In Creature Stage
In the creature stage, Alphas are stronger than normal creatures. They have about 25% more health and are harder to impress. Killing or befriending one will give your creature a new part.
In Tribal Stage
In Civilization Stage
Sometimes, Alpha sized creatures can be seen wandering around. They only attack other creatures wandering around, and will flee when approached by a vehicle.
In Space Stage
Same as Civilization Stage.
Alpha Creatures would not have appeared in the Molecular Stage as no creatures existed at that time. They may have appeared in the Aquatic Stage, and would have appeared in City Stage acting the same as Civilization Stage Alphas do.