Which animals are thought to possess some degree of a theory of mind? Most dog owners would insist that their dogs have a strong theory of mind, and I have read abstracts that support this idea - for instance, a dog who knows better than to snatch a piece of forbidden food from a plate on the floor while his or her master is looking becomes more likely to do so when the lights are turned off, which suggests that the dog understands that the owner can't see what he or she is doing in a dark room.  I've also noticed that a dog will react differently when he or she is intentionally hurt by a mischievous child than he or she does when someone accidentally steps on his or her tail or paw.  These phenomena suggest that dogs might understand that our perception is different from theirs, and that there is a difference between intentional harm and accidental harm.

Many of us would probably assume that higher primates are almost as skilled as we are in the use of the theory of mind, and again, I have seen research that seems to back this up.  A chimp is placed in a room with plexiglass walls.  The room faces a hallway.  A hole in the wall allows the chimp to grab fruit from a tray in the hallway.  A researcher walks into the hallway, picks up the tray, and throws it down the hall.  The chimp goes ballistic.  However, when the same process is repeated, but this time, the researcher pretends to accidentally trip over the tray, the chimp is less agitated, and instead of throwing a tantrum, he or she merely gestures towards the tray and waits to see if it will be returned to its original position.  This suggests that chimps know the difference between accidents and intentions, which is not particularly surprising, considering how complex (and dangerous) chimpanzee society is.  

Add to this anecdotal reports of whales and dolphins apparently showing gratitude when humans assist them (removing nets in which they've become tangled, for instance), and many similar accounts.

Do we have any idea which nonhuman animals possess a theory of mind, at least to some degree?
Well, the areas most responsible for social cognition (or theory of mind) appear to be the right and left temporoparietal junctions, the right anterior superior temporal sulcus, the posterior cingulate, and the medial prefrontal cortex. [1][2] Of those, the right TPJ is perhaps the most important; for example, the response in the rTPJ shows a peak just at the time when someone’s thoughts are described. [3]

Given the perceived importance of the temporal lobe to theory of mind, it is probably a safe bet that you wouldn't find many non-mammals that experience ToM the way a human does.

Furthermore, among the many hypothesized 'signs' of ToM possession is the ability to recognize oneself in the mirror. This ability implies a level of self-awareness and identity awareness in the individual, and it appears that primates (chimpanzees and orangutans) are the only non-human animals that have successfully recognized themselves in the mirror. [4] Monkeys are also the only other animals to have confirmed rudimentary mirror neurons, which are hypothesized to play an important role in empathy and social cognition. However, there are pieces of evidence that suggest that mirror neuron networks may possibly exist in elephants, dogs, dolphins, and whales.

That being said, the evidence isn't wholly clear on this one, and is further augmented by the fact that we don't necessarily have a working cognitive model for ToM (outside of our verbal conceptual models, which are not exactly scientifically rigorous). Some researchers even believe that ToM is a uniquely human experience. However, until we can lock down what exactly it is we are looking for, this remains a tricky question to make any sort of scientifically rigorous assertion.



Sources used:

[1] Dodell-Feder, D., Koster-Hale, J., Bedny, M., Saxe, R. (2010). fMRI item analysis in a theory of mind task. NeuroImage. 

[2] Deen, B., Koldewyn, K., Kanwisher, N., Saxe, R., (2015) Functional Organization of Social Perception and Cognition in the Superior Temporal Sulcus. Cerebral Cortex

[3] Young, L., Cushman, R., Hauser, M., &amp; Saxe, R. (2007). The neural basis of the interaction between theory of mind and moral judgment. PNAS, 104(20), 8235-8240

[4] G.G. Gallup (1982). Self-awareness and the emergence of mind in primates.
Am. J. Primatol., pp. 237–248