How much of your genetic material do you inherit from a particular ancestor? You inherit your mitochondria through your matrilineal lineage (your mum, your mum’s mum, your mum’s mum’s mum and so one) and your Y chromosome from your patrilineal lineage, but how is the rest of your genome spread across your ancestors in any given generation?
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.
As a rough rule of thumb the autosomes you received from (say) your mother, k generations back is broken into (22+33*(k-1)) chucks, as your genome comes in 22 chromosomes and there are on average 33 recombination events per transmitted genome. These chunks are spread across your 2^(k-1) maternal ancestors. So, for example, nine generations ago the autosomes you receive from (say) your mum are broke, on average, into 286 large chunks, and these are spread across your 256 ancestors. Thus on average each of ancestors has contributed only a single block to you, and by chance it is possibly that they contribute zero. This gets worse the further we go back in time, your genome is broken up into more and more chunks, but this does not grow as fast as your number of ancestors. This makes it increasingly likely that you inherit no autosomal material from a particular ancestor.
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: