I know this is an old game, but in the GameCube game Pokemon Colosseum (the first), you start off with an Umbreon and an Espeon. Do they always have the same natures and starting stats for each new game? I know they are always boys. I would guess yes for stats, but are the natures random?
The reason this information would be useful is for trying to spawn favorable natures in those two Pokemon if they are indeed random.