Animal Communication does it exist?

Yule states that "there are a lot of stories about creatures that can talk. We usually assume that they are fantasy or fiction or that they involve birds or animals simply imitating something they have heard humans say."(1) Do we as humans really believe that animals are capable of communicating because they imitate us? Or do we believe that they have their own way of communicating? I believe that animals may seem to have language based on sound. However, these sounds are not language because they lack displacement, arbitrariness and productivity.