[waterhouse]

Subpopulations B1 and B2 are supposed to be genetically distinct, in ways that change their variability. If it helps, imagine that subpopulation B1 has a gene that, at birth, flips a coin and will make the child either ugly or beautiful, and that subpopulation B2 has no such gene and they're all of average beauty. Based on this interpretation, in Special Case 1 as an example, if sex A is relatively selective and mates with only the top most desirable quarter of sex B, then all of the next generation will indeed be offspring of subpopulation B1, and they will presumably inherit the coin-flipping gene. It is thus that selectivity favors variability.

[brenschluss]

However, that's not how the paper defines variability.

I did think for a second that your definition was the case, and variability was a function of phenotypical expression, but it (as defined in the paper) is strictly about the statistical distribution of desirability within a population. See p4.

[waterhouse]

That's how variability is defined, yes, on groups (or, technically, on "probability measures")—which might be the entire population or a subgroup thereof. The term "subpopulation" isn't defined, and it isn't explicitly stated whether the high variability is a heritable trait. I believe your contention is that that the overall population has basically the same genes, everyone rolls the dice, and then the subpopulations are defined post hoc in terms of the resulting quartiles (or x-iles). Mine is that the subpopulations are genetically distinct and their die rolls behave differently.

Given that the paper is about evolutionary mechanisms and whether one group "prevails" over another, I think my assumption is reasonable; and I think that, given my assumption, the paper makes good sense in the examples under discussion.

[brenschluss]

I'd understand your assumption but think that it is incorrect, since the paper defines desirability not as genetic healthiness but as a mechanism for sex A to select sex B:

"The actual magnitudes of these desirability values are assumed to have no significance, and are used only to make comparisons between individuals. Here and throughout, it will also be assumed that the same desirability value is assigned to each individual by every member of the opposite sex. "

[waterhouse]

The desirability of an individual is often strongly influenced by heritable traits. In the example with my interpretation, "beauty" is a trait we assume to be desirable (for the sake of illustration I'm assuming it's the only trait considered), and how much of it an individual has is heavily influenced by the coin-flip gene. I see no contradiction here.

I might interpret the sentences you quote as "We can give each individual a beauty score from 0 to 100, and all members of the opposite sex agree on what beauty score an individual gets." And we might imagine the coin-flippers have beauty in the ranges 90-100 or 0-10 (depending on the flip result), while the others are all between 40-60 beauty.

[brenschluss]

> The desirability of an individual is often strongly influenced by heritable traits.

I don't disagree with you, but that is not what the paper states, and that is not how the paper defines desirability.

I am not saying that the paper's definition is correct for a broader understanding of biology. Rather, the paper's stance is to generate a simple model and to prove an argument within that model. I am saying that, within the definition that the model is using, the model is internally incorrect.