I was reading David Reich’s latest book and really trying to absorb it. I have really struggled with this figure though:
As a physical scientist (i.e. somebody that’s done a fair amount of math in my day) I’m somewhat nervous in saying, I don’t quite understand the difference between the left side and right side. I get, in theory that there is a difference because of recombination, but I don’t understand why the right side is additive (+71 each generation).
I do not understand how your statement applies to the topic of “miraculous” vs. “providential”.
Did you intend that it does apply to this part of the discussion?
It is plus 71 every generation because Reich is presuming that on average there is about 35.5 recombinations per generation, and each recombination creates 2 new pieces.
I don’t think making an argument from providence makes any sense (it is coincidence, arguable, etc.) where as a miracle might be used as the basis of an argument (if Resurrection, then Christianity is true) but using a miracle as a part of a scientific assessment of something is really problematic, for the reasons mentioned before.
But wouldn’t that end up being multiplicative, just like the number of ancestors? 
Don’t the X & Y cross over in the pseudoautosomal regions?
No, because there is less DNA subject to recombination in each ancestor going back.
Take your parents. They each have 1/2 your DNA, after each each of them apply 35.5 recombinations to all the DNA in their genome before passing it on to you. So 1/2 * 2 * 35.5 = 35.5 recombinations between your parents and you in DNA that passes to you.
Take your grandparents. They each have 1/4 your DNA, after each each of them apply 35.5 recombinations to all the DNA in their genome before passing it on to your parents. So 1/4 * 4 * 35.5 = 35.5 recombinations between your grandparents and your parents in DNA that passes to you.
It is easy to see how this extends every generation as you go back. The number of pieces of your genome increases linearly as you go back each generation.
Yes, quite right. In fact, like with the others, the crossover is essential for proper segregation. But it doesn’t contribute to genetic recombination, since there are no genes there. There may not be reliable markers, either. I’m not really sure.
Various sources I’ve just looked up put the average number of crossovers per chromosome at between 2 and 3. And isn’t there a fairly small pseudautosomal region on the Y chromosome?
This is very helpful. I do a demonstration with different colored magnets, but I can add this to my slides so students have something to look at later.
To clarify: the pieces are getting smaller and smaller as recombination breaks up prior linkage groups. On the other hand, this ignores the existence of recombination hot and cold spots. I seem to recall that linkage groups of around 10,000 bases persist for quite a long time. Accent on “seem”.
That is too high a resolution to matter much at all for understanding genetic ghosts.
Please show me. I’ve seen 1 or 2, which can yield 2 or 4 new blocks.
Not if you go back a dozen generations or so. I don’t think it changes the probability of lacking any content from an ancestor, but I do think it changes the distribution
Here’s the first one I ran into. Try googling “how many crossovers in humans” or some such.
Yes, I look at it more carefully than just the first hit at google, and used 30 in my book. Reich appears to have used 35.5, and if forced to choose I’d go with his number. @glipsnort or @evograd or @davecarlson might clarify with some real data here.
Part of the problem is that my students have all seen those stupid Ancestry DNA commercials and think that a simple DNA test can trace their great great grandfather back to a specific village in Ireland. I have to convince them that it’s not that simple.
Where did you get 30, and where did Reich get 35.5? The source I’ve cited gives real data for 8 sample points, and gets from 49 to 58 events. The data come from looking at meiotic chromosomes in a microscope and counting chiasmata. But why should that give a different figure from looking at SNPs?
I’m seeing that recombination rate changes with age (and oddly, in females as well as males), and that females have a rate 50% higher than males. I had no idea.
Lee et al. 2011 said this in their discussion (my emphasis):
The average number of recombination events observed with the PST approach was similar to the findings of other studies. The distribution of recombination events showed a mean value of 23.8 in paternal origin and 39.5 in maternal origin. Chowdhury et al reported the genome-wide recombination events in paternal origin ranged from 25.9 to 27.3 while in maternal origin ranged from 38.4 to 47.2 [20]. Another study by Cheung et al demonstrated that the mean numbers of recombination events were 24.0 in male meiosis and 38.4 in female meiosis [15].
A much more recent study by Xu et al. (2020), using a much higher resolution method (~3.5kb vs ~100kb-1Mb in the previous studies) found (my emphasis):
We applied MRLR to the six trio samples from GIAB and the HGSVC (Chaisson et al. , 2019). We identified 395 crossover events in total in twelve meiosis processes (Supplementary Table S3). The median size for the breakpoint regions is ∼4.5 kb. For each meiosis process, MRLR identified 18–53 crossover events. The median number of crossover events in paternal samples is 25, significantly lower than the 39 events in maternal samples ( p = 0.03, paired t -test).
Bleazard et al. (2013) have a nice figure of the number of of recombination events per meiosis in each chromosome for Asian women:
An average human value of ~30-35 seems about right, according to these 5 studies.
So what @NLENTS showed is a sperm cell on the lower end of the male distribution. Makes sense.
Don’t know about “on the lower end”, only Chowdhury et al. found a slightly higher rate (25.9-27.3), all the other studies averaged between 23.8 and 25. But I’m nitpicking…
