# How long would it take for heritable magic talent to become universal?

Inspired by a previous question on this site. If magic were real (handwave - see 1) and in some way heritable, would it be likely to become fixated in the general population?

If so, how long would it take? Would it become universal? I have some sense that this might depend on how many separate genetic alleles are needed.

If not, why not? How would magic have to be harmful to prevent it from becoming a universal trait? Could it even die out?

For a couple of real world comparisons, I imagine that the first humans to develop what we now call empathy (the ability to put oneself in someone else's shoes and imagine how they would feel and what they would do) must have gained a magical-like ability in terms of the advantage it offered. Yet we don't have 100% prevalence, since we a generationally stable minority of sociopaths who are literally unable to empathize. Speech (the ability to plant highly specific symbolic representations in someone else's mind) must have also seemed magical to non-speaking human-like predecessors. It conferred such an overwhelming advantage that it did become universal in baseline surviving humans.

1. A decent implementation of a gesture, token and voice based magic system, along with a plausible explanation of its existence is described in Ra and hinted at in HPmoR. Imagine that in addition to the correct gesture and voice patterns, the "magic system" would check for a specific set of markers in the invoker, and do nothing if they are not present.
• Interesting idea that coincides in my mind with a growing population with inherited magical abilities- if magic is based on drawing energy from some external source accessible only by sorcerors, then as more magicians are born the available energy is spread more thinly, so their abilities diminish. This has lots of potentially interesting narrative consequences. Jan 8 '15 at 13:12
• Thank you for the real world comparisons. Those will be very helpful in bounding answers. Jan 8 '15 at 21:17
• Can you elaborate on HOW magic is viewed in your world? This is very relevant to how it evolves. With humanity simple Darwinism does not always apply, we can choose for example to exterminate all magicians even though it may be biologically (or biomagically) superior to have the ability. Jan 9 '15 at 20:13
• (Agreeing with @James for elaboration), Consider the X-men universe, their "magic" is hereditary but every person's is unique - and they are looked at as freaks, which actually makes the trait undesirable by most "normal" humans - to the point where some want to wipe them out. Mar 27 '15 at 15:52

If the ability to do magic is very rare, then having it could provide great income potential and could make someone highly sought-after as a mate. Avenues for wealth include wall-street mogul, superstar athlete, dominating your way to the top of a Fortune-500 company, etc.

A few years ago, a professional basketball player claimed to have had sex with about 10,000 different women, based on his estimate of 3 women/day over a 10-year career. Some people are skeptical of this claim, but it is at least within the realm of posssibilty.

Assuming a fertility of about 10% (magic could help with this), and an income somewhere over \$\$$100 million/year, a mage could potentially sire and support a thousand children in a decade. As for desirability, "Hey baby, have sex with me and if you get pregnant I'll give you \$$100 thousand per year in child support" may not be the best pick-up line, but it would work often enough.

If magic ability is inherited via a dominant mutated gene, then about 1/2 of those children would have magical ability. That's 500 new mages this one guy could sire, per decade.

So, while magic ability might spread slowly at first, eventually that one guy would come along. And, of his thousands of sons, many would try to do the same. Magic ability could easily go from "very rare" to millions or billions in a few generations.

Once magical ability were very common, we would then enter the long phase known as "the decline of the muggles". People without magical ability would be seen as inferior and would make less desirable mates. They would have much lower earning potential and would often end up in poverty. Even if no one actively tried to kill them off, society might change so that magical ability became essential to survival. Eventually, the muggle gene would disappear.

But this would take a long time. If a population has a fraction 1/X of its people who possess a single copy of a recessive-lethal allele (like untreated hemophilia), then the number will naturally decrease to 1/(X+1) in the next generation. It would literally take billions of generations for a specific allele to completely disappear. The only way it would go away faster would be if genetic testing could identify it and people actively selected against it.

Things get interesting and weird if the magic ability gene were dominant, but two copies of it were lethal. The number of mages would increase to about 2/3 of the population and it would stabilize there. Even if muggle babies had low survivability, they would still continue to make up 1/3 of births.

Or if carrying a double-magic-gene baby tended to be lethal to the mother as well as the baby, then no woman with magic ability would dare to mate with another mage. Marriages would always be mage-muggle, and the population would stabilize at 50% mages, 50% muggles. This strikes me as a fascinating scenario.

• Outstanding thought experiment! Jan 12 '15 at 23:58
• This is an awesome answer Mar 27 '15 at 17:29
• In the very last paragraph, you could still have muggle-muggle marriages, so the mage population would probably be a bit less than the muggle. Also, mage-mage would probably still happen - they'd probably just neuter and adopt. ;) Mar 27 '15 at 18:11
• Double magic genes causes the baby to burst in a magical rainbow explosion at birth. Quite beautiful to watch. Jul 14 '15 at 18:13
• I don't think he would have to offer anything for women to have sex with him--he'll have fertile women beating down his door for the chance of conceiving a mage baby. Jul 14 '15 at 22:18

If mutation would be beneficial, it would spread out. How fast, depends on many factors including if it is recessive or dominant, and how big competitive advantage/disadvantage it would give it's holder.

