Spread of a rare heritable trait across generations

[Feo Takahari]

One of the founding citizens of a small town had a rare heritable trait. This trait seems very minor, and most people don't notice they have it, so it neither improves nor reduces one's likelihood of having descendants. Several hundred years have passed since then. I'm trying to determine a reasonable percentage of citizens to have the trait. (3%? 10% 30%?)

Relevant factors:

I have some leeway in how it's passed down--it can be either genetic and dominant or magical. In the latter case, all descendants of the first to have it would have it. (I'm leaning against that because it seems like it would create too many characters with it--they need to be a minority.)

The town's unimportant in itself, but it's on the road to the capital, so it does get travelers. Some stay, and the town acquires new blood.

The trait isn't completely unheard of outside the town, and the main character is an outsider who has it, but not many outsiders bring it in.

Anyone know anything about small towns and gene spreading?

 

[ThinkerX]

Anyone know anything about small towns and gene spreading?

For some reason this has me thinking about Country and Western 'cheating' songs.

But more to the point:

How large of a town? 500? 5000? 15000?

How many offspring did the founding citizen have? 2? 10? How many of them had offspring?

How prominent is the founders family? Respected citizens with their thumbs in half the towns enterprises? Or hillbillies? Or something else?

Also worth keeping in mind - family lines can dwindle as well as grow - diseases, going off to war and not coming back, low birthrate, all that stuff.

 

[Penpilot]

How isolated is the town? What I mean is there a constant flow of people moving in and out of the town? And yes I too will ask how big is the town? The reason I ask is that if the population is isolated, that gene will over time spread through the whole population.

Some geneticists think that we're all at least 50th cousins to one another--hi cuz--and that's over the population of the whole world. So the smaller the population and the more isolated they are, the more they'll intermarry and the more quickly everyone will eventually be related.

Here's an article and a video explaining the concept.
Why humans are all much more related than you think
We Are All Related - YouTube

But if you have a constant in and out flux of people, then you can isolate a few families that are constants in the town and give all of them the gene, or maybe you can create a special rule on how the gene is either passed down or activated.

 

[Feo Takahari]

"How large of a town? 500? 5000? 15000?"

It's a fanfic, and canon is really screwy, so it's hard to tell. It's a town where everyone knows each other's name, but it's also a town that has everything from a spa to a jewelry shop. It's probably closer to 500 than 5,000, though.

"How many offspring did the founding citizen have? 2? 10? How many of them had offspring?"

No canon confirmation, but I'll say 4 or 5 children from her, and several children from most of their children. They're a farm family, so they'd likely have a lot of kids.

"How prominent is the founders family? Respected citizens with their thumbs in half the towns enterprises? Or hillbillies? Or something else?"

They're one of the more respected farming families in the region. They don't seem to have much influence, and they can struggle financially when they have crop troubles, but they do all right for themselves.

"How isolated is the town? What I mean is there a constant flow of people moving in and out of the town?"

The town has had a rail station since it was founded several centuries ago. (Despite the "present time" period seeming medieval in many ways. Again, canon is screwy.) However, it's apparently considered a special event when a new person moves into the town.

 

[wordwalker]

Simple answer is that if each person averages two descendants (that are able to leave children of their own), your founder has 2-to-the-(generation) descendants in a given generation, and then you can compare that to the size of the town. But you can alter that figure with a few things like:

• "Two descendants" might be a low figure. The higher the rate gets, the more the trait spreads, but if the rest of the town breeds more too the percentage still gets lower. Then again, "farm families have more kids" is only true in context; some of those kids don't survive, and over time some towns may see a die-off from disease and hunger, or war, or may see some of its population leaving.
• How's the family compare to the neighbors in these things? You say they aren't especially influential (which would have brought the average up if none of them had trouble marrying) or rich (buy more food and medicine), but the magic might make them healthier if you wanted.
• The genetic spread slows down over time, because people aren't *trying* to choose partners that spread their genes evenly. Quite the opposite: in one town it might be a third or fourth cousin is the person you're more likely to know and wind up with, while the Other Side of the Tracks is a lot less likely.
• Outside contact does dilute the trait, with both new blood and departures-- but it partly depends on whether these people are more likely to be among the ones moving out of town. (If the founder's extended family only spreads so far, you might balance that by saying they tended to stay put.)
• And like you said, not every descendant actually gains the trait, so you could reduce the ratio that way too.