An upvote for Mr. West. And this is an example of one of the several reasons that it's tricky to do "cross platform" comparisons.
Andreas also said uptopic that 23andMe is the only company that includes the complete count of fully-identical regions (FIR) and that method is the correct one. I agree with him, and wish all companies would standardize and report this way. It's a simple point that has caused great confusion among not only genealogists but even geneticists who peek in on what we're doing.
Why? Because each parent can only, under normal circumstances (barring things like trisomy and Klinefelter syndrome), deliver about half their DNA to the child. It's not like one chromosome lifts weights and gets much larger than it normally would be: 22 haploid autosomes plus a sex chromosome, that all the parent can deliver. Geneticists will tell you that two full siblings will, as a general average, share 50% of their DNA.
So in the way genetic genealogy has evolved, if someone gives you very close to half of what they have, how much of theirs would you then have? The answer became 37.5%. Wait; what?
But that's what our centiMorgan calculations for genealogy have, for the most part, led us to. Two reasons for that, I think. One is that since parents will always show as sharing about 50% of their genomes with a child, it just doesn't work if then two full siblings also show as sharing 50%. We'll share roughly 25% with each of our four grandparents, so we can't be 50% with a parent and also 50% with a sibling, right? Besides, we know that any two full siblings won't carry, between them, their parents' full genomes. We can figure out how much of the parents' DNA is passed down in aggregate to any number of children by a simple formula: 1-0.5n where n is the total number of siblings. So we get 75% for two siblings, 87.5% for three siblings, and so on. The species wouldn't have enough genetic diversity to go around if it didn't work like that.
So... To grasp it logically, if we share 50% with each parent and 25% with each grandparent, it's gotta be something in the middle of 25% and 50%. Right?
In comes the whole HIR FIR business. If you simply look at counting where two people match an allele on either the father's or mother's chromosomes--assuming of course no pedigree collapse and that the paternal and maternal sides are unrelated in recent generations--and count that as a match (ticker goes up 1 and and you move on) you're going to get, ta dah!, about 37.5%.
Easy to calculate, easy to explain and, thankfully, looks much more logical to genealogists who might otherwise be confused by the 50% sibling matching thing.
But let's consider a simple example of what's actually happening. Completely arbitrary, let's consider SNP rs12511580 on Chromosome 4 at position 11,229,468. Let's say your mom gave you the allele A, or adenine, on her copy of Chr 4, and dad gave you G, or guanine, on his copy of Chr 4.
If we compare you to dad or mom, we always get a match because, obviously, we know that's where the A and the G came from. Now let's say you have a brother and he inherited an A from mom, but got a C, or cytosine, from dad instead. He will always also show as a match to mom or dad, and he shows as a match to you because at position 11,229,468 you both have an A...even though you additionally carry a G and he a C. It's a half-identical match and we click the counter up one point.
What if your sister also has the same A and C as you at that locus? Our counter sees a match on the A (click) and a match on the G (click). At the end of looking at all ~650,000 SNPs we'll end up with about 37.5%. HIR rules the day and we're done.
But wait, you say, your and your sister's chromosomes come in pairs. That's what makes that "X" shape we see in diagrams: the two haploid, or individual maternal and paternal chromosomes are joined together at the centromere. Those are two separate, double-helix strands of DNA, each with its own pairings of nucleic acids down the "ladder rungs" of its helix (nice, elegant visual, but real chromosomes are far, far messier and more contorted/compressed than the image implies).
Both you and your sister have matching haploid chromosomes at locus 11,229,468. We're only doing the either/or count once. You're both an A and a G. But you're an A and G on the other half of that chromosomal pair, too. Shouldn't that count for something? And indeed it should...though opinions vary.
We really only run into this quandary when dealing with full siblings and, to a lesser extent, double 1st cousins. Unless there is significant, recent pedigree collapse the percentage of FIR segments is negligible. Even in double 1st cousins it's only about 1.6%. But in siblings it's about 25%. Which makes it also a simple and immediate way to distinguish full and half-siblings: no FIR segments of note in the half-siblings.
