## How much of your genome do you inherit from a particular ancestor?

A generation ago you have two ancestors, your parents, two generations ago you have four grandparents (ignoring the possibility of inbreeding).
Each generation we go back your number of ancestors doubles, such that your number of ancestors k generations back grows at 2^k (again ignoring the possibility of inbreeding, which is a fair assumption for small k and if your ancestry derived from a large population).

However, you only have two copies of your autosomal genome, one from your mum one from your dad. Each generation we go back halves the amount of autosomal genome you receive, on average, from a particular ancestor. For example, on average 50% of your autosomal genome passed on from your mother comes from your maternal grandmother, 50% comes from your maternal grandfather. This material is inherited in large chunks, as chromosome fragments are inherited in large blocks between recombination events.

As you inherit autosomal material in large chunks there is some some spread around the amount of genetic material you receive; e.g. you might have inherited 45% of your autosomal material from your maternal grandmother, and 55% from your maternal grandfather. In my last post on this topic I looked at distribution of how much of your autosomes from grandparents, and I talked about why it was vanishingly unlikely that you received 0% of your genome from a grandparent.

We can take this back further, and look at the spread of how much of your autosomes you receive from ancestors further back, and how far we have to go back until it is quite likely that a particular ancestor contributed no genetic material on your autosomes to you. To do this I again made use of transmission data I had to hand to calculate these quantities using real data. Using data I had for one generation of transmissions, I compounded these together over multiple generations. After doing this I calculated a number of different quantities that I’ll describe below.

First lets look at the distribution of the number of autosomal genomic blocks you receive from a specific ancestor k generations ago

The black line is for a typical ancestor, where we do not worry about how many males and females there are along the particular route back through the family tree. While if we follow your Matrilineal line back we see there are more blocks as females have a higher recombination rate and so are breaking there genomes up into more blocks, following the patrilineal line we find less blocks as males have lower rates of recombination.

We can also calculate the probability that you inherit zero (large) blocks of your genome from a specific ancestor:

We can also do this for individual chromosomes:

The lower number chromosomes are bigger, recombine more, and so are broken into more chunks, making it more likely that a specific ancestor contributes one of those chunks.

Finally we can look at the distribution of the amount of autosomal material you inherit from an ancestor k generations ago:

note that these distributions are centered on 1/(2^k)

This entry was posted in genetic genealogy, personal genomics, popgen teaching. Bookmark the permalink.

### 33 Responses to How much of your genome do you inherit from a particular ancestor?

1. Many thanks for this interesting post. I think you got the terms paternal/patrilineal and maternal/matrilineal a little bit muddled up. Patrilineal means the direct paternal line (ie the surname line). Paternal means any relations on the father’s side of the family. Matrilineal is the direct maternal line (the path of transmission of mitochondrial DNA). Maternal means any relation on the mother’s side of the family.

2. cooplab says:

Thanks Debbie. However, reading over this, I’m not quite sure where the muddle is. Is it the use of maternal lineage?

• Graham, You’re using the terms maternal/matrilneal and paternal/patrilineal interchangeably but they don’t mean the same thing. In your charts for example you’re talking about matrilineal and patrilineal transmission but you are discussing autosomal DNA. Surely you mean autosomal DNA that is transmitted from all one’s father’s ancestors and all one’s mother’s ancestors rather than autosomal DNA which is transmitted on the two uniparental lines? I would imagine it would be impossible to measure how much autosomal DNA is inherited on the uniparental lines going back so many generations. You also talk about the patrilineal and matrilineal lines in paragraph 7 but I think again you really mean the paternal and maternal lines not the uniparental lines.

• Ann Turner says:

Debbie, I think the charts show simulated data over several generations, using different recombination rates for males and females Thus the blue patrilineal curve does refer to male-male-male-male transmissions, and similarly the red matrilineal curve is for female-female-female transmissions. The black curve is for a random mix of male and female transmissions, which we are forced to use when the actual line of descent zig-zags back and forth in an unknown fashion.

• cooplab says:

Hi Debbie,
Ann is correct, the matrilineal line shows results tracing back through only female ancestors (using only recombination events from female transmissions). Similarly the patrilineal line is going back through only male ancestors. So I think the post is correct as written, but I’ll try and make tit clearer.

Graham

• Thanks Graham for the clarification. It’s the use of the terms “maternal side”, “maternal lineage” and “maternal ancestors” that have confused us because those terms refer to all the ancestors on the mother’s side. Perhaps you should change the word maternal to matrilineal and perhaps define matrilineal at the first occurrence to avoid any misunderstanding.

• cooplab says:

Hi Debbie,
I used maternal lineage to refer to the matrilineal line (mum’s mum’s mum). That seems a reasonably standard usage (at least in population genetics). When I google “maternal lineage” I find a lot of tests of mtDNA ancestry called that. But I’ll avoid using it in the future, if it means something different to you/others.

I used maternal ancestors to mean the family tree on your mother’s side. For example, I say “These chunks are spread across your 2^(k-1) maternal ancestors” there I do mean ancestors k generations that you trace back to through your mother. Assuming no inbreeding that is 2^(k-1) individuals.

Hope that helps,
Graham

• Thanks Graham. The term matrilineal line is well understood by genealogists but the phrase “maternal line” seems to be used in different ways by different people. For example, this genealogy website defines the maternal line as “line of descent traced through the mother’s ancestry”: http://www.genealogy.com/genealogy/Glossary/NEWGLO_M.html The DNA testing companies often confuse matters by not defining terms properly. I find that I’m always having to spell out to people that a mitochondrial DNA test only covers the one specific line and not all the ancestors on the mother’s side. It’s your last sentence that confused me where you talk about autosomal material inherited from an ancestor on the “maternal side”. I took that to mean DNA inherited from any ancestor on the mother’s side of the family whereas I see now that you meant the matrilineal line.

