Why do AKA's collect frogs, mice, and rabbits?

Within the organization of Alpha Kappa Alpha it's not traditional that members collect animals of any kind.

The organization is represented by the ivy leaf and pearls only. Now some members do collect "frogs" which symbolize that the organization was growing in leaps and reaching new bounds. Some collect "rabbits" for it is said that when a baby rabbit is born the first sound it make's is a Skee-Wee. Then it's obvious why some AKA's collect "mice" for elephants are afraid of mice. Elephants are referring to a Delta Sigma Theta mascot.

What's the history behind the rivalry between the ladies of Alpha Kappa Alpha & Delta Sigma Theta, sororities?

This can be traced back to the year 1912 at Howard University. The 22 members of the Alpha Chapter of Alpha Kappa Alpha Sorority decided they wanted to change the direction of the organization. After splitting into committees and formulating reports on the idea at hand, they unanimously decided to change the name, colors, motto, creed, the shield, and the organization of Alpha Kappa Alpha. A graduate member (Nellie Quander) objected to idea at the finalizing meeting, and rallied enough support from other graduate members in the area and together they shot down the idea. The 22 members persistent in their cause were denounced of their membership in Alpha Kappa Alpha. They reorganized under their own sorority known as Delta Sigma Theta. Thus the 22 founders of DST were in fact members of AKA. Thus from this the famous rivalry was started. *HINT: Delta (means change). Despite this rivalry, Alpha Kappa Alpha and Delta Sigma Theta share some of the same goals---Uplifting the Community, Sisterhood, and Service.