# Could your grandchild be genetically identical to you?

Plain and simple: could your offspring's offspring be genetically identical to you? What conditions would this be possible under, if any?

• If you want this answered to a hard-science level of rigor, I think you at the very least will need to define "genetically identical". – a CVn Dec 29 '17 at 6:04
• Science-based and hard-science tags should not be used on one question. Decide level of scientific proof you need and then choose one. For now, I'm voting to close as unclear what you are asking because you don't say anything about mitochondrial DNA, telomers, gender of grandpa, parent and offspring... All the little things that matter. – Mołot Dec 29 '17 at 6:10
• Title and content of the question don't match. "You are your own grandparent" and "you are genetically identical to your grandparent" are not the same thing. (Consider twins. They are genetically identical, but they are still two distinct people - if I had a twin, he would not be me.) Please confirm which thing you're looking for and edit the incorrect version (title or content) of the question so they match. – Dave Sherohman Dec 29 '17 at 10:12
• To correct the inaccuracy of JDlugosz comment: A 'strain' is a variation of an organism/specie. Its akin to like a breed in dogs only offspring of a strain must retain "genetic uniformity" (up to a certain non-standard-declared generation). "Genetic uniformity" IS NOT synonymous with genetically identical !!!!!!!!!! genetic uniformity simply means that all members share certain desired expressed traits through every member of its lineage. This means that a member of a strain can have genetic differences that do not impact its membership to the strain. – anon Dec 29 '17 at 14:19
• You could probably go back in time and accidentally kill your grandfather. Then sleep with your grandmother to ruin the space time continnium. That may work. – user32862 Dec 29 '17 at 14:37

# Yes, but it'd never happen.

There's nothing to prevent it, though the chances of it happening in the wild are effectively 0.

From each grandparent you inherit 25% of your genes. Your parent inherits 50% and you get 50% of that.

Some freakish coincidence could mean that you get the remaining identical 75% from your other ancestors and end up your own grandfather through misuse of time travel.

# However

This 25% rule is a useful lie, you get a random 50% of your parent's genes, you could get more than 25% from any grandparent, in theory you could1 get the full 50% from one grandparent meaning you only need to get the other 50% from the other side, excluding the risk of inbreeding.

1 A non-zero probability is a non-zero probability, you could also win the lottery every week for the rest of your life, it's non-zero.

• Rep for the footnote! – JBH Dec 29 '17 at 13:35
• For your footnote: buying just one ticket a week... – jmoreno Dec 29 '17 at 22:44
• @arp Even with maximal inbreeding, you'd still be looking at a ~ 1 in 2^23. – Shufflepants Dec 30 '17 at 10:45
• @trysis In general; I don't think so. Each parent gives a gamete to the embryo. Each gamete is also a haploid, so you get a single set of chromosomes from each parent. Those form the pairs of chromosomes; which means each chromosome pair is half from each parent. – JMac Dec 30 '17 at 16:45
• @arp massive inbreeding tends to, um, not scale. Think about all of the health issues (including infertility) of the Hapsburgs for instance. Your inbred population would quickly become inviable. – Jared Smith Dec 30 '17 at 17:20

You can, under these conditions:

• you are a woman
• you clone yourself and bear the cloned fetus in your womb
• your daughter, when reaching sexual maturity, does the same.

Your grandaughter will be a clone of your daughter who is also your clone. So the 3 of you have the same genes and are also related.

• Likewise, if a child was conceived parthenogenetically. Very highly unlikely, because even if an egg was created with two sets of chromosomes, one set needs to be edited a little somehow for the ovum to be viable - of course transcription errors do happen and, I suppose, may be a genetic weakness or feature which might be inherited, so for the daughter to also conceive parthenogenetically more likely. This is essentially the same as your answer with the exception that yours is deliberate intervention and reasonably certain, whereas parthenogenesis is incredibly unlikely (near impossible). – Lee Leon Dec 29 '17 at 11:04
• Dang, that was clever. I took "offspring" too literally. – JBH Dec 29 '17 at 13:34
• You don't even need to do the first half, just clone you and put the baby inside your daughter. Then her offspring will be your clone. – A. C. A. C. Dec 29 '17 at 18:23
• @JohnDvorak: Where in the body? – ruakh Dec 30 '17 at 0:17
• @A.C.A.C. The trouble with that is that she would technically be your daughter, though birthed by your other daughter. – wizzwizz4 Dec 30 '17 at 14:50

### Linebreeding

I am going to be bold and answer this question by cheating a little. I will assume that:

• Genetically identical means "close enough", considering that it is not defined in the question.
• You have more time than is available for a normal human (this is worldbuilding after all).
• Grandchild is someone who is a child of your child (yes, we must point this out).

