Analysis of moa eggshells suggest that, much like modern ratites like the kiwi, it was male moa that sat on eggs to incubate them while the females went looking for food.
Female moa, which in some species were up to twice the size of the males, would have crushed their eggs had they sat on them.
An excerpt: (read in full here)
“Despite their large sizes, moa eggs were fragile and the researchers were able to show that in most cases the bigger and heavier females would have probably broken the eggs.
“The scientists at Auckland University and Auckland Museum worked with Queensland’s Griffith University to recover DNA from moa egg shells estimated to be 400 to several thousand years old.
“”The smallest species of moa weighed as little as 9kg and the largest up to 250kg, but in most cases the females were considerably heavier than the males – as much as twice the size,” said Craig Millar from Auckland University.”