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Parrot fish have more options than just male or female. Because they have been crossed with different species of fish that use different places in the DNA code to determine whether they will be male or female, parrot fish (the blood parrot hybrids in the hobby, not the true parrot fish of South America) parrots can have very mixed messages constructing their sexual organ, or no DNA instructions at all. They may be male or female. They may have some male parts and some female parts which means they are sterile. They may have all of the parts for both male and female, making them capable of both laying fertile eggs and producing viable sperm. They can mate with either a male or female, or simply lay "her" eggs and then fertilize them "himself". Their genome may not have had any comprehensible instructions for the sexual organs and so skipped this part of construction entirely. Normally you can say that a cichlid that lays eggs is a female and if those eggs hatch, the other fish of the pair is a male. it is more complicated with blood parrot fish. The shape of the head is determined by the gene for a deformed face. it has nothing to do with what sex the fish is. Many species of cichlid produce a few short faced (bulldog) culls. Ethical breeders remove these from the pool of breeders but some opportunist saw the "blood parrot" as a way to create a "new fish".