Protogynous hermaphrodite
Encyclopedia
A protogynous hermaphrodite is an animal that begins its life cycle as a female. As the animal ages, based on internal or external triggers, it shifts sex to become a male animal. Many fish, such as the gag grouper
Gag grouper
The gag grouper is a drab, mottled gray fish lacking the distinguishing features of other groupers. It has a pattern of markings which resemble the box-shaped spots of the black grouper. It lacks the streamer-points on the tail fin that scamp and yellowmouth grouper The gag grouper (Mycteroperca...

, undergo just such a metamorphosis. Male fecundity goes up greatly with age more than female's so makes sense to start off as a female and then turn into a male. Small males get very little reproductive success but as they grow they have better reproductive success.

For sea goldie
Sea goldie
Also known as the lyretail coralfish, the lyretail anthias or the scalefin anthia, but may be simply known as the goldfish. The sea goldie is a common sight to scuba divers in the Indian Ocean, and is a typical representative of the subfamily of Anthiinae.-Range:The sea goldie is found in the...

s, one of the females in the male's harem will undergo a sex reversal and become the male.

Protogynous hermaphrodites are quite common in the Anthiinae
Anthiinae
Perhaps the quintessential "reef fish," anthias make up a sizeable portion of the population of pink, orange and yellow fishes seen swarming in most coral reef photography and film...

family.
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