If the mother threw the egg out of the nest, maybe she had a good reason.I really need some help with my eggs a mom robin had made a nest very close to the ground in my backyard and there were 4 eggs she threw 3 out the nest left 1 in the nest 1 did not Crack when it hit the ground so I took it and the egg in the nest since mom had left the nest I put them in a plastic ben on a heating pad on 100 degrees fahrenheit and they have been fertile for 2 days since I saw them and the blood vessels but I candled them today and one still have blood vessels but in 1 I see it's watery when I move it a little and there is small bubbles in it but now alot and the air cell or whatever is still intact I think and I see a dark spot in the egg might be the chick but back with the air cell it is tilted a little I really want to do the float test but please help hoping to get these egg to live ( here's two pictures when she only layed three and the other is her in the nest and where she put the nest but once I get to candle the egg again without moving it much u can see a pink rope think we tied on it there was a baby in one that cracked when she pushed it out and the other had nun prob since it had a hairline Crack in it but when I candle the two again I'll post the pics of both of them
As for the egg left in the nest, there could be many reasons for that too. She might have gone to get a meal, planning to come back. Or she might have decided that egg was never going to hatch, so she abandoned it. Or maybe she decided the nest was not in a safe spot, so she made a new nest somewhere else and started laying new eggs there. Those are just a few samples of reasons the mother bird might be away from the nest, leaving an egg in it.
At this point, I would suggest putting it back, whether it is fertile or not, and then leave it alone. The mother bird can decide what to do with it.I did pit a new pic up there can u tell if it's fertile or not if I give it to a mom I found in the wild I don't wanna give her a non fertile egg
Wild birds generally do better if people do not get involved.
Many places have laws against taking eggs or interfering with wild birds' nests, which is another good reason to leave them alone.