There's a farm on Route 7 (next to the daycare) where you can farm 24 berry plots, definitely a welcome reintroduction since Gen IV. I've been using it to multiply the berries I collect throughout the game, but I've noticed a few things.

First, how do you get mutations, and what do they do?

Second, what types of mulch are there? So far, I've found Boost Mulch (use three different berries?), which increases the output of the tree, and Surprise Mulch (three of the same berries), which I haven't had the chance to use.

I think the mutations get you rarer berries, and I think the surprise mulch is what gets you those mutations. I haven't tried out berry growing yet, though, since in every game so far it's been really dull! ^^

Berry Mutations from the in-game text I've seen is like... berry breeding. The scientist said I got a mutant Hondew Berry from planting Leppa and Aspear berries next to each other.

Oh hey, I got a few mutations (three Qualot, two Pomeg)!

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Yeah, I got a mutation. I think it was Sitrus and Lum and got me a Tamato berry. Just one, though. ALREADY PLANTED TO MAKE MORE.

A tip: always use Boost Mulch (get some if you don't have any) if you're planting a single berry, and water it frequently. That'll bump up your numbers very quickly. I managed to get 12 Figy berries earlier from a single tree.