For example, can you be 20% Hawaiian.
Genetic makeup seems to me to be in powers of 2, which is never dividable by 5.
Even if there is inbreeding among your ancestors, the divisor is still 32 or 64 or 128 depending on how many generations you want to go back.
Genes won’t come out in perfectly even powers of two after several generations. And, of course, we all have a LOT of genes in common as human beings, which further muddies the issue.
3/16th is 18.75%, and this would be equivalent to having one great-grandparent and one great-great-grandparent (who wasn’t a parent of the first great-grandparent) of a particular background. You’d call that twenty percent if you wanted to round off to the nearest five.
shrug
How would you decide what “Hawaiian” is?
Given the population flows through the ages, it becomes problematic–OK; impossible–to define sharp delineations among populations.
There are certainly average prevalences for particular variants of particular genes among population pools, but beyond that it gets messy, including how to categorize a given population. Further, the “percent” notion is difficult to define because not all genes are active and we don’t really know which ones are silent. So what does it mean to say you are X percent? It certainly doesn’t mean X percent of your base pairs are identical to X percent of another’s base pairs…
I imagine if you’re patient and care to work enough generations of selective breeding, you can come up with 20% something. The official definition of a “full beefalo” is 37.5% American Bison the remainder beef cattle. Get a breeding pair of beefaloes and they’ll breed true.
No, you can’t actually be 20% anything. You do the calculations by looking n generations back. In that case you have to be a proportion that’s a multiple of 1/(2^n). 20% (.2) is not a multiple of 1/(2^n), not matter how large n is. It doesn’t matter that there will be duplications if you go back far enough. Suppose you look at your great-great-grandparents, which you will have 16 of if there is no duplication. Suppose on the other hand there is duplication, so instead you have only 10 great-great-grandparents, which can happen if 6 of the great-great-parents appear twice in your family tree and 4 of them only appear once. Suppose that 2 of the ones who appear twice on the family tree are (ethnically) Hawaiian, but none of the others are. That doesn’t make you 20% Hawaiian, even though 2 is 20% of 10. It makes you one quarter Hawaiian, since 4 is one-quarter of 16. This is because 4 of the 16 slots in the generation of your great-great-grandparents are filled by Hawaiians. You measure ancestry by the number of slots filled n generations back, not by the number of people.
Someone who claims to be 20% of anything is either rounding or doesn’t know what they’re talking about.
You have 64 great-great-great-great grandparents. If 13 of them are purebred Hawaiian, and the other 51 are something else (caucasian?), then 13/64 = 20.3125%. If you’re willing to round a little, then the answer to your question is yes.
That depends on what you mean by 20% something. When we talk about heritage and genetic averages it is impossible, but for numbers such as “4% neandertal” or “99% chimp” we look at the actual genes, not the statistical average.
It is for instance completely possible that someone with four grandparents of different ethnicity, an Aian and Beeian couple, and a Ceeian and Deeian couple, end up with a close to 50-50 Aian Ceeian mix. Statistically unlikely, but possible. Despite having nearly no Beeian genes this person would be, according to rules based on averages, 25% Beeian.
As a genealogist, I can attest that this is the correct analysis of the question.
Except the OP isn’t asking about genealogy, but about genetics.
There have been any number of projects looking at African Americans to determine how much of their genetic ancestry comes from Africa vs Europe (and possibly other places), and the answers are almost always not a negative power of 2 (that is 1/2, 1/4, 1/8, etc).
Since the chromosomes don’t just split perfectly and then realign in the offspring, you are going to get all sorts of combinations after a few generations of mixing.
Agree with those that say it is possible. Definitions of race/ethnicity are irrelevant - you can absolutely be 20% of something (although not easily exactly 20%).
Just to clarify what has been said - it depends on how you’re measuring it.
If you’re counting up by ancestral line (i.e., not doing any actual genetics, just looking at where specific ancestors came from), you’re going to be limited to numbers you get from 1/2^n. However, if you finagle those numbers enough, you can get close to 20%, if you’re willing to round.
