These ideas are based on imagination - very unscientific - open to discussion
So, for animals, what is identity - what is constant, what is security, 'what am I?'.
The section on Body and Breathing discusses the inside feel of our bodies. The Chapter on Tastes and Smells discusses the internal awareness of tastes and smells. I obviously have no proof, but i suggest being in touch with the inside warmth, taste and smell, and the feel of their own bodies from the inside, is a very intimate sense of being, and i believe this is central to an animals identity.
Smell, breath and taste stimulate and are regulated by the lower brain. These basic senses existed long before animals developed eyes and ears. Animals are far more in touch with and reliant on their lower brain. I feel sure this connection with the lower brain has a far greater significance than i can decribe, experts in the field would know more.
Added to this internal self awareness, animal identity involves their territory and usually a deep unquestioned sense of belonging and social confirmation with their partners or social groups.
THE TWO MODES OF SENSING
Animals are not lost in abstract thought about their identity. Life is immediate, and everything they want, like a child, has to be now. And animals have two different sensory systems for relating to the outside world now. Focussing and broadband.
And in the same way as : how we sense the world, determines how we we understand it and ourselves, - an animals sensory abilities, determines their understanding, their relationship with, and their feeling of identity in the world.
An animals experience of focussing must result in a feeling similar to ours, - of being an active subject doing things to objects.
But throughout evolution, going broadband has been their natural way to switch off, stop doing everything and be still and receptive for a moment. It evolved because it is the most direct connection with the outside world. And for animals, this is indirectly a constant reminder of how it feels to be still inside, now, and connected with everything around them.
So i believe, in the few moments animals have, when they can just doze and don't need to fight for survival, they are far more practiced than we are, and much more able to turn off and just be, and feel their bodies warmth and reality. It's a habit, an habitual rut which animals have. And this inner sense of contentment, self sufficiency in their own bodies, gives them an underlying background sense of peace in and with the world.
This is obviously all only guesswork, based on my personal experiences ... highly unscientific. But to go broadband it's necessary to turn off any focussed wanting at will, and this ability becomes habitual, an ability to shut down abstract thought, even when the thought seems very important. And this ability, can be used to stop any narrow minded concentration and thus avoid the human frailty of vicious circles and obsessions.
This all suggests an ego identity based in their individual internal bodies; a state of integration and connection with the world outside; and a social sense of bonding and belonging, far deeper than our human ideas on social confirmation. It's all very different to how humans sense their self-identity and the world around them.