When Should Isaac Laquedem Stop Reproducing?

April 15, 2008 10:37 PM

You're the Wandering Jew. When do you start worrying about sleeping with your own descendants?

You've been alive for, what, 2040 years or so, crossing the planet. You're a man of the world, of course, and you've had a few kids. In fact, you've produced one offspring every five years that has reached maturity and reproduced- 408 of them, in fact. They've reproduced as well, although they lack your immortality- let's say each of them has produced 2 heirs after an initial period of twenty years, with these heirs produced within ten years; each of these will produce 2 heirs, and so on. So, in A.D. 0, you have a single descendant; A.D. 5- 2 descendants; A.D. 10- 3; A.D. 15- 4; A.D. 20- 6 (5 children, one grandchild); A.D. 25- 9 (6 children, 3 grandchildren) and so on. Based on the LOWER population estimates located here, assuming an even descendant distribution throughout the population, when should you start worrying about reproducing with your own descendants?
I'm not really sure if this problem can even be answered- you'd probably need to consider the poor guy's rate at which he meets people and at which he sleeps with them, which I invite you to invent on your own. I'm just wondering, for a writing project, at what point poor old Isaac Laquedem should get a vasectomy.

posted by 235w103 to human relations (18 comments total)

I don't know if your question will be deleted or not, since you stated "I'm not really sure if this problem can even be answered"... But I think once he gets down to great-great-great-great-great-great-etc.-grandchildren, aside from the ICK factor, he wouldn't have to worry about any genetic problems.

One and one-half wandering Jews
Free to wander wherever they choose
Are travelling together
In the Sangre de Cristo
The Blood of Christ Mountains
Of New Mexico
On the last leg of the journey
They started a long time ago
The arc of a love affair

-Paul Simon, Hearts and Bones
posted by amyms at 10:46 PM on April 15, 2008

Well, I should have said- the percentage of the population can be answered in the form of a function, which I have absolutely no idea how to construct. The difficulty would be figuring out what percentage of the population you reproduce with- one in four thousand?
posted by 235w103 at 10:51 PM on April 15, 2008

You might want to ask when do you stop worrying about sleeping with descendants. I believe that US law allows marriage between second cousins (2 common great-grandparents) or 25% common source for DNA. By the time you get to the fifth generation of descendants, your guy is a potential source of only 1/32nd of the kids DNA. Unless you queasy about the social implications, I don't see why he should refrain from mating with distant descendants, particularly if he meets them as adults (it would probably violate most people's incest taboos if he was involved in raising the them and so had a semi-parental role)
posted by metahawk at 10:55 PM on April 15, 2008

Let:
g = number of years between generations
t = time (in years; independent variable)
r = number of years between Isaac's reproductions (e.g., 5)
b = avg. number of children had by Isaac's progeny (e.g., 2)
D(t) = Number of Isaac's descendants as a function of time
W(t) = World population as a function of time

If D(t) is unbounded by real-life things like food and geographic constraints, then it grows exponentially. For convenience, assume that t is divisible by r.

First consider the number of descendants of Isaac's first child at year 0. By the time year t rolls around, we have b^(t/g) of them. That's a lot. For the second child, born in year r, there are b^( (t-r)/g ) descendants by year t. And so on, such that the total number of descendants living and dead at time t is:

D(t) = Sum over [i = 0 to t/r] of { b^(r/g)

(assuming t is divisible by r for convenience)

Of course, the descendants will die. Assume that only the most recent generation is still alive, and you get:

D(t) = (b-1)/b * Sum over [i = 0 to t/r] of { b^(r/g)

Now, assuming you have world population P(t) from some external data, and assuming the descendants are uniformly distributed, then the probability of any random bride in year t being a descendant of Isaac is D(t)/W(t).

You can use this probability to figure out when he should get a vasectomy.
posted by qxntpqbbbqxl at 11:34 PM on April 15, 2008 [1 favorite]

metahawk has it - the question is entirely backwards. At least, from a biological (as opposed to social taboo) standpoint.

The more generations that intervene between him and his descendants, the less important (biologically) incest becomes. After a while, him sleeping with his direct descendant is no more of a (biological) issue than you sleeping with your wife, who are basically just as related to each other as he is to his great-great-...-great-grandchild.

So the question should not be "when does he start worrying that he might accidentally reproduce with one of his descendants". It should be "when does he stop worrying that he might accidentally reproduce with one of his descendants".