If, on the other hand, you take a look at actual DNA sequences, using some database to assign specific unique sequences to specific regions of the world, then you can get pretty much any number you can imagine, because of the way DNA, chromosomes, meiosis, and recombination work.
So it depends on what you mean.
I took the OP as asking about the average person who makes a claim like “I’m 20% Hawaiian.” Yes, it’s vaguely possible that they have paid for an analysis of their DNA. That’s rather rare though. It’s much more likely that they are talking about doing a genealogical search. In that case 20% has to come from rounding the real figure. That is, unless it’s someone simply making up (or at least just guessing at) the real figure, which is the most likely thing of all.
You are not limited to 1/(2n) but to j/(2n)…you still can’t be exactly .2, but you can come as close as you are willing to go back in generations, mathimatically anyhow. In reality family trees start narrowing as they go up, and of course you eventually get back to “Adam and Eve”.
I’ll bet the Bene Gesserit could manage it. Though it sort of backfired for them, didn’t it?
Bingo.
And yet, you’re incorrect, as pointed out above, unless you’re talking about “exactly 20%”.
I believe this is the correct expression.
Look at it this way. If we go back enough generations, each ancestors is either 100% Hawaiian or 100% not, because before this, the populations didn’t meet. That generation will have 2^n people (ignoring inbreeding). Any number could be Hawaiian. This leads to Keybo’s result. Allow some inbreeding (which is likely, given enough generations), and there are more possibilities, but that can be compensated by counting those ancestors twice (or 2^n times, as appropriate), which still gives us the same set of possibilities.
J is the number of Hawaiian ancestors, and n is the number of generations back to before the cultures met.
Practically speaking, though, someone who claims 20% heritage probably just doesn’t understand the facts. It would be a very difficult figure to arrive at, normally.
Not quite. If all 64 of your great-great-great-great grandparents bred with each of the others to produce one child, you, then this would be correct. But I think that we have to assume that there are 5 generations in between, and that they’re marrying outside of the family bloodline. And not all of them will breed with people who have the exact same pedigree. In those 5 generations, the 20.3125% Hawaiian mix is going to get pretty diluted.
If they do have the same pedigree? If pretty much the entire population has a 20/80 Hawaiian/caucasian mix, and people breed more or less randomly, then yes, generations later, you will be 20% Hawaiian, and so will everyone else.
Good point. Correction noted.
Your caveats don’t make much sense to me. For the sake of clarity, I’ll assume that Machine Elf is talking about my own genetics below.
“If all 64 of your great-great-great-great grandparents bred with each of the others to produce one child,”
It doesn’t matter how many ‘other children’ any of my ancestors have as long as those children are not also my ancestors. If they are, then I have a kinduv weird family tree, and I don’t have 64 unique great-great-great-great grandparents, but I still have 64 ‘slots’ on the family tree at that level, and need to count by slots not by people, as has been explained upthread.
All 64 great-great-great-great-grandparents are obviously not going to breed with each of the others, (especially since some pairs will be male-male or female-female.) Like the animals on Noah’s arc, we would usually assume that they pair up two by two, though it’s possible that some of my great-great-grandparents are half-siblings. We don’t really need to get into those complications though.
“I think that we have to assume that there are 5 generations in between, and that they’re marrying outside of the family bloodline.”
Yes, obviously, there are 5 generations in between.
Well, they’re probably marrying outside of their existing family bloodline as it existed before they married. They’re not marrying outside of MY family bloodline, though, by definition, because my family bloodline was formed by mingling theirs.
“And not all of them will breed with people who have the exact same pedigree.”
Again, this is stipulated in the hypothetical. We’re assuming that some of them have ‘pure Hawaiian’ pedigree, and some have ‘pure Caucasian’ pedigree. Of course, these are idealized simplifications, but I don’t think what you’re saying gives any more precision to the situation.
What I’m trying to say (and badly, I must admit), is having 64 great great great great grandparents of a certain racial mix is no guarantee that the last resulting child will have that mix. Those 64 will have 32 children with more or less that mix, but then you’d have to bring in 32 new spouses, and who can tell what they are? You’d have to control the racial makeup of every new spouse for every generation to get the 20% mix.