The way societal traumas manifest is tied to the types of trauma each demographic experienced and experiences (including their own self-perceptions of the ways in which they have been victimizes).
Poverty is often a stressor that squeezes out behavior we tend to identify as criminal, but it just a common factor in exposing the wounds.
Depending on the group in poverty, it may manifest as gun violence, physical violence without guns, domestic violence, theft, stimulant abuse, opiate abuse, and a myriad of other things.
i.e. if your cultural wound is to feel powerless, a gun may make you feel powerful; in charge.
If the wound is anxiety, you might choose to numb out.
Controlling for wealth only gets you so far because it is a single dimension.