Most modern birds will sit on clutches of eggs to incubate them (this is called 'contact incubation'). And the bird lineage stretches back to the Late Jurassic and Cretaceous (during the Mesozoic). But when did birds start to contact incubate their eggs? We know that these Mesozoic bird eggs were, on average, a lot smaller than modern bird eggs. Does this mean they were too fragile for the adults to sit on?
An obvious place to start might be to look at the fossil record for bird nests and eggs compared to the size (and weight) of the parents. But the problem is that we often don't know which Mesozoic bird laid the fossil eggs that have been found. And there aren't enough fossils of birds sitting in nests.
They found that the pelvic canal width of the Mesozoic birds ranged between 10 to 26 mm (except for a particularly hefty species, Sapeornis chaoyangensis, with a pelvic canal width of 42 mm). These birds likely laid eggs that were 8.6 to 33.9 mm wide (which are a similar size to fossil eggs already discovered). The eggs probably weighed between 0.6 to 10.8 grams (except for our hefty friend who probably laid 41 gram eggs). The birds themselves were calculated to weigh between 120 to 750 grams.
The authors found that these Mesozoic birds could not have contact incubated their eggs without breaking them. Modern birds of a similar weight to these ancient birds typically lay much larger eggs. These Mesozoic birds laid eggs only 25% of the weight you would expect from a similarly sized modern bird!
Of course the paper uses a lot of estimates for body mass and egg mass, so there may be room for movement in the calculations. And the authors state that without knowing exactly what shape ancient eggs were or how thick the shell was, it is difficult to prove their hypotheses. But for the moment, it seems that these Mesozoic birds most likely did not sit on their eggs.
Deeming, D. C., and Mayr, HG. 2018. Pelvis morphology suggests that early Mesozoic birds were too heavy to contact incubate their eggs. Journal of Evolutionary Biology, Accepted manuscript, DOI: 10.1111/jeb.13256.