Short answer: The trait choices are random.
Long answer: Each trait is more or less likely to pop up in the list of 5 choices based on it's rarity (common, uncommon, rare) and also your specialization pick (Assassin, Governor, etc). There is a general pool of traits everyone MIGHT see, and a secondary pool of traits added to that once you specialize. You're likely to see the "strength" trait eventually, unless you're a dedicated spell caster (the spell level ranks seem to be VERY COMMON, and if you have 4-5 spell schools they will often take up most of the leveling choices). If you are desperate for that particular trait you could save the game prior to a level up fight. You will get a different random list every save game reload, however, since the game only counts what you have EQUIPPED against your encumbrance... I've found "strength" is nice, but not something I'd resort to save game reloading over.
Now a 0 essence capital city starting location... reload map generation. 