Even such minor trait like blue eyes which has only slight advantage of beauty (which is slight personal preference), spread over 6-10KY.

There are formulas for that somewhere, but without numbers (which you did not provide) I can only say: if benefits outweight disadvantages, it would spread. And to get universal, it would have to be dominant, be extremely advantageous, and even then it will take long time.

• You sure that the "blue eyes gene" spread just because they're pretty? Often, one gene is responsible for a number of otherwise unrelated things. So if this particular gene spread in the last couple of thousand years, I would assume it's because it has some other advantage, not because of the eye color. Jan 8 '15 at 18:15
• No, I am not sure. I assume. I do like blue eyes. :-) Are you sure that it does have some other benefits? You assume too. It would be fun research project, if someone can get funding for it. Unlikely. Jan 8 '15 at 18:25
• It has been researched, of course, I was just too lazy to google. "The genetics of eye color are complicated, and color is determined by multiple genes. So far, as many as 15 genes have been associated with eye color inheritance. Some of the eye-color genes include OCA2 and HERC2.[9] The earlier belief that blue eye color is a simple recessive trait has been shown to be incorrect." en.wikipedia.org/wiki/Eye_color Jan 8 '15 at 18:39
• OK "blue eyes" gene is not recessive and it is interplay of some 15 genes (note to self: check wikipedia more often). Even better. Magic talent might be driven by complicated interplay of genes, making it even harder to spread. But spread it will, and speed will depend on how big advantage it provides to it's carriers. Jan 8 '15 at 18:54

A trait becomes fixated if it raises the number of healthy children. In our Western society high intelligence correlates with its owners making decisions to have fewer children.

Women in poor third world countries have more children than women in Western countries.

Magicians might have working contraception spells while the rest of the society has no reliable ways of contraception and use that magic to limit the number of children they get.

Furthermore children by magicians might kill themselves in some way by misusing their magic.

Generations to fixation = 2 ln(N) / s where N is the population size, and (1 + s) is the fitness. (If each bearer of the gene has 1.03 times as many children as a non-bearer, s = 0.03.)

Probability of fixation = 2s

If having magic lets you have 10% more reproducing children than people who do not have magic, there is a 20% chance that magic will become fixated, and it will take 20 * ln(Population size) generations for it to do so. In a population of 7000000000, that's 400 generations. If it doubles the number of kids the magic user can be expected to have, it's almost guaranteed to become fixated and will take 22 generations to do so.Put in your own numbers as needed.

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. :-)

• I'm not saying I speak from personal experience or anything, but why would going to graduate school, as it were, make you less likely to have sex and/or kids? Mar 28 '15 at 3:09
• @serban it is level of discipline and dedication most magic systems seem to require. You have to get a rather extreme level of control over your emotions and impulses, or you can't control the magic. After spending years putting the damper on such things, the interest in children and sex tends to be greatly reduced, particularly since they make it harder to maintain the necessary level of control. Grad school is only comparable in the sense that it requires lots of study, it doesn't need the extreme level of discipline in other areas. Mar 28 '15 at 6:38

This is a difficult question to answer with any precision - it depends on a great number of factors, which basically boil down to the magnitude of the advantage.

Like any trait - such as the ability to see - it will never be truly universal, as in "no-one lacks the trait", but may become typical, as in "the numbers of people who lack the trait are not statistically significant, so less than 5% of the population lacks the trait".

Certainly, the ability to use magic should be a significant advantage that would lead to the ability to produce greater numbers of offspring surviving to reproduce themselves than those without the ability. However, the answer depends on how many more. If it is 1 or fewer, it could take a very long time, on the order of thousands of years. On the other hand, if there was a war between the magic users and the non-magic users or some other factor that made the difference in offspring survival much greater than 1, it could take only a few generations to become a majority trait, and a few more generations for magical disability to become as unusual as blindness or deafness.

The nature of the advantage provided by magical ability would depend on social factors such as whether the magically-able made a habit of assisting the magically-unable in their lives and the magically-unable tolerated this assistance, or if the two groups were antagonistic, the magically-able feeling superior to the magically-unable, and the latter feeling threatened by the former.

This really depends on how much of an advantage the magical trait has. If the only way to make any use of it is through extensive and intensive schooling or if it had other consequences such as making you physically weaker or give you special requirements then it might spread slowly.

If it had no downsides and gave you a noticeable competitive advantage then it would spread fast.

This is a difficult question to answer. You can't use pure mathematical formulas to map out the "magical diaspora". Even the genetics side isn't very easy to figure out. These genes could lie dormant in people for many generations before it expresses itself. Perhaps it is a recessive gene and skips generations, or you need to have parents that both have the gene for magical traits to be present in their offspring.