Linebreeding can not give 100% equality but can get you arbitrary close given enough time.

It works by breeding with your own children repeatedly, until you reach a satisfactory genetic closeness. Using the illustration from wikipedia, you are S, your initial partner is D, and your children and grandchildren are DN:

What happens is that you initially breed with D. Your child D1 has 50% of your genes. Now you breed with D1. Your new child D2 has 75% of your genes, and 25% of D's. Again you breed with the latest child, and get a new child, D3, having 87.5% of your genes.

D3 will be your grandchild. It is also your child, but an individual can be both. You are D3's parent's (D2) parent.

To calculate how close you get, you can use this function: $$f(g) = 100*(1-2^{-g})$$

The tenth generation has 99.9% of your genes, and the twentieth generation shares 99.9999% of the genes with you.

• Except that you won't be alive to breed with the 5th generation (probably not be able to breed with the 4th or 3rd) much less the 12th. Also, "identical" means "close enough" when comparing cars, but not genes. – RonJohn Dec 30 '17 at 3:03
• @RonJohn - as the answers says, this is worldbuilding. The subject may have access to some form of hibernation technology, routinely take long trips at relativistic velocity, or be a time traveler of some kind. – Jules Dec 30 '17 at 7:45
• Right, exactly as mentioned in a comment at the top: "take a look at lab mouse strains. They are inbread to the point of being genetically identical — so identical parents then have a matching identical offspring. – JDługosz" Essentially, the only way offspring would be "identical" in the sense of the OPs question, is, in a (presumably!) dystopian society where, for whatever reason, all humans are linebred. Then, quiet simply, everyone in that group would be identical, including offspring/grandchildren etc etc. – Fattie Dec 30 '17 at 14:37
• "Except that you won't be alive to breed with the 5th generation" trivially solved by merely storing sperm/eggs. If (for some bizarre reason) a dystopian society wanted to achieve this, it is technologically trivial even today (you just need "a refrigerator!") - as easy as we currently do it with mice, horses etc. But it's sort of a trick answer to the question ("everyone would be identical"). – Fattie Dec 30 '17 at 14:39
• @Fattie good point about cryogenically storing sperm and eggs. – RonJohn Dec 30 '17 at 14:46

In light of the answers from other people, I'd like to offer some basic math for how likely this is to occur.

The scenario I'm considering is as follows: You, an ordinary human, have two children. Those children have a child together (yes, I know incest is bad - this is purely hypothetical).

You, as an ordinary human, possess 46 chromosomes in 23 pairs. When you have a child, they receive one of each of these pairs from you (assuming nothing strange1 happens). As a side note, barring any medical breakthroughs that I'm not aware of, you would have to be genetically male (XY) so that your two offspring would be able to have children with each other.

For simplicity, I'll call the set of chromosomes that your first child got from you 'set A' and those that your second child got from you 'set B'. In order for your grandchild to be an exact genetic duplicate of you, set B must contain all the chromosomes not found in set A, and then both children must pass on those specific chromosomes to their child. (This assumes that you do not have any chromosome pairs where both chromosomes are identical, which you probably don't unless you're the result of inbreeding).

Now that we have established the scenario, let's talk about the probabilities:

Let's assume the chance of someone's child receiving one specific chromosome from a pair is 1/2, as there are two possible outcomes.

With 23 pairs, the likelihood of passing on any one combination is 1/(2^23) (roughly one in 8 million). In our scenario, we see this happening 3 times: you passed on set B to your second child, your first child passed on set A to your grandchild, and your second child passed on set B to your grandchild. 2

So, the likelihood that your grandchild would be a genetic duplicate of you is 1/(2^69), or roughly one in 590 quintillion.

