You’ve got two copies of each chromosome, having received one copy of each chromosome from your mother and one chromosome from your father (this is true for your autosomes, but not for your X, Y, and mitochondria). When it comes time to pass on your DNA to the next generation, you in turn package up a single copy of each chromosome into a sperm/egg. Sometimes you pass on either mum or dad’s copy of a chromosome at random, often though you pass on a mosaic consisting of the two chromosomes (a recombinant chromosome).
The question came up (via a article by Razib Khan) of what is the probability that by chance your parent entirely failed to pass any autosomal DNA from a grandparent to you (e.g. your father fails to pass on any autosomal genome from your paternal grandfather)? There are 22 autosomes, so if there was no recombination that would happen with probability 2 x 0.5^22=4.7×10^(-7). But this probability is very much lower with recombination, as a recombinant chromosome necessarily has material from both parents. A discussion of how to do this calculation with recombination came up via Mike Eisen on twitter .
In order for you to receive your parent to transmit the entire autosome only from one grandparent, your parent also have to transmit all of their chromosomes without recombination . Recombination also makes this probability differs between the sexes. This is because the probability that a chromosome is transmitted without recombination depends on the sex of the individual, females recombine more than males and so are less likely to transmit a chromosome without recombination. The probability of a chromosome being transmitted without recombination also depends on the size of the chromosome, big chromosomes recombine more. For example, chromosome 1 has a 2% chance of being transmitted to the next generation by females, but a 7% chance of this happening in males. While chromosome 22, a much smaller chromosome, has a 37% chance of being transmitted with out recombination in females, and has a 44% chance in males (you can look up this frequencies in the supplement of a paper I wrote with Adi Fledel-Alon and other folks from Molly Przeworski’s lab).
To work out the probability of all chromosomes failing to be transmitted with recombination for a particular sex we simply multiple together the probability of each chromosome being transmitted without recombination . Doing this, we find that the probability that a male transmits every chromosome without recombination is 8.8 x 10^(-16), and this probability is substantially lower in females at 2.8×10^(-23).
Then having not recombined on any chromosome that parent would have to also transmit every chromosome without recombination (with probability 4.7×10^(-7)). So the probability that your mother fails entirely to transmit any autosomal genetic material from a particular grandparent to you is 1.3×10^(-29), and your father does this with probability 4.2×10^(-22). So it’s pretty bloody unlikely.
Perhaps a more interesting question what is the distribution of the fraction of the autosomal genome that your parent transmits to you from a particular grandparent (e.g. your maternal grandmother)?
This question has been considered mathematically by a number of authors, as it has important applications for identifying unknown genetic relationships between individuals and estimating various heritability measures. However, to my knowledge no one has actually done this calculation using real recombination data (so I thought it would be fun to do). For each chromosome in turn, using recombination data from real transmissions, I simulated the amount of grandparental chromosome that was transmitted by a parent. For example, here’s the histogram of the distribution of the amount of chromosome 1 and 22 a father or a mother transmits.
These distributions are less variable in females than in males due to the greater number of recombination event in females than in males, and the fraction transmitted is more variable for small chromosomes as they have fewer recombination events. The pdf showing these histograms for every chromosome is here.
I then looked at what fraction of the entire (autosomal) genome from a particular grandparent was transmitted to the next generation.
I was a little surprised by how long tailed this was in males. Roughly 5/1000 fathers transmit less than 20% of one paternal grandparent’s autosome to the next generation!
Sometime soon I’ll generate these numbers for longer transmission chains, e.g. what’s the distribution of the fraction of your genome could you expect to receive from a great-grandparent.
1. I originally messed up this calculation, Mike Eisen got the right answer and pointed out my error. Thanks also to Amy Williams and Adam Auton for motivating some of the questions addressed here.
2. The probability of failing to transmit the entirety of one grandparental autosome is actually a lot lower than this, as gene conversion also can lead to transmission of small chunks of genome even if there is no crossing over. Gene conversion is thought to be ~10x as common as crossing over, and I estimate the probability of no transmitted crossovers or gene conversions to be <10^(-90). However, gene conversions are very small, so we might think the calculation above is for the bulk of the genome.
3. This isn't quite right, as the recombination rates of different chromosomes aren't independent of each other.
A few more details of how I obtained the distributions of transmitted material. I started with a set of 1374 parent-offspring transmissions that we had information for.
For each transmission I took the observed set of crossover events for each chromosome. If a chromosome had no crossovers, with probability 1/2 the parent transmitted the entire grandparental chromosome, otherwise they transmitted nothing for this chromosome.
If a chromosome had one or more recombination events in its transmission from a parent, both grandparents will have a contribution. We then have to decide who contributed what material based on the locations of the recombination events. The crossovers define a set of intervals transmitted together, which alternate between which grandparental material is transmitted. So for each transmission with probability 1/2 I make the parent transmit the grandparental corresponding to the odd inter-recombination intervals, else they transmit the even inter-recombination intervals.
Thus my simulations represent real transmissions, the only simulated part is the realization of Mendelian transmission (i.e. the 50/50 transmission probabilities). This means that the chromosome specific plots are not really simulations, and truly reflect these transmission data (each transmission contributing two datapoints, corresponding to the two grandparents).
My whole genome simulations are simulations, that assume independence of mendelian transmission across chromosomes. Only strong selection on viability/meiotic drive at individual loci could violate this assumption, and in general their is little evidence for this in humans. Given this assumption I can simulate vast numbers of transmitted autosomes due to the different realizations of Mendelian segregation across chromosomes. These represent pseudo-samples, in the sense that they only reflect the variation in the placement of recombination events across our 1374 parent-offspring transmissions. But overall I think this is not a bad way to approximate the distribution of transmitted material. It won’t be quite right in the very extreme tails, and that would need data on vast more transmissions.