Self-recognition is usually shown by species having encephalisation, i.e. a:

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Self-recognition is usually associated with species having a larger cerebral cortex, as this region of the brain is involved in higher-order cognitive processing such as self-awareness and attention. A larger head or hind-brain does not necessarily indicate the presence of self-recognition abilities. A larger visual cortex may be important for processing visual stimuli, but is not directly linked to self-recognition. A smaller brain is also not necessarily an indicator of self-recognition abilities.

Self-Recognition Is Usually Shown by Species Having Encephalisation, I