some dinosaurs are hollow. So I conjecture that the forearms could be doing something for respiration.
http://www.ucmp.berkeley.edu/diapsids/birds/birdmm.html
‘Bird bones are hollow and filled with extensions of the body's air sacs, which are extensions of the lungs that allow for increased respiratory efficiency. ‘
Many birds that don’t fly have a very small sternum and no keel. The keel is obviously necessary for flight.
http://www.ucmp.berkeley.edu/diapsids/birds/birdmm.html
‘As birds go, the domestic chicken is hardly built for high-performance flight. Yet even in the chicken skeleton shown here, many of the flight adaptations found in most birds can easily be seen. The sternum, or breastbone, bears a prominent keel where the flight muscles attach. (Note that Archaeopt eryx and several other early fossil birds lacked this sternal keel, and the flightless ratite birds -- such as the ostrich, emu, and rhea -- also lack the keel.)’
http://www.life.illinois.edu/ib/461/Internal_Anatomy.pdf
‘Air sacs also help to dissipate heat, as air passing through the air sacs absorbs heat and is then expelled from the body. Birds also lack a diaphragm thus breathing is thus powered by the intercostal muscles.’
https://en.wikipedia.org/wiki/Intercostal_muscle
‘Intercostal muscles are several groups of muscles that run between the ribs, and help form and move the chest wall. The intercostal muscles are mainly involved in the mechanical aspect of breathing. These muscles help expand and shrink the size of the chest cavity to facilitate breathing.’
I think the theropods had hollow bones in their forearms. Furthermore, the ribs and sternum were important for breathing. So maybe the question has to do with pneumatic breathing.
So it seems to me that even if pneumatic bones lost their original grasping function, or their original flying function, they would still retain some use in respiration.
I have no doubt if I died in the henyard they'd have my bones picked clean before I was found.
Yeah, we had some pretty mean chickens too. I remember one once had a 3 or 4 foot snake caught killed and slowly eaten. The snake was too big to swallow, and chickens cant really chew off pieces, so the chicken after pecking and shaking the snake until all the bones broken ran around with part digesting in it's craw and the rest hanging out. It took 2 days to finally swallow and digest the whole snake. The chicken of course had all the hundreds of other chickens chasing it around trying to steal the exposed tail the whole 2 days!
