Howdy from the American Society of Human Genetics 2019 Annual Meeting. I never asked on G2G if any other WikiTreers would be here; if you are at the George R. Brown, give me a shout. I plan to be back for Friday afternoon and will likely skip Saturday altogether. Been a long week. And it's like taking a month to travel mainland China after doing a few Rosetta Stone lessons in Mandarin. You thought you understood most of the lingo, and in some instances you can follow along. But elsewhere, there's definitely a foreign language being spoken. 
Taking a break before "Haplotype-level Interrogation of the Genome" at 4:15, and just wanted to make a quick comment. First up, so that there's no confusion, the DNA of two people doesn't split and then recombine. Recombination, technically crossing over, happens during the first of two iterations of prophase during meiosis. No recombination happens when the zygote forms. That's when the haploid chromosomes from each parent join to make our 23 pairs of diploid chromosomes. They don't mix and match at that point (if you arguably discount the tiny PAR regions on the Y). Your mother's ovum has, in fact, been recombined and waiting for you since she was still a fetus herself.
And I'm afraid Erik's explanation of tiny segments sticking to adjacent segments may throw some folks for a curve. Recombination is not a totally random thing; it isn't like throwing chromosomes into a Waring blender for 60 seconds and then just piecing together what comes out. If it were, for one thing we'd never be able to calculate a centiMorgan at all...because it's a mathematical estimation of the probability that a crossover has occurred between two specific loci on a chromosome: one cM equals a 0.01 probability of a crossover in a single generation.
We have a pretty good handle, thanks to numerous peer-reviewed studies, on the average number of actual crossover events per generation per gender. There are a lot more crossovers that occur in the female genome than the male; far more than the X-chromosome alone can account for. About 70% more, in fact. But even then the per-generation numbers aren't huge.
I tend to use the round numbers from Harvard geneticist David Reich: about 45 crossovers for the ovum, and 26 for the spermatozoa, for a sex-averaged 35.5 per parent...call it 35. All the centiMorgan calculations we see use only sex-averaged values, so we might as well average the crossover discussion, as well.
Most studies I've seen are right in that same area. IIRC ranging from a sex-averaged low of about 31 crossovers to a high at about Reich's 35.5. There are a couple of studies that have been done using the DNA mismatch repair protein, MLH1, as the indicator for crossover, but these produced outlier-level results from the others that were all pretty much in that low-30s range.
So there simply aren't hundreds of segments created during meiosis in a single generation. You're basically working with about 70 segments from your maternal grandparents, and 70 from your paternal grandparents. When comparing sibling to sibling, the number of HIR segments will likely come in at around that figure, about 70. I can only speak experientially here, but in families I've dealt with that included multiple siblings I'd hazard that the typical average is slightly under that; but it wouldn't surprise me to see it climb into the 80s.
The actual number of expected shared segments is almost impossible to predict due in large part to our current atDNA tests. Our microarray tests only examine about 670,000 reference sequences and, depending on the test you take, from 8% to 18% of those are going to be in protein-coding genes...meaning they likely aren't going to be as significant to genealogy and population studies as SNPs that are not in protein-coding genes. In effect we're testing ~600K SNPs out of about 4 to 5 million that are relevant in distinguishing your genome from mine.
The whole segment issue is fuzzy math. Yet another reason to discount very small reported segments. We can't tell, with inexpensive microarray testing, where segments actually begin or where they end. We're simply guessing, even when applying genotyped imputation. But segments can't "drag" adjacent segments around with them. A segment is either created via crossing over during meiosis or it isn't. And two siblings can't have hundreds of different shared segments. Simply not enough crossover events within their two parents to allow that.
There are arguments on both the pros and cons of small segments. At the end of the day, though, there have been no scientific, peer-reviewed studies to indicate what may and may not be genealogically useful segment sizes using our microarray tests. Dr. Tim Janzen and others have posited pretty good information that very small segments are likely to be just noise.
A corollary--not to start a debate here; just stating a fact--is that there is also no scientific, peer-reviewed evidence that autosomal DNA triangulation is a genealogically valid method. We think it probably is because there's a whole lot of anecdotal and individual-case evidence. But we don't actually know. There have been no published studies.
The number of crossovers during meiosis isn't large per-generation, but as we move back in time each set of grandparents contribute a potential 70 crossovers. Theoretically, there's no real reason to think that, for example, the same segment(s) regularly passes along during the course of several generations. A valuable study by Brenna Henn demonstrated that we'd likely have only a 15% chance of sharing any detectable DNA at all with a 5th cousin. AncestryDNA published some info a while back that indicated the odds of finding the same matching segment shared by a group of three or more 5th cousins was essentially zippo (here's a blog post by Debbie Kennett referencing it).
I use autosomal triangulation myself. But sitting here at the ASHG conference--where I have the smallest brain in this and all contiguous buildings--I'm reminded the fact remains that we have no scientific evidence that autosomal DNA triangulation is valid. Assuming that small in-common segments shared among multiple distant cousins means anything in relation to a hypothetical MRCA is just speculation.
