Final answer:
The incorrect pronoun in the sentence is 'their,' which should be replaced with 'his' to correctly refer to a single male peacock. The tail display is a courtship behavior that serves as an honest signal of the male's quality.
Step-by-step explanation:
In the sentence, 'A male peacock will fan open their brightly colored tail in order to attract a mate,' the incorrect pronoun used is 'their'. This should be replaced with 'his,' as the sentence refers to a single male peacock. The correct sentence would read: 'A male peacock will fan open his brightly colored tail in order to attract a mate.'
The action of fanning the tail is part of the peacock's courtship display, which is intended to signal to females that the male is a suitable and attractive mate. The display of tail feathers is an example of the handicap principle, as it can prove to be a disadvantage by making the male more visible to predators. However, a large and bright tail is also an honest signal of the male's health and genetic quality, making him more appealing to females.