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A Pokémon's Nature affects the growth of it's stats. The only Natures that don't seem to effect a Pokémon's stats are Bashful, Docile, Quirkey, and Serious. The other Natures increase the growth rate of one stat, while decreasing the growth rate of another (for example, if your Pokémon has the NatureAdamant, it's Attack stat will rise quicker than normal, while it's SP. Attack wil rise more slowly. Natures also affect what flavour of PokéBlocks it likes, and which ones it detests.