# How quickly would a genetic trait originally found in only 1 village spread across Earth?

The main trait of my story originates from a village in what's now the Belgian city of Tongeren, around 1000 BC in our timeline. Anyone born there after that trait arrived will have the trait, as will their children, recursively, regardless of where they are born. The trait doesn't have a single Patient Zero like Mitochondrial Eve or comparable people, but rather that everyone born in that village after the date the trait started appearing has the trait.

In the backstory, the Belgian empire that sprung from this city gradually takes control of Earth, with Europe being fully theirs in 500 BC, The Middle East around 1 AD, Africa and the rest of Asia at 500 AD, the Americas at around 1000 AD and the remaining landmasses of Earth at around 1200 AD, with tech being roughly at our level at around 1400 AD. These are rough estimates that aren't fully established yet, but the idea is that in 2050 AD, the Belgian Empire has developed interstellar travel, contacted and befriended other aliens and is a relatively new player at the galactic table.

Judging by the above estimates, how likely would it be for humans WITHOUT this trait to exist and be adults in 2050 AD?

information requested in comments:

• the trait always gets passed to the descendants and is always active. The trait doesn't directly increase survival through resistances or similar, but it does indirectly increase survival by providing the affected party with additional inherited knowledge, increased mental acuity and being able to use senses remotely. There are ways to lose personal access to the trait, but it doesn't affect how the trait gets passed on.

• the trait is not genetic in nature! I see many people assume it's genetics and thus obeys the normal Survival of the Fittest criteria where it only gets passed on if the trait is beneficial for survival. The trait is not dependent on the genes of either the mother or the father and will always be passed on to any children of the person affected.

• The empire achieved global dominance through a mix of diplomacy and military strength. Where possible, countries were annexed through treaties, royal marriages and other nonviolent means. when the empire is attacked, the offending nation is conquered, although this is mostly happened in the pre-BC days, when the Romans invaded from Italy and were conquered.

• It depends on the trait. If the trait is immunity to historically significant diseases like boubonic plague, black death and the flu, the odds will be lower than if the trait has no effect on its carrier's survival. – Henry Taylor Feb 28 '17 at 13:48
• Concur w/Henry that we cannot answer sensibly without knowing more about how pro-survival this trait is. – Catalyst Feb 28 '17 at 13:50
• Generally speaking, things will also depend heavily on population sizes and propensity to travel and settle elsewhere. Realistically, it might be that only the population in a very small area will have that trait, with maybe random pockets of genetic relatives springing up elsewhere due to someone having once traveled and settled elsewhere. If the trait doesn't die out in the intervening centuries, it will probably take a millennia for the trait to spread worldwide. – AndreiROM Feb 28 '17 at 14:00
• This kind of trait isn't really compatible with genetics. – ratchet freak Feb 28 '17 at 14:05
• It depends also on how this empire building took place. If it involved generous genocide, or bonding via settling/marriage/rape of natives, it naturally spread faster than in a multi cultural empire. – ths Feb 28 '17 at 14:07

# Estimating the spread within a population

Initially, one person has this trait. Assuming it is passed on each time, to children of either sex (which it seems like you are implying) then we can estimate the number of generations it would take for everyone in a population of size $x$ assuming anyone in the population is equally likely to intermarry with and reproduce with anyone else.

When there are $t$ people with the trait, each of $x-t$ people who do not have the trait in the intermarrying group, have a $t$ in $x-1$ chance of marrying someone with the trait.

Thus for the first generation, $t=1$ and lets say $x=100$, $$(x-t)\frac{t}{x-1} = (99)\frac{1}{99} = 1$$ more person will gain the trait in the next generation. This is because this simple model assumes the population stays constant, and every two people have two offspring. Thus the one trait-haver has two children, so the second generation has two trait-havers.

Applying this function (with a little python script), we can calculate the number of generations it takes for this trait to spread through 90% of a population:

  Pop Size  Generations
100       9
1000      13
10000      16
100000      19
1000000      23
10 billion      36


# Estimating the spread between populations

That last assumption is probably not the best for a lot of reasons, but mostly, it should be good enough. Where it breaks down is in population transfer between groups. How well do people spread between groups?

