[brenschluss]

The paper seems to have some egregious and basic errors.

Take a look at the paper: https://arxiv.org/pdf/1703.04184.pdf

On page 2, it says (in discussing Special Case 1): "If sex A is relatively selective and will mate only with the top most desirable quarter of sex B, then all of the next generation will be offspring of the more variable subpopulation B1"

However, if you look at the histogram in Figure 1, it's clear that if sex A mates with the top most desirable quarter of sex B, then sex A is choosing most desirable mates who happened to be part of the subpopulation B1.

That is, as diagrammed in the histogram, variability is not a function of the population any more, since the red rectangle noting 'B1' with desirability 3 to 4 is no longer variable. It would be absolutely incorrect to say that "all of the next generation will be offspring of the more variable subpopulation B1".

In other words, it's like saying:

"In Sack 1, I have a mix of of blueberries and watermelons. Sack 1 is varied in fruit size, and has a high variability. I've sorted them by size, and taken the most largest fruit and put them in Sack 2. Now Sack 2 is full of variable sizes of fruit, since it came from Sack 1, which had high variability."

(EDIT: to be clear, I think the above sack example is incorrect; I'm illustrating the logic in which the paper seems to be incorrect, according to my understanding.)

[quotemstr]

You've identified the mechanism by which sexual selection operates. It's clearly a powerful force.

This paper is arguing that in addition to sexual selection's first order directional effect, there's an overlaid second order effect on variability, and the argument makes sense. Male reproductive success is already highly variable, because male gametes are cheap. Some males end up being disproportionately successful, e.g., Genghis Khan. From a gene's point of view, being hosted in Khan was winning the jackpot.

If you have a number of male offspring, some of them will be evolutionary "duds" no matter what. If you increase the variability in reproductive success of your male children, then some of them will be less reproductively successful and others will be more successful. But there's an asymmetry: "duds" are already duds and can't be made less successful, but on the other side of the curve, by increasing variability, you increase the likelihood of a jackpot.

The effect doesn't apply to female children, since a female mammal cannot have 200 offspring in her lifetime, but a male mammal certainly can.

(Your fruit analogy is inapt, since fruit in a bag don't reproduce among themselves and regress toward the population mean.)

[mirimir]

> ... since a female mammal cannot have 200 offspring in her lifetime ...

Ah, but now she could. With enough money to pay for enough surrogates (or eventually, machines) and childcare.

So maybe, going forward, there'll be more variability in human female reproductive success. Interesting.

[quotemstr]

Yeah. Various kinds of reproductive and genomic technologies invalidate general evolutionary assumptions, but the techniques haven't been around long enough or been common enough to matter so far. But in the future? Who knows?

[haihaibye]

And if there was any kind of genetic motivation for doing that (and almost everything is partly heritable) we'd see more of those genes next generation, so likely some of her kids would go down that route too and there we go...

[brenschluss]

>The effect doesn't apply to female children, since a female mammal cannot have 200 offspring in her lifetime, but a male mammal certainly can.

From the paper:

"Note that this theory makes no assumptions about differences in means between the sexes, nor does it presume that one sex is selective and the other non-selective"

So the reproduction capacity of sex A and sex B is equal. I'm attempting to debate the paper strictly based on its own arguments.

[quotemstr]

The paper then goes on to discuss, in detail, how differences in selectivity drive differences in variability, so the passage you quoted does not mean that the author is imagining A and B to be equally selective. The author is just asserting that both of his arbitrary sexes might be selective in an absolute sense.

I'm not sure what point you're trying to make, especially since you've opted not to quote or address the majority of my comment.

[brenschluss]

> This paper is arguing that in addition to sexual selection's first order directional effect, there's an overlaid second order effect on variability, and the argument makes sense. Male reproductive success is already highly variable, because male gametes are cheap. Some males end up being disproportionately successful, e.g., Genghis Khan. From a gene's point of view, being hosted in Khan was winning the jackpot.

The paper makes no distinction between sexes -- so a discussion of male or female differences, whether in reproductive success, does not discuss on the paper's model.

> If you have a number of male offspring, some of them will be evolutionary "duds" no matter what. If you increase the variability in reproductive success of your male children, then some of them will be less reproductively successful and others will be more successful. But there's an asymmetry: "duds" are already duds and can't be made less successful, but on the other side of the curve, by increasing variability, you increase the likelihood of a jackpot.

Your argument holds the selectivity of the female sex as constant, and discusses variability of the male sex.

The paper's argument is about variability in one sex ('sex B') being a function of the selectivity of sex A. These are fundamentally two different arguments, and so whether your argument is true or not, your argument does not discuss the paper's model.

> The effect doesn't apply to female children, since a female mammal cannot have 200 offspring in her lifetime, but a male mammal certainly can.

Addressed in a previous comment.

> (Your fruit analogy is inapt, since fruit in a bag don't reproduce among themselves and regress toward the population mean.)

Thank you - I did not know this until now. I assumed that fruit reproduced asexually in bags.

My fruit analogy is presented because the error that the paper seems to make happens at a simple statistical level -- because the paper assumes that you can 'sort' a two variably desirable populations (B1 and B2) on a histogram by desire, find the top 25% of the population (B11), and assume that the top 25% desirable population (B11) is as variable as the original population it came from (B1).

