From the divided dorsal shield, apparent phoretic association with the beetle, and size, this mite appears to be a deutonymph of Parasitidae, Parasitinae (Acari: Mesostigmata).

Seems to be a rather big mite for a small beetle, but if this is one of the dung-feeding Ataenius, then the association is not unlikely. Parasitines are often predators on insects, their eggs, and nematodes in dung. Dung occurs in patches and mites don't have wings, so they like to hitch rides on insects. If one of the turf feeding Ataenius, then it is more likely an accidental association.

Re as many mite species as insect species, probably not - mites aren't as diverse in their feeding habits on plants. But mites probably come second in animal species.

something along the same lines from this past winter. Evidently, there is a massive shift of opinion on mites in the wind if it isn't already here. BTW, I should elaborate that the mites *looked* the same (color, apparent segmentation,etc.) but varied in size... Truth to tell, I am ill-equipped to make the judgement that they *are* the same species (or even in the same genus).