"Representing oneself as an existing entity like conspecifics are represented" is a step of an evolutionary approach to self-consciousness.
In a few words:
Our pre-human ancestors were capable of intersubjectivity and had a very limited representation of themselves made of representations of parts of their bodies and of interactions with elements (seen feet&hands, heard shoutings, felt grabbed objects,...). Let's call it an "auto-representation" (to avoid the word "self").
Conspecifics were represented as entities existing in the environment.
Evolution of intersubjectivity toward identification with conspecifics produced a merger of the auto-representation with the representation of conspecifics.
By this merger the auto-representation acquired a characteristic of the representation of conspecifics: be a representation of an entity existing in the environment.
So the auto-representation slowly became about an entity existing in the environment like was the representation of conspecifics. Our ancestors became progressively conscious of themselves as existing entities like conspecifics were represented as existing. This was for our ancestors an elementary version of self-consciousness that can be called "ancestral self-consciousnes" 
You will find a description of that process in a paper (http://philpapers.org/rec/MENPFA-3) and in a TSC 2014 poster (http://philpapers.org/rec/MENCOO)