Antler Valley, we believe the pied gene is dominant. BUT deer will have one dominant gene and one recessive gene. Their offspring will depend upon which gene is passed on. If they pass on the pied gene the offspring will be pied. If they are breeding brown does and the brown gene is passed on it will be brown. We have pieds and we always breed pied to brown. Our deer then can have one of 4 combinations, since each parent has two genes and passed on one of them. The end result depends on the combination. Observing what we have raising pieds for many years, we feel the pied gene is dominant over brown, but it will depend on what the pied deer is breeding to. Whether they are a little pied or a lot pied doesn't matter - they are still pied. That is why sometimes a pied deer shows up and you can't figure out where it came from - one of the parents was pied but with very few markings - they essentially will look like a brown deer.
We did an entire segment on our TV show on this. WE are now on the Pursuit/Hunting channel airing on Thursday nights at 8 PM eastern and 7 PM central time. The episode on pieds and whites will air again but not for quite a while.