I think the hardest thing to nail down is the varying definition of the soul throughout time. For example Aristotle speaks about animal souls in Περί Ψυχής (On the Soul), but his use of this word "ψυχή" certainly doesn't carry the post-christian meaning that soul has taken up. It would be more accurate to say that he believed that animals like man had a life giving force or animating energy summed up in the soul, but he believed only the soul of man carried intellect.

To this end Marcus Aurelius would have carried a stoic perception of the soul which would have been a bit closer to ours in that stoics believed that souls were fractions of the "πνεύμα" which can be thought of as this much larger universal animating force, and that these souls would coalesce after death. To what degree he thought that animals were part of this too is most likely debatable, but one could argue that his using the same word for human and animals souls may link these arguments.

As for a source of this stoic physics I know that there are many Greek sources that I have read summaries of, but I only have read Ciceros "De Natura Deorum" in the original, where he also cites the stoics as having this belief.