Population Density

[BigIrish77]

Hello again, everyone. Here I am with yet another question.

In my story, I have a village of people who live on an island off the coast of SW Ireland that will implode on itself around the year 1750. These people have powers that can be passed on, but only if they have a child with someone else from the island.

This can continue after the island has crumbled, but they must be direct descendants from the island. Now, obviously, through the years, people marry people with no relation to the island, so the powers don't transfer to their kids, lessening the prospective gene pool until now, when we are dealing with the last family to be able to pass on powers.

My question is, how many people will I need to have on that island when the time comes to evacuate to keep the powers gene pool running, without inbreeding (obviously), for those 263 years?

I was thinking 4000 surviving people on the island when it implodes, but if I can do fewer, I would love to.

So, what say you all?

 

[Susan Boulton]

I say you can work with a lot less.

Take for instance from the time of your great great grandparents you could have had 30 direct ancestors in total: 2+4+8+16=30. Do the math 4,000 is lot!

Also most of the islanders will be at least second cousins, or cousins. If they have been a closed society. Most small villages were

 

[BigIrish77]

I say you can work with a lot less.

Take for instance from the time of your great great grandparents you could have had 30 direct ancestors in total: 2+4+8+16=30. Do the math 4,000 is lot!

Also most of the islanders will be at least second cousins, or cousins. If they have been a closed society. Most small villages were

Good, awesome.

I was just worried about the lessening "powers" gene pool, not surviving to now, what with people from the island marrying others that have no connection to the island over the years.

Kind of confusing, no?

But, even if we just assume that half of the survivors are going to have children with powers, then that does expand the pool.

So, I may go with 1000 to 1500.

Which works so much better. I could probably even go smaller.

This links back to my previous thread about the size of the island. The fewer people I can use, the smaller I can make the island, which helps my story.

 

[Dozmonic]

It sounds like the power is a recessive allele if it requires both parents to have it and pass it to their children.

If a person with power breeds with a power who doesn't have it, they are passing along the gene to a child who will be a carrier but not have the power. If they have a child, this child has a 50% of of getting said gene. This will slowly die out from a small population.

When you get two carriers of the gene, they will each have a 50% chance of passing the correct gene along, which means their children will have a 25% chance of having the power.

If you're having 263 years pass and assume 25 years between each generation, that's pretty much 10 generations. The chance of a child then having the gene will be 1/2^10 or 1 in 1024, not high. This assumes nobody from the island breeds with each other, only with non-carriers. This will get offset a little if they stay localised, because sometimes two carriers will interbreed. This means you'd still have magical people, only the numbers will diminish each generation and occasionally one will pop up unexpectedly.

That's assuming you're using the power as a genetic ability, which I assume is so as you mention a gene pool. If you're doing it through some other means, you're free to make up the rules yourself

Edit: I said assume wayyyyy too much there!

 

[BigIrish77]

Well, except it's either you have it powers 100%, or you don't.

Once the chain is broken for your bloodline, it cannot be brought back.

So, say there is a kid who has one parent who had power and one who didn't. This kid marries a person with powers. Their kid will have no powers at all.

 

[Dozmonic]

In that case you only need a really, really small number. With 3 magical people being AA, BB and CC you can have kids with parentage of AB, AC and BC. The next generation can have kids of AA, BB, CC, AB, AC and BC. Add a couple more families and you've no interbreeding for a couple of generations by which time there's suitable genetic variety to keep going. 4,000 is massively more than needed

 

[BigIrish77]

In that case you only need a really, really small number. With 3 magical people being AA, BB and CC you can have kids with parentage of AB, AC and BC. The next generation can have kids of AA, BB, CC, AB, AC and BC. Add a couple more families and you've no interbreeding for a couple of generations by which time there's suitable genetic variety to keep going. 4,000 is massively more than needed

See, you did math.

I was hoping to avoid math...

Just kidding. But, for real, I could not figure out the formula I would need.

Thanks!

 

[BigIrish77]

So, the smaller the better for me. I may knock it down to just about 1000 then. Or even less.

They will be tracking their linage, to a point, in the story, so I kinda need to set up a ballpark number.

750 to a thousand seems like it should work.

 

[Dozmonic]

Those kind of numbers are absolutely fine, yeah

 

[chrispenycate]

Four thousand from the island, surely. Any survivors on an imploding island wouldn't be for long.

The genetics of your situation are shaky. If the gene for the powers were a simple recessive, then islanders mating with outsiders would have children who did not appear to have the powers, but held the potential, and should two 'half breeds' team up, a quarter of their offspring (statistically; you wouldn't be able to predict anything for a particular family, obviously) would have the powers, and half would be carrying the potential.

