This is really great and starts answering a question I've been asking around about, viz. How many generations down are we only averagely related to our descendants -- that is, no more related to them than to non-kin? Do chromosomes play a larger part than you're suggesting? Wouldn't I expect a descendent of mine six generations down to have none of my forty-six? Or does genetic cross-over play a big enough part that it's irrelevant to think in terms of chromosomes? Or are they statistically the same? (I think that's probably the case, but maybe you know.)
Of course you are making a point nicely analogous to homeopathy: culture or the disposition of the gene pool at any moment will contain memories of us, even when we're completely diluted away.
Ah, whoops I see you mentioned crossover in your previous. Another couple of minutes of thought make me think that crossover doesn't matter to the statistical argument: you win sone, you lose some, it foist matter whether the split occurs in a base-pair, a gene, or a chromosome. I guess mutation hastens the process but probably not much? So, yeah, even without considerable relatedness due to interbreeding of third or fourth cousins, our descendants are probably only averagely related to us after 5 generations or so.
I'm curious about this because of Fisher's attractive sons argument. That suggests that our genes strategiize to produce fit grandchildren, rather than children. Where do the opposite curves of reproduction and dilution sum up to our optimal goal? Better, genetically, to aim for fit children or grandchildren or great-grandchildren? Any ideas much appreciated.
By and large, "I don't know". But you have to remember that for each randomizing event, if the majority of the chromosome is the same, crossing over isn't going to change a lot. I've attached a visualization showing my brother's genome compared with mine at a somewhat random sampling of base pairs known to carry mutated differences, called SNPs (single nucleotide polymorphisms). For example, there might be a stretch GATCGGTC vs GATCGATC on each of the pair of chromosomes, in which case they would not be shown as having identical regions when compared. If my brother had two GATCGATC and I had the above, we would be shown as "half identical" (HIR) in that range because the SNP at the sixth position (which is the only thing that was actually tested) is typically the only thing that is "different". The tests don't show all of the SNPs, and don't show repeats or deletions. (of course, our Y is identical, and there's only one of them generally for males, so it's not even measured in this visualization)
I'm writing these posts for crossposting to a more public area as well, where I don't post some of my more controversial beliefs or feelings (read- family friendly content) but I don't buy into a "fitness" mechanism. Again- as far as I can tell it's random, and any evidence of an "invisible hand" or some such in the process is not there for me. Note: I realize the oxymoron in looking for an invisible hand. I'm pretty sure much of the so-called "fitness" happens long after meiosis, when you're drowning the inconvenient truth in the river because you can't take it.
Based on comparisons of my chromosomes with a third cousin once removed, with whom I only share two tiny HIR regions with, and who is "1.65%" shared as opposed to my brother who is "52.46%" shared, I would say that after five generations there's at least a good probability that there's about 3% of the genome left around in common, and based on what I'm seeing out of 23andme.com, which is where I've been tested, you can find potential cousins out about 6 generations or so, or more, but it's unclear how much of that is "false positives" in terms of actual, blood-line relatedness. The fact that I knew nothing about this cousin prior to 23andme.com is about as "blind" an experiment as I can perform. If you procreate with someone who is very similar to you in genetic makeup, there might be less measurable dilution, but in looking at genomes of someone who has a known history of cousin intermarriage within 5 generations or so, the picture is quite a hodgepodge of dozens of HIR's. It's not like the randomization across the human genome is super dramatic, we're not dropping chickens or kittens out the other end. I'm mostly just idly musing about dilution, and randomization, and not producing "serious science" here. But I do welcome the feedback.Edited at 2011-01-01 07:03 pm (UTC)
Great -- thanks for this. What I'm trying to think about is how many generations down my descendants I become as indifferent to my descendants as to non-kin.
The attractive sons argument explains sexual display as a handicap or costly signal, while also explaining why sexual display can change in isolated sub-populations. It's the biological version of a Keynesian Beauty Contest. There seems to be good evidence that selectors take receiver psychology into account and pick mates who they anticipate other selectors will pick, apparently because the next generation's selectors will pick similar mates.
I don't think I buy Fisher's attractive sons argument. By that, I'm not suggesting that having an "attractive" son as a sexual selection strategy is invalid, per se, but I think that there are numerous strategies, each more complicated than the last, and they're derivative of the original thesis of sexual selection. At some point, it's like, yeah, the bowling ball can drop to release the canary and boil the teakettle to etc etc but just because it's complicated doesn't mean there's a theory driving it. It could be that there was sufficient food or insufficient competition to allow for unconstrained variation, and that strategy got lucky.
Furthermore, genes don't necessarily have anything to do with it. Why does the host of the parasitic cuckoo take care of the invader? Why are non-paternity events as common as 10%? Mostly, in my opinion, because all animals (including humans) are pretty dumb, and mostly, doop-de-doo, just going about the act of living. Life happens to the dumb.
It also depends how much actual genetic variation actually exists. Fruit flies are the common example- reproduce by the millions, live for a few days, and every possible mutation will eventually be seen. Even through we might have a genome of 3 billion or so base pairs, the amount of actual variation between people is quite small. You might, for example, have trouble detecting that your brother swept in and cuckolded you. Even harder to detect, maybe, a twin. At some point, it doesn't really matter what comes out the other end, unless you're going to let that bother you, and unless you're facing some other survival pressure, like having to choose who to feed and who to drown. Or, living off that fat Maury check.
I think it's a case of failing to distinguish what is statistically true, with what is actually true. Statistically, over many generations, a characteristic which can survive, will. We can't predict what's a successful strategy for survival because, like the bowling ball, teapot, and canary, sometimes improbable mechanisms work. If you're a Chinese aristocrat, you might have your family names planned out for a thousand years, even though by that point, QED, they're almost certainly indistinguishable from the Fong dynasty across the river, especially if you marry a few daughters off to them to keep the peace. Or, like Tevye, you're ready to have a daughter be dead to you in a generation. They're all successful strategies.
Thank you -- I'll try to read it this (busy) week, since the whole thing looks interesting.
I also remember that I meant to say that the question of dilution came up for Darwin and bothered him. He saw that his "gaseous" theory of inheritance meant that new traits should get diluted each generation qua traits. Mendel saved the day by showing inheritance wasn't gaseous. James Schwartz talks about this in his really good book In Pursuit of the Gene.