How big does genes play for those who stutter?

How big does genes play for those who stutter? My wife and I are expecting our first child later this spring. We have over the moon and blessed to become a family of three however my wife is considered about one thing; her stutter. From what I under stand stuttering is genetic for the most part. My wife is the only person in her family who stutters (she had a grandfather who stuttered). She also told me that when growing up in Puerto Rico - her family didn't have a lot of money and couldn't afford proper speech therapy as a child (my wife is convinced had attended speech therapy as a kid - her speech would have been either stutter-free or barely noticeable). I do not stutter not have any family members who do. How big does genetics play for those who stutter? Do you (as a person who stutters) have a kid(s) who stutter? Do you have any advice?