Ok, cool. I just googled it. Nobody has done a study, but Cornell is working on it.
Brooks Equine Genetics Lab - Cornell University
I have been around gaited horses all my life, and I think that it is a straight recessive gene. But that is what I think, not evidence. I hope to follow this study.
Again, it doesn't matter at all, I am just curious about it because it will take a couple years to find out- at least under saddle. I have not seen him gait since just after he was born, but people tell me that is common in foals to do some funky things with legs right after they are born, so it probably means nothing that he gaited for a little while after he was born.
This is Zane gaiting shortly after he was born. He did this for a couple of weeks but not since that I have observed. He really loves to trot and canter.