• cooplab says:

I’ve now updated the post to make this clearer.

Thanks.
Graham

• Thanks Graham. It’s now very clear what you mean.

• Wendy says:

I am asking a totally different question since I am not really a genetics whiz, so…if I trace my ancestry back to say my 35th great grandfather, but I get there starting from my maternal grandfather and then his father’s wife and back and forth between husbands and wives….can I prove my 35th great grandfather is related to me through DNA testing?

I am so confused….

Thanks

Wendy

3. David Benn Crawford says:

Okay, let me get this straight. If we inherit nothing from more than 12 generations ago, are zombies real?

• cooplab says:

So in any given generation in the past, there are a set of people in your genealogy who we can trace the various sections of your genome back to (lets call them your genetic ancestors). The probability we inherit any autosomal DNA from a specific ancestor from more than 12 generations ago is small (~82%), because you have vast numbers of ancestors that far back (e.g. 12 generations ago you have 4096 ancestors) and your genetic ancestors are a very small subset of these people (on average around 700 people).

4. David Benn Crawford says:

Is this to say that our lights are on, but no one is at home? Is this mathematical proof for out-of-body experiences? This explains everything I observe at faculty meetings.

5. RCBlake says:

Your discussion does not reflect the real existence in inter-marriage of ancestors. In the not too distant past people let say six generations, people did not travel more than 25 miles from their homes or villages. The gene pools were smaller then than now with modern means of travel. This will make the mathematics a “bit” more non linear.

• cooplab says:

Agreed. I mentioned throughout the post that the calculations ignored inbreeding (i.e. inter-marriage of ancestors). I’ll likely tackle this in a subsequent post, as my first aim was to help people to have an intuition for the basic calculations.

• It would be very helpful if you could do some simulations on the number of genealogical ancestors that the average European would be expected to share within the last five to ten generations as a result of what genealogists call pedigree collapse:

http://www.isogg.org/wiki/Pedigree_collapse

This is the timeframe covered by the cousin-finding autosomal DNA tests.offered by the commercial companies. The models used in scientific papers tend to have focused on the bigger picture looking at the population level rather than the implications for the individual. It is very difficult trying to trace most genealogical lines back beyond five or six generations but that is probably just the time where pedigree collapse starts to kick in.

Very informative post! A few of questions that I am intrigued by ( as a layperson ) are as follows:
1. Given a shared IBD segment of length L between 2 individuals: can one ascribe a time or generation range to the corresponding TMRCA based on that?
2. This question is based on the 2013 paper ( fig 4 ) , can the average number of common ancestors per generation be derived based on a single IBD segment of length L or is it based on a distribution of all IBD segments that are shared between 2 individuals, with each segment ascribed to a MRCA?

7. Samuel says:

Thanks for your work on this post. I just had one question. So If I had an ancestor living some time in 800 A.D., I am basically not related to him??

• cooplab says:

Sorry for the slow response. Yes, you are very likely not genetically related to him. But you are genealogically related to him. However, you are also genealogically related to most of the individuals alive (who left descendents) back then.

8. Kate says:

To add to Samuel’s question, how is it that our DNA can be traced back many thousands of years to Africa?

• cooplab says:

Sorry for the long delay. The key is that while the probability that you share DNA with a particular ancestor decreases as we go back over the generations, your total number of genetic ancestors is increasing. By the time we get back to 10s of thousands of years ago you are descended from everyone (who left any descendents to the present day ~80% of the population). As >50kyrs ago the vast majority of everyones’ ancestors were in Africa, the majority of your genome traces back to African ancestors.

9. rkmvclm says:

I am fascinated by this as I know that many of my wife’s relations are consanguineous. Several branches have great grandchildren marrying each other – albeit from the descendants of siblings. There is also a scattering of French and Scandinavian ancestry way back which I assume would impact the autosomal whilst not showing in the mtDNA analysis. ? I welcome any comments from the scribe and fellow bloggers.

10. James says:

n generations ago you have m=2^n ancestors within that particular generation, and as n increases the probability of inheriting from a particular ancestor tends to zero.

I’ve only seen calculations of NOT inheriting from a single person within a generation.

My question is, what is the probability of NOT inheriting from say two, three, four, or all m of the ancestors within a given generation?

• cooplab says:

Thanks for the question. So in any given generation back you have to inherit genetic material from some of your ancestors (otherwise you’d not have any genome). The calculations you ask about are much more complex (see Donnelly 1983 http://www.ncbi.nlm.nih.gov/pubmed/6857549 ). I have some simulations showing the distribution of the number of genetic ancestors (I’ll post them sometime), but the approximations described here work reasonable well more than a few generations back.

11. Jon O says:

If I understand this, since all of our autosomal dna came from particular distant ancestors, the problem is hat we just cannot assign a % to a particular individual due to the mixing over generations. You would have to compare the dna from a distant ancestor (dig up a grave) to your current dna and check for matches. Obviously, all of our dna came from our ancestors that we ultimately all share at some point.

12. Rebecca says:

Those of us who do IBD cluster analysis (Identify a group of people who share the same segment of the same strand of the same chromosome and then compare pedigrees or as nearly complete a set of pedigrees as we can devise) find that most CAs for most IBD clusters of any size were a set of ancestors born in the 1600s if not earlier. This would point to conflict between your theoretical probabilities and actual atDNA inheritance patterns.