There will have been a fair amount of inbreeding in the island population before the implosion (I'm quite interested as to how one could implode an island; explode, yes, I can see possibilities, most of them noisy enough to be written down on the mainland, or subsidence, but how to dispose of enough matter to deflate one…). Most small isolated island populations display less genetic diversity than coastal settlements (there are mountain villages with the same situation). But this also means that, assuming life was challenging and death frequent, a lot of lethal recessives will have been weeded out already, slowing that side of the problem.

If you allow first cousin marriages (genetically questionable/socially common) and accept a certain percentage of deformed or non-viable babies, how many original islanders you need to cover the fourteen or so intervening generations depends largely on how rigid they were on discouraging outbreeding; presumably the first wave didn't even recognise the problem, and were pushed like to like merely by language and custom, and only later did it become obvious that the powers were not being transmitted. How early do these powers manifest, anyway? At birth, at adolescence (so the fact that they were not being handed down would not become apparent until the mother was reaching the end of childbearing)?

And then the great decision; risk getting burnt or dismembered as 'witches' or simple, power-free obscurity?

But I don't think you need as many as thousands to get that far. Insular, I wouldn't expect many of the first generation to marry outside the group, and the evidence of none of their children inheriting would slow the dilution considerably (and the worst of the witch hunts were over by then). Hundreds, certainly, probably high hundreds, and all of them would have a family relationship 'Oh, she's one of the islanders'. But that was true when they first made landfall.

 

[BigIrish77]

Well, while what you say is correct in most cases, my story is a bit different, as the island will only have "existed" for about 150 years, and any "original" inhabitants will have come over from the mainland.

I know that is a little cryptic, but I am one of those that is overly careful about how much information I actually put out there.

EDIT: And implode was a horribly inaccurate term for me to use. It's pretty much going to crumble into the ocean.

 

[chrispenycate]

You do realise that, unless the island is in some way magic, to get a population entirely imbued with a particular characteristic they'd have to have had a massive genocidal culling some time in the past; and, with only a hundred and fifty years to do it in, this has to have been brutal (somehow it's less worrying if it was neolithic ancestors doing it). But it does mean the language will not have drifted too much.

Incidentally, don't believe the earlier equations (well, logic analysis). Population dynamics equations do not look like that, they've got strange squiggles and limit factors and Greek letters all over them, not simple algebra. And I'm never going to solve any for anybody ever again, so there. (Actually, I get the feeling nobody solves them any more; they put the figures into a computer, dial up recommended algorithm, and believe what comes out.)
It's all to do with lethal recessives, but in a closed population you can never add diversity - ninety percent of mutations are lethal recessives - so you're shuffling the same pack of cards over and over. In the long run exogamy's the only solution – but long runs with humans are quite a bit longer than with most mammals.

But inbreeding does not have to be catastrophic, if you don't care about individuals. In SE Asia there is a species of bug – that's true bugs, hemiptera, not the American 'anything small with legs' - tens of thousands of them that are clearly descended from South American stock. Best bet is that a single gravid female scrambled off a sailing ship a couple of centuries ago, and brother/sister matings did the rest. Really restricted genotype, a single well adapted disease could have wiped them out at any time, large percentage of non-viable offspring, but Look mum. My own species!

 

[psychotick]

Hi,

Given the scenario that you've described, one where normal rules of genetics and in particular recessive genes don't apply, then I don't think that normal statistical analyses will work either. If once that initial passing on to offspring of powers chain is broken it's broken forever, than you need more people to begin with - depending of course on how many you want to have powers at the end.

So lets look at this as a static non growth situation. So the island explodes and 4000 people get off the boat in a new land and start the settling process. Now lets for the sake of argument assume that two parents have two children that survive until adulthood and reproduction - which is more or less static growth. (Note that in older societies people had more children but more died before adulthood, so poulation growth existed but was limited.)

Now we have ten generations of descendants, and for the sake of argument we'll assume that half of those descendants will marry other islanders, and half will wed outsiders in the new land. Which means that we get this picture.

G1 4000
G2 2000
G3 1000
G4 500
G5 250
G6 125
G7 63
G8 31
G9 15
G10 7

So my question is - is seven magically powered people enough in 2013 for your story?

Having said that, people are not numbers and they don't act like them. They make choices. So lets say that instead they have a strong preference to stay among others of their own kind. So say three quarters marry other islanders, your numbers become very different. That gives you 225 magically powered people in the tenth generation.

If it's ninety percent inbreeding you get 1394.

And then they could also have a higher fertility rate due to their magic, or their kids might be better survivors until the age of reproduction.

The only thing that is almost certain is that unless they reproduce practically solely among their own and they have more than two children surviving to the age of reproduction, is that that number will always be decreasing.

Cheers, Greg.

 

[psychotick]

Hi,

Forgot - the formula is simply a geometric regression.

The number of people on the island - NP
The proportion of couples that marry in house i.e. from 0 to 1.0 - IH
The number of generations - NG

So the number of descendants in each generation is NP x IH(to the power of NG)

Cheers, Greg.