I believe the HIR FIR thing can be confusing to folks new to genetic genealogy, so I decided it's a rabbit hole I would dive down. But nobody reads my way too long posts anyway.
More specifically to 23andMe--and I'm afraid this also raises the constant refrain of "centiMorgans are not a measurement; they're only an estimate of where and how likely crossovers are predicted to, as a broad average, occur during meiosis"--for females the company considers the whole genome, including the two X chromosomes, to calculate to 7439cM. For males, with only one X and an uncounted, much smaller Y, the number is 7257cM. GEDmatch changed a bit at, I believe, the same time they merged Genesis into the production "Classic" version, and they consider the whole genome to be 7174cM. At AncestryDNA that number works out to be 6950cM, and at FTDNA 6768cM.
Same genome, same physical size of about 3.1 billion base pairs, but you may see centiMorgans representing the whole genome range from 6768cM to 7257cM, a variance of over 7%. So at 23andMe two full-sibling sisters would be expected to show a total sharing of about 3629cM; at GEDmatch that would be around 2691cM; and at FTDNA roughly 2538cM.
Now to throw one last wrench into the works. All of those are sex-averaged values. It's really the only practical way we can look at centiMorgans for genealogy. The female genome undergoes crossover, or recombination, approximately 70% more frequently with each gamete created than does the male genome. Since cM calculation is a predictive estimate, not an actual measurement of something that has occurred, the only way we can apply the significant difference in the two genomes is to a known lineage, and then by taking into account that females are likely to go through crossover about 45 times for each gamete, and males about 26 times (these approximate numbers I took from Harvard's Reich Lab; there are other estimates out there but most are in the same area). When it's working, the map interpolator in the Matisse Lab at Rutgers University can provide you with female, male, and sex-averaged cM values for your segment start and end points.
In very rough numbers, though, as a comparison to the values above from the different companies, the female genome actually represents somewhere around 9086cM while the male genome is around 5336cM. At the end of the day, the 22 autosomal segments you got from your mother consists, on average, of 45 segments from her, comprised of the 71 segments she received, collectively, from her parents. Same for your father, but he's working with only 26 segments composed also of 71 input from his parents.
How many segments could possibly be floating around in your own genome? Well, we can take that two-parents-combined number of 71, average it to 36, and then get a pretty good idea. Starting the count with your parents as generation number 1, a simple equation would be 36*2k, where k is the number of generations. For example, 576 segments at the level of 2g-grandparents; 2,304 segments at 4g-grandparents; and 18,432 at the level of 7g-grandparents.
Because they are larger, crossover happens more often on the smaller numbered chromosomes than the higher numbered ones, all things being equal. If you were to get a chromosome passed down intact from a grandparent, 20, 21, or 22 are much more likely candidates than 1, 2, or 3. The biggest chromosomes will almost always crossover during gametogenesis, so the by-chromosome distribution of those 45 or 26 crossovers is not equally distributed. If we look back along the strict patrilineal and matrilineal lines--the extreme left and right sides on a genealogy fan chart--you'll find, on average, larger (in terms of number of base pairs) but fewer segments inherited along the patrilineal line (with a corollary that the sex-averaged segments might in fact be smaller than their linear size when represented by a centiMorgan calculation, but show as being more generationally persistent because of the fewer number of crossovers at each generation). Along the matrilineal line, it would mean a significantly larger number of segments produced at each generation and they can be expected to show more diverse segmentation on a greater number of chromosomes, but the way centiMorgans are calculated the actual segments may appear larger than they really are.
As a quick example, let's hop back over to Chromosome 4 and consider start/stop segment positions of 5,575,751 to 10,702,156 under human genome assembly Build 37, which all our genealogy companies are still using eight years after it was replaced (different subject). On the female genome, that segment represents 18.2cM; but on the male, 10.2cM. What would then be reported to us is a sex-averaged value of about 14.2cM. It's generally irrelevant for matching cousins within a few generations, but when we start trying to deal with small segments you can see how it might lead to a misreading of the data and some incorrect assumptions. Also a different subject.
