It needs to be a closely related species with similar color pattern. And even than it will not be certain. You can sometimes have two females of the same species and neither change sex.
Sex change is a socially induced event, not all females in the wild turn into males. Since they live in harems, there needs to be considerably more females than males. As a result, there needs to be certain cues for a female to change to a male. For some species, absence of a male is enough. For others there needs to be several females and no male.
Leopard wrasses, melanurus wrasse and fairy wrasses are in different genuses. I don't think presence of these will have an influence on pink margin.
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