I think the existing answers cover the mechanics of genetic propagation thoroughly. What I wanted to add to the conversation is a counterpoint as to why a desirable trait may not spread.
In many magic systems a great deal of study, practice, discipline, and emotional control is needed to perform magical feats, and control the effects you produce. The notes on the question imply that this is the case, just having the gene is not enough, you also have to develop the capability to do anything with it. If we assume such a system, then the mages may actually reproduce less than the average person, reducing the odds of, or at least extending the time for, the trait becoming fixed.
In order to develop their gift to a point of being recognized as a mage, a person would have to reign in their emotions and impulses, and devote copious amounts of time to study. As such they will have less time for/interest in raising a family, and they will be less likely to engage in casual sexual encounters. Under such systems, many schools strictly forbid any sexual activity among their apprentices due to it being distracting, and thereby dangerous. So even though the society may see a mage as a desirable mate, the mages themselves would generally hold back from having numerous offspring. Given enough time, assuming society continues to hold them in high regard, the trait would most likely become fixed, but it would be a VERY slow process. A shift in the way the mages are perceived by society as a whole could very well result in the trait dying out instead.
Now the above scenario applies to those who develop their heritage into a notable ability. What happens to those who possess the trait, but never develop it? If we assume that it has no effect other than giving them access to magic once trained, then these people gain neither advantage nor disadvantage in terms of their mating potential. Some will have many children, others few or none. The distribution of the trait through the population will be like hair color, eye color, or any other trait that doesn't convey a significant advantage/disadvantage to the one who possesses it. It will probably never die out in this population, but it probably won't become fixed either. End result is that the untrained that have the trait would not significantly influence the above outcomes.
However, many people who have devised similar magical systems have included an element where someone who is born with the magical gift, and does not receive training in how to control it, gets killed by runaway magic as the gift awakens. If we add this element into the mix, then the chance of the trait becoming fixed drop significantly. Our untrained population that could keep the trait alive in light of limited breeding on the part of the trained mages no longer exists. This would potentially mean more mages, as everyone will want to make sure their children get enough training to survive, but those who don't have access to such support die, probably before they pass on their genes. The catch here is, what incentive does the average mage have to train such people? Sure having a few apprentices to boss around can be nice, but I don't want to take time out to have my own children, why should I invest years in somebody else's child? I see such a situation going one of two ways (or possibly both in different regions).
Route one is that anyone with the trait has to find a willing mage to take them on as an apprentice in order to receive training. Presumably any such person is the child of a mage, but there are any number of reasons that their parent may be unavailable to train them. Maybe they are illegitimate and their mage father doesn't even know they exist. Maybe their parents were killed before they were old enough to receive training, the child survived but doesn't know of their heritage, or have a friendly mage around when they need one. Whatever the reasons, there will be cases where the children do not receive the needed training in time and the magic kills them. Under this structure the mage population slowly shrinks, and eventually dies out. Or perhaps they manage to survive, but they become such a minority that most of the population never sees one, and doubts that they really exist.
The other route is that the mages establish a school system to train anyone that shows indications of having the trait. Those mages that have an interest in such things serve as instructors. The students have a strong incentive to pay attention and learn, I mean their life quite literally depends on it. Never the less, there will be some that fail to learn fast enough, or make mistakes, and the magic kills them. But overall the mage population slowly grows, and eventually we are all one people. :-)