[yorwba]

> It would be absolutely incorrect to say that "all of the next generation will be offspring of the more variable subpopulation B1".

No, that's exactly correct. The example is set up so that no individual from B2 gets to mate with A. Therefore, the next generation only consists of offspring of B1. (I think you understand that, since you say "sex A is choosing most desirable mates who happened to be part of the subpopulation B1".) B1 is the more variable subpopulation. Therefore, the sentence "all of the next generation will be offspring of the more variable subpopulation B1" is correct.

I suspect you are interpreting it as making a statement about the subpopulation B11 (of the subpopulation B1) that actually gets to mate. But if you split B1 into the more desirable B11 and the less desirable B12, then you can't even talk about their variability relative to B2, because the paper only defines comparisons of variability for distributions with the same median.

So the sentence "all of the next generation will be offspring of the more variable subpopulation B11" is not only incorrect but meaningless. Although they seem to be talking about the same individuals (and "all of the next generation will be offspring of the subpopulation B11" is true) they are talking about different populations, and "more variable" can only be applied meaningfully to B1.

In terms of your fruit example, the correct translation would be "All fruit in Sack 2 came from Sack 1, which had high variability." without any implications about variability of Sack 2.

Heritability of variability is only introduced on page 6: " it will be assumed that the pace of evolution is negligible compared to the pace of reproduction, so the two subpopulations remain distinct, with offspring distributed the same way as the parent subpopulation". In other words, although three subpopulations B11, B12 and B2 can be clearly distinguished, only membership in B1 or B2 is actually heritable, with B11's offspring either in B11 or B12. If B2 ever got to reproduce, it would have B2 offspring, while B12 would produce B11 or B12. So although B12 never reproduces, it never dies out due to offspring of B11.

Of course the conditions in those examples are contrived and that makes the conclusions almost trivial (a caveat that is noted in the paper: "The precise formal definitions and assumptions made here are clearly not applicable in real-life scenarios, and thus the contribution here is also merely a general theory intended to open the discussion to further mathematical modeling and analysis") but it is certainly free from egregious and basic errors.

[brenschluss]

This is helpful, thank you.

> If B2 ever got to reproduce, it would have B2 offspring, while B12 would produce B11 or B12.

Okay, this is clear regarding the paper’s assumption of heritability of variability. Assuming that variability is a completely static characteristic innate to a population and perfectly heritable seems to me such a simplistic assumption as render most of the conclusions ineffective or correct only within a narrow set of assumptions.

After all, every GA would never work if this was the case.

[brenschluss]

Actually, I change my statement upon rereading the paper: If offspring is "distributed the same way as the parent subpopulation", then B12 would only produce B12.

In other words, if subpopulation B11 is chosen by A, then B11 would produce B11, this reducing the variability, not increasing it.

[yorwba]

The paper only recognizes two subpopulations with their respective probability distributions. I only introduced B11 and B12 to be able to talk about different outcomes within the B1 subpopulations. Otherwise you could just choose any arbitrary grouping (e.g. mixing B11 and B12) and get completely different results depending on how you do it.

Maybe it's less ambiguous if we talk about machines which spit out a randomly sized ball when you press a lever. After collecting a certain number of balls from the machines, you determine what proportion of the largest p% is from each machine and replace all balls by selecting from the machines according to their proportion.

If you have a machine M1 producing very large balls and very small ones in equal quantities, as well as M2 producing medium-sized balls, then the prediction is that the proportion of balls coming from M1 will increase if p < 50% and decrease otherwise.

In that model, although you can clearly group the very large balls as B11, there is no machine M11 only producing those balls. Both very large and very small balls will, if they are in the top p%, require you to press the lever on M1. The size of the balls only influences which machine will be chosen, not what kind of balls will be coming out of that machine.

In genetic terms, B1 and B2 carry different alleles of the same gene and have different genotypes, while B11 and B12 are different phenotypes possible for B1. If B11 were to produce only B11, that would be inheritance of phenotype, i.e. Lamarckian evolution, which is also interesting, but less relevant for real-world genetics.

[tomjen3]

Honestly, if there had been basic errors in the paper, they wouldn't have had to ban it.

[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.

[zeth___]

You misunderstand the argument.

It's like having a bag 1 filled with equal quantities of capsicums, cherries, and apples, then selecting the top reddest 25% of bag 1 and moving them to bag 2.

You will have much less variability of fruit type in bag 2 because you used color selection to fill it (apples and capsicums come in three colors at will be selected 1/3rd the rate of cherries).

That's the whole point of sexual vs natural selection.

[brenschluss]

> You will have much less variability of fruit type in bag 2 because you used color selection to fill it

Yes, I completely agree with you! You will have much less variability.

However, that's not what the paper argues. The paper argues that you would have more variability.

I'd appreciate you taking a look at the original paper (specifically, the bottom of page 2 [edit: and Figure 1]) and understanding my original argument.

[zeth___]

Right, and now compare it to the original bag.

You have increased variability between generations by reducing the variability in the second generation.

[brenschluss]

I agree with you that there is a difference in variability between generations.

I agree with you that the variability has been reduced in the second generation.

It seems that we both disagree with the original paper, then, as it states

"If sex A is relatively selective and will mate only with the top most desirable quarter of sex B, then all of the next generation will be offspring of the more variable subpopulation B1"