This is very much an open question. While it is very much not hard to imagine some trait-haver captured and sold into slavery in the Middle East and spreading the genes there, it is much more difficult to imagine that trait going to China.

Your history will have to give us a clue. If this Empire did expand around the world, then there is a good chance that the conquering population distributed their DNA through various conquered populations by various means.

In that case, it takes 36 generations for such a trait to spread among 90% of 10 billion people. Assuming a 25 year generation, that is about 900 years. Since it only takes 4 more generations to get from 90% to near 100%, it is a good bet the whole world has this trait.

If we start with a million Belgians conquering the known world in 1400 AD, then it will take 14 generations to pass on to 10 billion people, or 350 years. So again, everyone in the world should have this trait by 2050 AD.

# Conclusion

If this trait is beneficial, and there isn't some caste-system keeping the conquering Belgians from interbreeding with the lesser conquered, then it is reasonable to assume that this trait will spread to the entire world population soon after the Belgians complete their world conquest.

• So what you're saying is that if I want to have a character who was born without the trait, I'm going to have to make some kind of excuse for it? – Nzall Feb 28 '17 at 15:40
• @Nzall Yeah, some sort of group that isn't big into intermarrying with outsiders, or whatever. Orthodox Jews fit the bill, for example, and probably some castes in India. – kingledion Feb 28 '17 at 15:41
• There are populations eg. in the amazon region which haven't seen a white man to this day. – ths Feb 28 '17 at 17:34
• @ths On a tribal level, and for the Amazon specifically, that is most likely untrue. It is likely that over 450+ and ~18 generations years since the first Europeans showed up in the Amazon, that some branch of someone's family meet so Europeans. Which means it is even probable that someone descended from someone else with European DNA. The conquistadors were not known for not raping natives, you know. – kingledion Feb 28 '17 at 17:46
• The Nanti aren't uncontacted now. But, a generation ago, they were uncontacted and they have paid an immense price in terms of loss of life to epidemics in the process, lost a third to a half of their population to disease. – ohwilleke Mar 1 '17 at 4:48

Short answer: it is extremely likely

Long answer: I would look at the spread of lactose tolerance as a real-world example. https://en.wikipedia.org/wiki/Lactase_persistence#Global_spread It arose 10,000-5,000 years ago, was highly selected, and spread rapidly throughout Europe, so now over 80% of all Europeans have the gene, while it is barely present in Asia/Africa. But it really depends on how heavily selected the gene is. Remember that fitness depends entirely on the number of surviving children, not how long the individual lives. It the case of something highly selected, the gene will spread very fast, and dominate the gene pool rapidly. If the gene is only lightly selected or neutral, then it will not spread rapidly, as mutations that delete or knock the gene out will trim the population.

So, lets make some assumptions here. If your gene follows classical Mendelian inheritance and is dominate, then having one copy from a mother or father will give it to the child. I’ll also assume the trait is highly selective. After 2500 years, the nearly, but not all Belgians would have the trait, because of things like mutations, genetic drift, etc. It would spread in decreasing amounts from that centerpoint, mostly likely concentrated on the ruling classes. This is just spitballing here, but I would expect a majority of Europe to have the gene, with Africa/Asia only having a minority with gene. For example, if a Belgae with one copy of the gene (Gg) married a native foreigner (gg), then only half the kids would carry the gene

Eventually, the gene would become fixed in the population, but that could take tens of thousands of years

• "Remember that fitness depends entirely on the number of surviving children, not how long the individual lives." It depends upon the average number of surviving children per generation and the average length of a generation. The difference between a twenty year generation and a thirty year generation is equivalent to the difference between having three surviving children per generation and one surviving child per generation. (Strictly speaking "probability distribution of the" should be placed where I used the word "average"). – ohwilleke Mar 1 '17 at 4:51

The genetics underlying this story point to your space empire being a culture of genocidal matriarchal witches. Allow me to explain.

It is not easy for all descendants of trait carriers to have the trait which I think is what @ratchet freak meant with "isn't compatible with genetics". Since we are a mix of mom and dad some people will be heterozygous for trait - I am a heterozygote if I received a copy from Belgian dad but not from African mom. Assuming the other parent of my own child is a noncarrier, my child might get trait from me if she gets the Belgian copy but not if she gets my African copy. If you try to prevent this by making heterozygosity lethal it is impossible for a chromosomal trait to disseminate out into the population because then homozygotes can only have children with other homozygotes.

