Zebra finches are small songbirds that are both wild and domestic. Pet zebra finches are able to reproduce in captivity, if a male and female bird are present. Parthenogenesis is possible; however, it is the exception to the rule. Because zebra finches lay eggs whether a male fertilizes the egg or not, knowing if a zebra finch is going to produce offspring is a matter of keeping track of her before egg-laying and checking the eggs after egg-laying.
Watch the male zebra finch for the mating dance. He will approach the female while moving his body from side to side. His feet will move in a back and forth motion and he will move closer to the female. While he does this, he will sing.
Inspect the bird enclosure for evidence of nesting. If the female is about to lay eggs, the birds will try to make a nest for those eggs. This is no guarantee that the eggs are fertile.
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Check the eggs three to four days after laying by candling them. Wash your hands thoroughly. Pick up one egg at a time, turn the lights off and shine an LED flashlight through the side of the egg furthest from you. The light will shine into the egg, revealing red blood vessels inside. If these vessels are present, the zebra finches will have babies. Eggs that are infertile will smell within a few days and possibly go untended by the parents.
Provide nesting material for the birds, if they start trying to build a nest.
Do not handle the eggs too much. It could damage them or stress the parents.
Do not hold the candling light up against an egg for too long. It could heat the egg.