And apart from that, you're telling me that Christianity is true and that I am one of its biggest villians. I think I've got bigger things to worry about than whether I might sire a kid with twelve toes.
posted by Flunkie at 12:18 AM on April 16, 2008

believe that US law allows marriage between second cousins (2 common great-grandparents) or 25% common source for DNA.

Plenty of states even allow the marriage of first cousins, with a 50% common source.
posted by Dee Xtrovert at 1:11 AM on April 16, 2008

To do this calculation correctly, you'll need to consider noise. For example, imagine that each person has, on average, two children. But this varies -- sometimes it's three, sometimes it's zero. Now, the one with zero children has doesn't have any grandkids, either, or great-grand-kids, etc. Of course, if you have kids but your children do not (or, more likely, none of them survive), your line also stops. How rare this is depends on how many children you have and how common it is to have no children. Only when you have a number of generations, and a very large number of descendants, can you be safe from the noise. If the rate of childlessness is decent compared to the average number of kids, a large fraction of family lines will never make it past this noise "hump".

Now consider the fact that we reproduce sexually. This dampens exponential growth -- after a few generations, we do tend to start sleeping with relatives. If two of your grandchildren get together and have one child, that doesn't count as two great-grand-children for you!

On the other hand, sexual reproduction allows mixing which can cause an already dominant ancestor to become more dominant. Imagine that in one generation, 75% of the people are your descendants. Chances are good that many of the 25% who are not your descendants will mate with people who are your descendants. Result? In the following generation, you claim a larger fraction of the population.

Now the end results here all depend on the exact numbers. But I was told the following by my advisor, who thinks about this sort of thing and is a very smart man: most humans from many generations ago have no living descendants today. But those who have any descendants are likely to have nearly all humans as descendants.

Which is where, finally, I get to the question at hand: the Wandering Jew should just give up!
posted by wyzewoman at 4:32 AM on April 16, 2008

Hmm, really good points from metahawk, Flunkie and qxntpqbbbqxl. Maybe I should be thinking of the descendant problem as thus- a rolling population that consists of the first two generations coming after Isaac's heirs, which I believe should eventually reach a constant- by year 200 or so, there should be a set population of children, grandchildren and great-grandchildren which doesn't fluctuate, as Isaac's reproduction doesn't wax and wane on account of external events. So his chances of biological problems in offspring actually decreases as the world population increases. I can't believe I spent the time thinking about the time between descendants, etc., without thinking of that!
posted by 235w103 at 4:32 AM on April 16, 2008

Assuming about 80 generations since the year zero, and 2 offspring per generation, random distribution, and no reproduction among descendants, the number of offspring from just Isaac's first descendant in the year 0 would be 1.2089 x 10^24, by qxntpqbbbqxl's formula above. That's 1,208,900,000,000,000,000,000,000, or clearly more than the earth's population. Therefore, of necessity, Isaac the odds are 100% that Isaac is sleeping with descendants. The point in time where that first offspring's descendants begin to outnumber the population of the earth as given in your linked table is sometime in the 7th century or between the 27th and 28th generations. This is accelerated by Isaac's continued reproduction in the meantime; someone can do the calculus on that.

The other implication of these figures is that all human reproduction today is among cousins; because we are all descendants of Charlemagne as well as of Muhammed, as well as of Isaac.
posted by beagle at 6:02 AM on April 16, 2008

Well the problem with some of this is that there are also random things to figure in here, for example infant mortality and, much more cataclysmically, bubonic plague. Thus a lot of these descendants would not have lived beyond childhood and thus couldn't reproduce, and many generations would have been decimated by plague, malnutrition etc. Such things were very capable of keeping population booms in check.
posted by ob at 7:06 AM on April 16, 2008

metahawk writes "You might want to ask when do you stop worrying about sleeping with descendants. I believe that US law allows marriage between second cousins (2 common great-grandparents) or 25% common source for DNA."

Even better first cousins are permitted to marry in half the states of the union. Also legal throughout Europe, Canada and Mexico.
posted by Mitheral at 7:14 AM on April 16, 2008

Oops, I made a typo. In the summations, it should be b^(i/g), not b^(r/g)

That said, beagle is quite right--- the unbounded exponential growth formula quickly exceeds the Earth's current population, so it's not a very meaningful model.

