Here’s a short-term analysis that may be more convincing.
I assume perfect heritability and pm’s choice of 50% selection, both to make the effects larger. I assume additive genetics because that’s what we expect from the assumption of a bell curve. The far right tail is largely produced from two parents both on the right half, even on the tail. The farther right you go, the more true this is. Assuming mating is at random. For each person who could have a right tail child, if only they found the right mate, eliminating half of the population that wouldn’t do doubles their odds of having an appropriate mate and thus a right tail child. Thus, the right tail is twice as big. The further out we go, the closer it is to twice as big. If everyone has twice as many children to make up for the population being cut in half, then the tail is four times as big.
If there is strong assortative mating, the people on the right tail weren’t going to going to have children with the left half and the first effect doesn’t apply, since the selection only eliminates pairings that weren’t going to happen. Indeed, assortative mating is very similar to truncation selection, so combining the two is redundant in the first generation.
In the first generation, the left tail does not look at all gaussian. In the long term, it does become gaussian. In the short term right becomes a thicker tail, but in the long term the variance has gone down and the right tail becomes smaller, starting at two standard deviations from the original mean.
Here’s a short-term analysis that may be more convincing.
I assume perfect heritability and pm’s choice of 50% selection, both to make the effects larger. I assume additive genetics because that’s what we expect from the assumption of a bell curve. The far right tail is largely produced from two parents both on the right half, even on the tail. The farther right you go, the more true this is. Assuming mating is at random. For each person who could have a right tail child, if only they found the right mate, eliminating half of the population that wouldn’t do doubles their odds of having an appropriate mate and thus a right tail child. Thus, the right tail is twice as big. The further out we go, the closer it is to twice as big. If everyone has twice as many children to make up for the population being cut in half, then the tail is four times as big.
If there is strong assortative mating, the people on the right tail weren’t going to going to have children with the left half and the first effect doesn’t apply, since the selection only eliminates pairings that weren’t going to happen. Indeed, assortative mating is very similar to truncation selection, so combining the two is redundant in the first generation.
In the first generation, the left tail does not look at all gaussian. In the long term, it does become gaussian. In the short term right becomes a thicker tail, but in the long term the variance has gone down and the right tail becomes smaller, starting at two standard deviations from the original mean.