Only 3% at the best of times have the ability at all. It cannot be as simple as "both parents can channel, therefore the kids can" like blonde hair or blue eyes on those grade-school level explanations of heredity. Even for two channelers, the odds of a channeling child have to be slim. The uberchannelers would be unique, so who can explain what their rules were? Maybe the circumstances of their conception imparted the ability, rather than any hereditary factor. After all, if it was heredity, then Elayne's kids should have been even more likely than Aviendha's to get it, since their parents were equally as strong, and their maternal grandmother could channel too.

As far as Rand's ancestors, at least one did have a son who had the ability, and some of them married Dreamwalkers and Wise Ones, some of whom might have carried an untutored ability, and then there is the point about the potential for training, which is supposed to include the vast majority of channelers. I can't imagine that failure to exploit a hereditary capacity excludes your descendants from inheriting it.

Also, men spark later. It can happen as late as thirty, which gives plenty of time to reproduce. My father didn't start a family until age 23, which would be a bit late for a preindustrial world, and his fifth child was conceived before his 31st birthday. Allowing a couple more years for him to notice the insanity and remove himself, and that's plenty of time for Rand's ancestors to A). Pass on their genes and B). die of the taint or try to kill Sightblinder or die something else in the Waste before anyone realizes he's a sparker.

Also, according to Verin, most wilders' initial tricks come in two categories, one of which is mild Compulsion. A young man or adolescent with such an ability would almost certainly have many more opportunities to pass on his genes, given the first thing that would pop into any teenager's mind when he realizes he can make people do what he wants.



Who says it did? Who was the mother of her grand-daughter who visited Andor? I don't recall any specific mention in the books, though Aiel customs being Aiel customs, she was very probably Padra's or Marinna's daughter, as the boys' children would feel as closely related to their fathers' parents. For all we know, the later generations could have been descended from different children. Or one of the girls didn't reproduce, and Aiel matrilineal preferences mean that the "line of the Dragon" only extends through the daughter who did, while the children of the sons would have been subsumed into their matrilineal lines.