Descendants reproducing with each other can be represented by reducing the average number of children, e.g. if 50% of descendants marry another descendant, then the average number of children-per-descendant would drop from 2 to 1.5.

The thing this model wholly ignores is fractional ancestry. If Isaac reproduces with his nth great-great-great-great grandchild, the results will be different if that descendant is genetically 1/64th Wandering Jew or 100% Wandering Jew. (the latter may cause flipper babies, but the former is pretty safe)
posted by qxntpqbbbqxl at 7:45 AM on April 16, 2008

The 100% # is a bit misleading, as are the Charlemagne and Mohammed arguments. Just because the number of descendants is greater than our population does not mean we are all descended from Charlemagne. The "we are all sleeping with our cousins" argument only holds up when dealing with parts of the world with a history of shared migration.

So, it is a safe bet that our wandering jew could go to somewhere in the remote Congo and sleep with the hot African girl of his choice without worrying about her being a descendant. Likewise, should the folks in the Congo have a "Wandering Congolese" myth, that hypothetical fellow could sleep with the Siberian babe of his choice without a worry that she was a descendant.
posted by charlesv at 7:47 AM on April 16, 2008

The question is unanswerable because you cannot know who your progeny will be sleeping with. You can predict statistically what your chances are, but you cannot know.
posted by gjc at 7:59 AM on April 16, 2008

that hypothetical fellow could sleep with the Siberian babe of his choice without a worry that she was a descendant.

True, there is a greater statistical likelihood that the Congolese villager and the Siberian babe do not have a common ancester around the year zero, but you can't say that absolutely. There was much more long-distance trade going on, both over land and over sea, from ancient times through the Middle Ages, than most people would guess. If, in the early middle ages, one of Isaac's progeny accompanied Marco Polo to the orient, and another made a trading voyage up the Nile or along the African coast, with sufficient hanky-panky in each case, then statistically it is nearly certain the Congolese and the Siberian, today, are distant cousins.

This is supported by the study cited here, which suggests that the most recent common ancestor for all humans today lived just 3,000 years ago.
posted by beagle at 9:32 AM on April 16, 2008

Plenty of states even allow the marriage of first cousins, with a 50% common source.

First cousins share ~1/8th of their DNA (unless one or both parents are twins). Siblings share ~50%, as do parents and their children. Reproducing with your cousin increases your chance of a deleterious recessive gene being expressed by 2-3%. So he shouldn't worry at all.

Did you think of this question while watching New Amsterdam?
posted by Thoughtcrime at 2:09 PM on April 16, 2008

... when should you start worrying about reproducing with your own descendants?

Never. In terms of shared genes only people in your immediate family (siblings, parents) justify significant reproductive worries. First cousins are sub-optimal health and fitness-wise but historically extremely common. Second cousins and less related are not only not worrisome, but possibly genetically optimal from a health and reproductive standpoint. A recent study using detailed historical records from Iceland found that third and fourth cousin marriages consistently resulted in the most children (interpreted as a biological effect due to optimal genetic compatibility).

So, to use your Jewish Highlander as our example, making some baby with his own kids (50% shared genes), or grandkids (25%) would be bad - but he would know these people personally, so it wouldn't happen. Making some baby with his great-grandkids would be sub-optimal (but no different than making baby with a first cousin - 12.5% shared genes). Making baby with his great-great grandkids would be fine (no different than making baby with second cousin - 6.25% shared genes). To put this perspective, 80% of marriages in history have been between 2nd cousins and closer.

Further, making baby with his great-great-great grandkids (3.125% shared genes) or great-great-great-great grandkids (1.56% shared genes) would actually be biologically beneficial.

Making baby with people less related than that is no different than making baby from people randomly selected from within your ethnic group, or from outside of it. There are no reasons to worry, and there is nothing conceptually or empirically different from fucking your own mildly distant descendants, and fucking people in general. Shared genes are shared genes.
posted by dgaicun at 6:09 AM on April 17, 2008

By the way, all human beings share recent common descent; just as evolution shows all biological life shares descent. You and your dog, and you and a spider, and a mushroom literally share relatives. You and a mushroom share a great-great-great-(1 million more 'greats') grandfather.

All the white people on Metafilter probably share a common relative sometime in the last 300 years. Geneticist Stephen Oslen believes that every human being on the planet shares a relative if you go back only 2000 years.
posted by dgaicun at 6:28 AM on April 17, 2008