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>Trade Evolution
1. The process of going through a trade cable/machine effects the certain species of Pokemon's genes in a way where it forces evolution.
2. The Pokemon does not feel like it has to evolve any higher than it is until it feels unwanted/neglected (how it might feel if it got traded). This would cause it to want to become stronger to satisfy it's next trainer.
>Evolution Stones
Same idea as #1 on trade evolution, being in contact with the Pokemon alters it's genes in a way to force evolution. This could also explain why Eevee do not react to Leaf/Ice/other stones, because those just don't cause Eevee to have a genetic reaction, while the Ice Rock/Leaf Rock in areas do.
>Held Item Evolution
Special items that allow evolution. Rhydon holds the protector to evolve into Rhyperior, so when the process of getting traded happens, it absorbs the item, and that effects something in the genes to force evolution.