Since the world is so diverse, it would most likely take thousands of generations for the majority of people to have magical powers. Many of the traits we have today such as eye color developed in our distant past when there were much fewer people on the planet. It is very unlikely that a gene like that would ever completely dominate the human population if it appeared now.

If we were able to master the human genome and use gene therapy to artificially create the magic gene and give it to people, then anyone that had the means and wanted it could have it.

Amongst other factors, when does magic occur? (ie: people learn the correct gesture and other stuff: ie: is this an easy problem (happens accidentily, often), or a very difficult problem (biological forms developing mitochondria: happened once))

If magic is hard enough that it didn't develop until later, after other civilized effects - it might not be as common, even if it does have evolutionary benefits.

If you realize that magic is heritable, you might be careful spreading your genes if it means you might have to compete with your progeny. This is especially true if magic can extend your lifespan. Or if the number of magic-users impact the magic auras/ability to use magic.

If decreasing the number of mages increases your available personal power... having magical genes might not actually be an evolutionary benefit. :)

After a little research I found this article in which they explain that when you go back 20 generations on earth, basically everyone is related to everyone at some point along the way, so that would be your 'longest time it would take' assuming the inheritance is (close to) 100% and assuming you WANT magic to become universal. If the ability to do magic is tied to having a specific gene, the time would obviously be longer.

• Going by Saidoro's answer, I don't think that your answer is fully accurate. Mar 28 '15 at 3:08
• As I tried to state, my answer assumes inheritance through other means than genes. I guess it wasn't clear enough :) Mar 30 '15 at 7:42

While I'm late to the party, I'd suggest that the answer is easy: magic, while beneficial to the possessor, is potentially lethal to the people around him or her. For a classic take on the concept, try Bisby's "It's a Good Life" http://www.fys.ku.dk/~thoeger/its-a-good-life.pdf. For a slightly less extreme version, consider the possibilities inherent in powerful magic combined with adolescent hornones.

Under these conditions, it becomes quite possible for the surrounding population to cull magic-bearers when the ability begins to manifest itself. Particularly if magic use (rather than ability) requires practice to become effective, such culling efforts would presumably be successful while the user's effectiveness is still developing. It's just a matter of self-defense. This will, in effect, cause the gene to be selected against, and the standard analysis will apply.

Genetically, you already have some great answers. However, most answers here assume that "being a mage" is viewed as a good thing, so that will help you spread your genes. Someone took into account magic being dangerous and causing accidents, but still there's an important point missing.

The more magic is perceived to be too powerful (or, even worse, too scary), the more is likely that a witch hunt will occur, which one way or another will completely skew the results: this might exterminate all the mages, or slow them down, or, if they "win", might even spread them faster.

So there must be a careful balance in order not to mess everything up: magic has to be good enough to increase your desirability, but not so powerful that it attracts hostility and fear.

More than sheer "power to kill things", the most dangerous powers to have are:

• creating illusions: if people no longer know what's real, they wouldn't appreciate. This is only a problem if this "illusion power" is quite strong.
• teleportation: this is a dangerous since it would change drastically physical security. Banks and military will want you dead, very fast, and many people would approve.
• mind-reading: people would at the very least avoid mages if those could read minds.
• mind-altering: this is the worst of all. If you could alter other people's minds, any sane person would want you dead ASAP. Not knowing what's real in the world is bad enough, risking becoming a puppet without even realising it is orders of magnitude worse. Especially if you also consider you would start doubting about anyone.

Also thanks to @James and to @DoubleDouble for pointing this out in a couple of comments.

In you are interested in actually computing how many generations fixation of the trait will take the math is pretty straightforward and people have created websites that will even do it for you. Here is one such site: http://www.radford.edu/~rsheehy/Gen_flash/popgen/. It allows you to define the characteristics of your starting population and then run the simulation for many generations to see what happens. This web application takes a long time to run if you set the initial population too high, but there is other software that you could download in order perform a larger simulation.

All you need to do is first decide how your magic is inherited. Is it recessive or dominant or somewhere in between? You also need to decide the initial frequency of the allele. This isn't necessarily the initial frequency of mages though, as that also depends on the dominance of the trait. If the mage allele is recessive and only people with 2 copies become mages then the initial frequency of mages is equal to the initial allele frequency squared.

Once you have decided on that, simply decide how much more successful your mages are at having children than normal people. For instance, if the mage allele is recessive and individuals who are mages have twice as many offpsring as individuals that are not mages, then the relative fitnesses of A1A1, A1A2, and A2A2 will be 1, 0.5, and 0.5 respectively. But if the mage trait is codominant so heterozygotes or people with an A1A2 genotype are more fit than complete non-mages, then you might set the fitnesses to be 1, 0.75, and 0.5 respectively.

The tool let's you run the simulation simultaneously for multiple populations to see what sort of variance there may be.