1 By "nothing strange", I mean there are no errors in the replication of the chromosomes, and nothing along the lines of having 3 chromosomes of the same type, such as the case of Triple X syndrome, or anything else I haven't thought to list here.

2 If you're wondering why I don't count when you passed set A on to your first child, it's because there are actually 2^23 different set A's that are possible, so the math cancels out. This is based off the assumption that there is already some set A you passed on to your first child.

• I was going to answer in this direction, but you were faster. You can improve upon those numbers by choosing the right parents. Because of the birthday problem you only need to father a few thousand children (so you will need to be male) to have a good chance of having a pair with opposing chromosomes (i.e. 23 different of yours each) among them. (which as a nice side effect will automatically be of opposite sex) Using them would increase your chances to 1 in 2^46. You could even increase on that number with a few generations of inbreeding. Obviously this is proper mad scientist territory... – mlk Dec 30 '17 at 0:15
• Do you include the chromosonal cross-over that occurs during meiosis? – James K Dec 30 '17 at 1:03
• @milk I mean it's not that mad if you branch out of the human territory - aren't all lab mice genetically identical? I seem to remember reading that. – childofsoong Dec 30 '17 at 1:29
• @JamesK I have no idea what that is. – childofsoong Dec 30 '17 at 1:29
• @childofsoong - there are enzymes that bind the two copies of each chromosome together during the first stages of replication. Those enzymes have a chance of swapping a section of DNA between the two chromosomes. It isn't simply that you inherit one chomosome from one parent and one from another, the genes on them get mixed between the two. As you've ignored this in your analysis, it means the actual chance of this happening is substantially less than you've estimated. – Jules Dec 30 '17 at 7:40

Is it possible? Yes.

Is it likely? No.

The only way to get an identical grandchild is if you have two children, one male and one female. Each of those children will get half of your DNA; in order to conserve 100% of your DNA, there can't be any overlap between their copies. They then need to have a child that combines the two half-copies into an original whole. The odds against this working out are pretty low.

Humans have 23 chromosome pairs, for a total of 46 chromosomes. Each of your children has, under normal circumstances, one chromosome from each of these pairs selected at random. That gives a 1-in-8,388,608 chance of child "A" and child "B" getting non-overlapping copies of your DNA. Not too unlikely, as such things go.

However, the same process applies to the grandchild: there's a 1-in-8,388,608 chance that the genetic contribution of each of its parents consists entirely of "your" DNA. Multiply that out for both parents, then multiply by the odds of the parents having the correct genetic makeup, and you get a 1-in-590,295,810,358,705,651,712 chance of the grandchild being genetically identical to you (give or take mutations). Yeah, not going to happen.

• Chromosomal crossover occurs during meiosis, that makes the odds a lot longer. – James K Dec 30 '17 at 1:04

# Practically speaking: No

Now, I'm not just talking about the absurd odds against it when going with the single-generation inbreeding method, the time it takes with the line breeding method, or the wild cost it would have if you use a gene editing based method.

The fact of the matter is that we don't really have one set of genes; due to mutations, both deleterious and potentially intentional ones that happen at different rates throughout our bodies, we all have several very similar but still distinct genomes throughout our cells.

Even if we use the most reasonable method of making a closely related grandchild (clone of a clone), we have to make a series of choices that will prevent us from making a perfect copy.

First of all, from whence do we get our DNA template for our clone? A skin cell? A blood sample? A brain neuron? It matters, because they may well have different (although very similar) DNA. This choice has to be remade for the clone of a clone, compounding any errors.

Second, how would we guarantee that each clone is subject to the same environmental stimuli and ionising radiation and viruses that can mess about with their DNA, and that they have the exact same number of cells in the exact same places to respond to these stimuli? The answer, of course, is that we can't. It might not even be theoretically possible.

Finally, how would we ensure that the genetically identical clone stays genetically identical? Again, we can't. As I alluded to earlier, our body engages in an act of intentional messing about with our genome, specifically in our brain. Although the mechanism isn't completely understood, it appears as if memories are, in part, printed onto the genomes of brain cells, in addition to being stored in the network of neurons. This leaves brain cells with a lot more mutations than other cells in the body.

