(Note: I am not yet sure about the population numbers involved here, but if it is a very crucial aspect of the answer, somewhere between 1 million to 100 million at the start is almost certainly correct. The tech-level when magic appears is late bronze/iron age, and technological progress is similar in order to our world, but about ~30% slower.)
A group of people (a few dozen people) in my world were given the ability to access magic. The only way (as of now; I'll have to add other ways if this method is too slow) to gain the ability to access magic is if one of your parents also had that ability.
This "gene" is guaranteed to pass to one's children, and doesn't get "weaker" or "diluted" if only one parent has it vs both parents had it.
This "magic" is not strong but IS desirable; individual strengths vary considerably but almost all magic users can access this magic to temporarily become stronger, faster or use magic tools (though magic tools are a much later invention; they are very hard to invent)
Some other points:
- The group that gains magic originally as a founding principle wants to spread magic all over the continent. This sentiment may not be shared by those who they give it to, however.
- One of the major religions is against this magic, but soon enough it splinters off into more moderate sects who are not. The priests and hardcore followers of this group aren't counted in "everybody" for the purposes of this question.
It originally seemed to me that this method would not work and "magic" would remain confined to the nobility. But after reading that pretty much all of humanity is a descendant of Charlemagne, I think it might be possible.
Is it feasible that in around 2000 years, every human (on this continent; there's nothing else that's relevant) has this "gene?" If not, is there a number of years when this is nearly guaranteed? If yes, what would be a reasonable estimate for that number of years?
A clear timeline of when which group (ie nobility, then maybe rich commoners, then later peasants) gain this ability would be very helpful. This might be too story-based, though, so the main question is just the upper one. Insights would be appreciated.
EDIT 1: Since someone asked, I'm providing some clarifications of the most common ways magic can be used. Not everyone can use all of these, but most users can use most of these.
- Increase muscular strength
- Increase the speed of perception. Essentially makes one see the world as slow-motion
- Detect other magic users
- Produce body heat (More of a side-effect. All magic use produces body heat but this can be exploited by intermediately skilled users to pretty much never freeze as long as they aren't too tired to do magic)
- Produce flame. This is pretty hard as it involves controlling your body's rate of magic "combustion" to overheat a very small part, like your fingertip, then use it to heat something flammable. If done badly (or deliberately uncontrolled), a user can burst into flames or even explode.
- Most other uses require specially designed tools. They really didn't come into play until much later, some 1500 years down the line and remained primitive for thousands of years more (mostly due to extinction level events that reduced knowledge. However, these events happened after everyone already was able to do magic)
The previous mention of "extinction level events": Possibly it can be said that only people with magic survived those events. But this is not true as per my current iteration, unless no other possibility can be.