The central concept in The Wheel of Times is the so-called One Power, a force that drives all of creation. In the series some people are able to channel the one power, these people are known as channelers. Throughout the story it’s strongly implied that the ability to channel the one power is a genetic trait. In this respect WOT is quite similar to to Harry Potter, though in WOT the heritability of channeling is not a great issue as it is in HP.
In respect to the ability to channel, there is a distinction between two classes of channelers: those who have an innate ability to channel (“born with the spark”) and those who are able to learn channeling. People who belong to the former category will inevitably channel sooner or later the one power, whether they want to or not. However, the majority of channelers are in the latter category.
Considering this, I will present my theory on the genetics of channeling. I will assume that the ability to channel is a pleiotropic trait, i.e. determined by one set of genes.
From the evidence in the books we can conclude that the channeling gene is recessive. If it were a dominant one, then channelers would have become extinct in the Westlands (as Aes Sedai rarely reproduce) and probably also in Seanchan. (In fact the numbers of Aes Sedai is dwindling and it is suggested that the celibatarian lifestyle of most Aes Sedai is the cause of this.)
So the “channeling gene” has two alleles, the dominant A and the recessive a. Someone who has the aa-genotype is able to channel the one power, while people with AA cannot channel. However, genetics is not as simple as is often portrayed in school books.
An important concept in genetics is incomplete dominance. A (now out-dated) example would be eye-color. People with two dominant alleles (BB) have dark brown eyes, while people with only one dominant allele (Bb) have light brown eyes.
My theory is now as follows. People who are born with the spark have genotype aa, people who can learn to channel have Aa and the non-channeling population has the AA-genotype. This theory is supported by the fact that those who are born with the spark are outnumbered by those who can learn te channel.
An counter-argument would be that if this were the case, that by eliminating male channelers also the number of female channelers would be lowered. But the evidence in the books suggest that the Aes Sedai only hunt down men who are actually able to channel, i.e. men who are born with the spark. And since many women who are able to learn to channel are unaware of this, the same is likely to be true for men as well.
Further only few men who could learn to channel would even think about channeling, due to the reputation and history of male channelers. Hence they would pass by unnoticed and be able to pass on their genes to their off spring.