In other words; if you're not genetically identical to yourself, how could you hope someone else to be?

One exception: It can be done if you are a single-celled organism that reproduces quickly and asexually.

• As per the footnote - the OP never specified that we’re talking about humans... – DonielF Jan 2 '18 at 21:25

No. Even if you could have a "grandparent" and "grandchild" who were genetically identical, perhaps by two generations of cloning, they would not be the same person. Just as identical twins are not the same person.

Of course you could, given the appropriate technology, have multiple generations of genetically identical clones. That's quite commonly done with plants. For instance, every plant of a particular rose variety is a clone of a single original plant.

Since copying of genetic material occurs with errors (mutations), whether you can get an identical copy even in the case of cloning (as mentioned above) depends on mutation rate.

In DNA-based organisms like humans mutation rate for point mutations is about $10^{-10}$ per DNA base pair per cell division. Human genome is $3 \times 10^9$ base pairs. The number of cell divisions in the germline is about 20. Thus you get around 6 errors per each genome copied from grandmother to mother and another 6 from mother to daughter.

The probability that you get an identical, mutation free genome is given by Poisson distribution and is about exp(-12) ~ $10^{-5}$, or one in a hundred thousands. Since humans are unable to produce such a large number of offspring, there is no chance to get an identical child or a grandchild.

Actually we are rapidly degrading genetically as a species: Mutation and Human Exceptionalism: Our Future Genetic Load http://www.genetics.org/content/202/3/869.full

• One in a hundred thousand isn't that unlikely a chance. Given that there are seven billion people on Earth right now, that works out to about a 70% chance that somebody has a mutation-free grandchild. – Mark Dec 31 '17 at 19:39

Could your grandchild be genetically identical to you? Plain and simple: could your offspring's offspring be genetically identical to you? What conditions would this be possible under, if any?

Sure, but it is unlikely.

Suppose that the grandparent's ("your") ("GP's") genome has about 20,000 protein coding genes and that about 2,000 of these vary across the human population and (to oversimplify) that when a gene varies, there are two equally likely variations.

To be genetically identical, the grandchild's ("GC's") genome has to match all 2,000 of the variable genes which, in this simplified model, has a 1:2^2,000 or 1:1e+600 likelihood if the matching is random and independent.

But the matching is not random and independent because GP contributes on average 25% of the genes to GC so the likelihood increases by 2^500 (!) to 1:2^1,500 = 1:1+e450.

If GC were the offspring of an incestuous relationship between GC's children, GP contributes on average 50% of the genes to GC so the likelihood increases by another 2^500 to 1:2^1,000 = 1:1+e300.

If GC were the offspring of a disgustingly sick incestuous relationship between GP and GP's child, GP contributes on average 75% of the genes to GC so the likelihood increases by another 2^500 to 1:2^500 = 1:1+e150.

Since the number of people alive is about 1+e10 and the number of people who have ever lived is probably at most 1+e12, the likelihood of a 1:1+e150 occurrence in 1+e12 events is materially zero.

• Genes are not inherited independently. They're bundled into chromosomes, which are inherited in an "all or nothing" fashion (usually). – Mark Dec 31 '17 at 19:35
• Chromosomal recombination and crossover mix up genes within a chromosome. While the bundles of genes represent significant correlation for the offspring of any individual, within the population this is not so significant. You are correct that the model above does not incorporate every complexity possible: it is simplified. It could be improved and lengthened from a few paragraphs to a book. I am sure that would be more accurate. In the end, I believe the odds would still be miniscule. – Joseph Nye Welch Jan 2 '18 at 11:17

Someone could arrange for that to happen in a way that would be sort of a cheating method.

1) It is certainly possible for someone's grandchild to have by chance the exact same genetic code; but the odds against that ever happening are astronomical.

2) Therefor some medical way to ensure that someone has a grandchild with their exact genetic code would be needed.

Someone could clone themselves and have their daughter serve as a surrogate mother for the clone. Thus when the clone was born it would be the (nongenetic) child of their daughter and thus their grandchild. That seems like using a loose and somewhat cheating definition of grandchild but it is something that it might be possible for medical science to achieve only decades in the future.