Ayaapia Kiilhswa ‘Buck Moon’ (listen to the pronunciation on the Myaamia Online Dictionary) is one of two lunar months named for moohswa ‘White-tailed deer (Odocoileus virginianus).’ To the best of our knowledge, this month is associated with the end of the rut (breeding cycle) and the older males losing their antlers.
Today, there is a lot of variation within moohswa populations regarding when bucks drop their antlers. It appears that historically, the older moohswa bucks dropped their antlers after younger males. The loss of antlers marks the end of the rut for these more mature males.
You can learn more about White-tailed deer by visiting Wikipedia.