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Nature replacement:
All Pokemon stats are the equivalent of a neutral nature by default.
There are five martial art schools in the game. Each school teaches a different "martial art" which focuses on a different stat. The schools have dumb names life "School of the Speedy Pikachu" and "School of the Defensive Snorlax". You can have your Pokemon get trained in a school. Training in a school improves the respective stat, but the school tells you that the Pokemon must choose to "sacrifice" a stat because focusing so much in one way of fighting means they have no way to train in another way. So if you make your Pokemon a Disciple of the Speedy Pikachu, then its speed is increased and you decide which other stat you decrease. The five schools would be available in the first five gym towns, and the corresponding gym would have Pokemon that emphasize that stat. I.E first gym focuses on Defense and has the school that lets you improve your Defense, the little dude at the gym's entrance warns you about Defense and tells you to use special attacks, etc.
Of course you can choose to go train in a different school at any time to change your Pokemon's discipline.
EV replacement:
There are tales of a legendary martial artist who reached enlightenment and now lives as an hermit with his Pokemon away from civilization. He lives in a post-game area and when you reach him he explains that he can realign the chi (EVs) in a Pokemon to focus on different stats. However he cannot create the chi, the Pokemon must earn it by himself through training. If you bring him Pokemon with max EV, then he can readjust the stat in any way you want, literally bringing up a window with the Pokemon's stats and sliders to change them.
