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Ultra Beasts are from a dimension where Pokemon and the Pokerus virus developed a symbiotic relationship and were integrated into one species (similar to how mitochondria used to be separate from cells). This altered form of the virus is apparent in the ability Beast Boost, where defeating an opponent raises stats temporarily (rather than raising stats through EVs); it is effectively a faster-acting, but far less permanent boost, integrated as a defense mechanism in the Pokemon.
See also: "This neurotoxin stimulates intense feelings of excitement while causing a loss of inhibitions, which acts to forcibly bring out any latent potential within the host while wearing away at their minds." The "neurotoxin" is actually an adapted form of Pokerus, which brings out the latent potential in its human host, while causing other side effects.
"By absorbing the energy of its foes, it triggers a chemical reaction within its body fluids that causes its muscles to grow at explosive rates." Experience gained by defeating foes causes Buzzwole to get massive gains.
This explains why Pokeballs don't recognize Ultra Beasts as Pokemon (while they still recognize other extra-dimensional Pokemon, such as Giratina, Dialga, Palkia ... Haunter -- "Because of its ability to slip through block walls, it is said to be from another dimension"). They are close relatives of Pokemon, but not quite Pokemon.
This may also explain why what seem to be incredibly common Pokemon in Ultra Space (Nihilego) have such high base stats, but that's even more of a reach.
