Pokemon in this game do evolve- enough time spent working with a pokemon and using it to fight will let it evolve into a more powerful form. Be alert, though- a new form also means a new attack move, and while the evolution always causes a change, that change may not be an improvement to your way of thinking.
Pokemon do -not- have levels, however. Instead they track their evolution with two different elements- the pokemon’s energy, and its Link.
Energy is how positive or negative the pokemon is feeling. When it gets knocked out in battle or affected by certain abilities its energy goes down. When it wins a battle, eats ponegiri, or does something else with its warrior (goes shopping, digs in a mine, helps turn on a machine, et cetera) its energy will improve a certain amount. This is indicated by a small arrow that appears with the pokemon’s info- a redder and more upwards arrow is a more positive energy, and a bluer, downward arrow is a negative energy. Additionally, every three months or so, each pokemon’s energy will improve or degrade slightly, randomly determined. This means that you cannot just get a pokemon’s energy up and then leave it there- over time, it will often even out unless you keep that pokemon active. As if that were not enough, energy affects random chance- a pokemon with a more positive Energy is more likely to hit with its attacks and scores critical hits more often. A pokemon that is feeling ‘blue’ will often fail to connect its attacks, wasting valuable time. Similarly, energy affects a pokemon’s chance of dodging incoming attacks.
Link is even more important. This measures the connection a pokemon has with its warrior. A higher Link not only gives the pokemon more raw power in terms of its ability scores, it improves the strength of the pokemon’s attack as well. A pokemon with a poor Link will have a -1 or even a -2 next to its attack, indicating a reduced power of the attack, and a pokemon with a strong Link can have as much as a +2 rating on its attack.
Link and energy go together to determine a pokemon’s evolution- pokemon will not evolve when their energy is not strongly positive, preventing them from gaining power even if their Link rating increases. As far as Link is concerned, if a pokemon would evolve in the core games at a given level, you generally will need to get it to have a Link rating whose percentage is about double the level it would have needed to evolve. Pokemon that previously evolved through a high Happiness or ‘love’ rating, and pokemon that originally evolved via the use of evolutionary stones or trading have an even less clear method of determining their evolution that I have not yet devised. I’ll certainly place an article on it when I do, though.