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It would happen in your model, if there is no perfect overlap between the set of sites in one population and the set of sites in the other population. With two populations, you have more sites. The smartest possible mega-genius is from the mixed population and has + alleles on each site; none of the original populations can have a genius this smart at all.
To see that on less extreme rarity (and approximately for a large number of alleles), write down the ratio of two Gaussians with different means and variances. Simplify. Observe that the ratio of the larger variance Gaussian to the smaller variance Gaussian gets arbitrarily high far from the mean.
Okay but that is an incredibly weak claim - I'm not interested in switching all of the plus alleles on because additivity starts to break down and having an IQ of say 500 isn't particularly meaningful. For any reasonable definition of genius, artificially selecting for the smartest members of a population (what super-Hitler is doing), will increase the number of them.
Assume total heritability, random mating, additive genetics, and a single 50% truncation event. In the first generation, the right tail becomes 4x larger as a proportion of the population, but it gets smaller in equilibrium. The new mean is 0.8 standard deviations above the old mean. The new standard deviation is 0.6 times the old one. When it reaches equilibrium and becomes a Gaussian with those parameters, the crossover where the old population had a thicker tail than the new is about two standard deviations. At three standard deviations, the new distribution is only 1/10 of the old distribution. But I don't know how much time it takes to get there.
Thank you, I'm pretty surprised by that result. Two questions: does assortive mating merely slow down that process? And is there any way to increase the both the average and the standard deviation?
You need new mutations to increase the standard deviation, that takes a lot of time and a big population size.
Also, having a genetic disorder applies larger selection pressure to the other genes.
If we are to think of some real 'eugenic' population bottleneck, such as WW2 related, the correlation between intelligence and survival is, frankly, shit, plus a lot of small, geographically co-located sub-populations where a bunch of beneficial genes have been slowly increasing in prevalence get completely wiped out, with loss of all copies of that gene.
Bottom line is, selective breeding of larger corn kernels works quickly because the nature hasn't been breeding for larger corn kernels to begin with, it has been breeding optimum kernel sizes, and to get large kernels you're just selecting genetic disorders. There's nothing that you can wreck about the brain that would turn you into a genius, there's a plenty of things you can wreck about growth that would make corn kernels big.
Or just some mutagens.
It seems to me that this would work much better for traits that can be accomplished through loss of function (e.g. larger corn kernels, through loss of function of regulator genes) than in general. At too high mutation rate, complex functionality can't be preserved.
One thing to keep in mind eugenics wise is that pretty much all the breeding methods we employ for other species are dysgenic - we are producing cripples to our own benefit or amusement. Damage this, damage that, select this bad gene, that bad gene, and you get yourself docile floppy eared dog with the IQ equivalent of severe mental retardation, compared to a wolf.
I assume by 'dysgenic' you mean 'less fit than unbred specimens for reproductive fitness in the wild'. (You couldn't mean 'reproductive fitness' in general, given how many dogs there are compared to how many wolves there are now.)
This seems like an odd point to make. Of course we breed animals to be less-reproductively-fit-in-the-wild - if they were already ideal for our multifarous purposes, why would we be explicitly breeding them at all? (If they were already ideal for eating or being pets or whatever, we would simply capture & use them or raise them normally without any interference in their reproduction.)
It'd be a pointless point if there was a symmetry between fitness in the wild and fitness for our purpose. There isn't - fitness in the wild is very seldom improved by loss-of-function mutations, whereas fitness for our purposes, starting from the species that have been evolving for fitness in the wild, very often is. Rapid success at breeding larger corn kernels is not going to generalize into rapid success at breeding ubermensch.
There's no reason evolution would have already have optimized for all the intelligence-related alleles; if it had, they would have reached fixation.
I think it is. All the genetic data seems to point to: much of intelligence is genetic, highly polygenic, not fixated, and additive. All of that translates to breedability: we have a lot of easily identified variants present in only parts of the population; hence, breedable.
I am not sure this is generally true.
The wild equivalent to "fitness for our purposes" is a drastic change in the environment which starts to select for different criteria. In such conditions organisms certainly select for new-useful-function mutations, but they also select for loss-of-no-longer-useful-function mutations. Functionality tends to be expensive (e.g. in energy) and if you don't need it, you're better off discarding it.
Remnants of lost functionality are common.
Many breeds of dogs are certainly very dim compared to wolves, but I'm not so sure that some aren't just as intelligent, perhaps more so. It can be difficult to evaluate the relative intelligence of dogs and wolves, because some of the hallmarks by which we measure the most intelligent dogs (such as the complexity of tasks they can be trained to perform) do not apply to wolves because they're so much less cooperative.
Considering the intellectual tasks the smarter breeds of dogs are capable of though, I wouldn't rule out the possibility of eugenic selection for intelligence relative to wolves, for e.g. border collies, standard poodles and such.
Wolves are under strong selection pressure as well, though.
Intelligence comparisons are of course tricky, but one could compare brain volumes as a proxy, and the comparison is not in favor of dogs.
Thing is, of possible mutations within any gene (coding for a protein), vast majority cause loss of it's original function. This makes the speed of evolution dramatically dependent to the specific details of how the change is accomplished.
Brain volume isn't necessarily a very good proxy, some animals are significantly smarter than other animals which have larger brains. Rats, for instance, may be more intelligent than some animals which are capable of eating rats, and have much larger brains due to greater body volume.
The vast majority of the difference between dogs and wolves isn't due to mutation, but selective concentration of genes which already existed within the grey wolf gene pool.
If you truncate less of the tail, it takes more generations to move the mean, but I believe that by the time it moves the same distance, the variance shrinks less.
If you have a randomly mating population, apply assortative mating for a few generations, apply one generation of selection, and let randomly mix, it costs less variance for the same mean as if you don't do assortative mating. That's because assortative mating is a kind of selection, so this is like several generations of selection. If you start and end with an equilibrium of assortative mating, I'm not sure what happens. Also, assortative mating increases the variance, so you have to distinguish between the variance of the population and the variance of the population that would result if you switched to random mating.
I made a weak claim (all sites) to make it easier for you to see how that works within your own additive model. Of course, you don't have to have plus alleles on all locations for a genius to be more common in the mixed population than in the original populations.
This would depend on the population sizes involved, number of locations, and overlap between locations.