One way which might work for your story is to put the trait on mitochondrial DNA instead of chromosomal DNA. Then all children born of a mother with trait have trait because mitochondrial DNA is inherited only from the mother.

https://en.wikipedia.org/wiki/Mitochondrial_Eve#Female_and_mitochondrial_ancestry

This fact was used to trace back how long ago "mitochondrial Eve" existed. She is the most recent common ancestor of all humans. Wikipedia has a nice table showing how randomness over time will cause extinction of all but one variety in the population. I was skeptical when I initially read this but even with my very rudimentary skills it was not hard to model in basic or even Excel. Each female has a random plausible number of offspring, and then a random % of each die before reproducing. Set the death rate such that your total population is stable or grows / shrinks according to your wishes. Half of each new generation are females and they determine the next generation. Eventually all individuals have 1 mitochondrial type.

Mitochondrial Eve was roughly 100,000 years ago.

• If you give the trait a selective advantage you can make that happen sooner: for example % of death is lower for trait carriers

• If % of female offspring is higher trait will spread faster (which would have interesting ramifications for a story). % of female offspring could be something inherent in the trait. Or they could practice selective infanticide of male children. Or they could use witchcraft to make sure the babies were girls. Witchcraft has a long history in this context.

• If you make your total human population smaller it can happen sooner too, like in the tiny population in the Wikipedia figure. One way to do this is to ram the population thru a bottleneck and make it temporarily very small. https://en.wikipedia.org/wiki/Population_bottleneck A genocide of all nonBelgian females would work for this. I suspect historically genocidal conquerors had a different agenda so that would be interesting for a story also.

Is this trait selective? That is, is someone who doesn't show this trait less likely to have offspring?

To meet your conditions, the trait is dominant. One copy is sufficient for the trait to be expressed.

If not selective, then the stable levels for genotype to be TT, Tt, tT, and tt with 75 percent showing the trait and 25% not showing the trait. A close model right now in human physiology is the inheritance of eye colour.

If there is selection, then the population will become homozygous for T, with very few expressions of t very quickly. Albinism for example. Or Tay-Sachs disease.

The rest of it will depend on the interaction between populations. A selective gene can dominate a local population very quickly, but if that population doesn't out-breed into neighboring populations, then it will sit in that corner of the world. One of the reasons we have 'races' in humankind is that genes don't flow well between continents.

If your culture was at a crossroads, such as what is now modern day Israel, where invaders from 3 continents pillaged their way through every few generations, taking slaves back to their own lands, then the time span will be measured in centuries. If your culture is isolated, such as the natives on Tierra del Fueago, or Austrailian Abos up to the invasion from England, then the time to spread could be essentially infinite.

You are assuming that being smarter is an advantage. I am not so sure that it is.

Evidently, the "Belgians" would be able to defeat the non-Belgians. But then what do they do? They exterminate the vanquished? They randomly intermarry with them? Or do they enslave the non-Belgians, or establish another kind of exploitative relationship with them?

If so, they don't want their underlings to be as smart as them; if they have any clue of their intellectual superiority, they will strive to keep it, by systematically avoiding interbreeding. If they don't, then their superior gene will spread downwards their society, and soon they will have smart slaves realising that slavery is not something to be cherished.

Your society will have a Newton by the 14th century. But then it will have a Marx by the 15th.

So it is very likely that non-Belgians would exist, and would abound - they would be purposefully kept like that, in order to better serve their Belgian masters.

Then the problem is that slavery hampers technological progress. You don't need windmills if human brute force is available and plenty.

• They don't do slavery. The Belgian empire treats conquered and annexed nations as equal. – Nzall Mar 1 '17 at 10:54
• In which case, it isn't much of an Empire, is it? Anyway... what kind of economy does the Belgian empire deals in? When was wage labour introduced? How was excedent extracted before such introduction? If they have never had slavery, did they deal in serfdom? – Luís Henrique Mar 1 '17 at 12:08