Since I read it, I've been thinking about the previous response in this thread by Raevmo. (The topic is questions about Fischer's ratio, but that is beside my point in this post.) He wrote, in part:

Raevmo: The problem is, Fisher's argument presupposes that parents have a way to manipulate the sex ratio of their offspring somehow. So far, no plausible mechanism has been identified. It could be that the human sex ratio bias is not an adaptation at all, but an accidental result of physiological mechanisms.

That level of frank, straight talk was very refreshing and welcome. It impressed me, and it boosted my impression of Raevmo. NOTE: I'm not claiming he has given up on Fischer — that's not the point.

What I wish more evolutionists would realize is that their words are more persuasive and carry more credibility, even when they are defending evolutionary theory — if it is plain that they are straight talkers when it comes to points that may present a problem for some aspect of evolutionary theory.

All too often it seems that a true blue Darwinist is incapable of seeing any true difficulty or seeing any real possibility that the standard NeoDarwinian grand scheme has any weak points, while at the same time being incapable of granting any serious possibility to any design inference.

If someone like that tells me I'm wrong, it is easy to write off. That type of critic would tell me I'm wrong no matter what I said, if it wasn't down the party line. They are blind to all else. This undercuts all of their statements, since such a person must find a way to disagree. When a Darwinist insists that there are no scientific controversies regarding Darwinism, that level of devoted faith not only counts for next to nothing, it also subtracts from their defense of Darwinism even on genuine strong points.

Consider the difference when someone establishes that they are willing to acknowledge points that may not be in favor of their own preferred conclusion. That carries weight. It earns them increased credibility.

I will not be surprised at all when Raevmo disagrees with me, but I think everyone should note that when he does disagree, the credibility of his statements is enhanced by prior indications of objectivity and willingness to be plain about points that may not be complimentary to the defense of evolutionary theory.

As I've mentioned before, I also greatly appreciate the fact that keiths has bothered to understand positions I've taken well enough to recognize when others have not understood.

For some, it is important to understand first, including recognizing legitimate points where they may be found. For others, it is mostly about "winning" against "them" which translates into finding ways to disagree, wherever they may be found.

Please ask yourself: If someone from each of these groups were to tell you that you were mistaken, which one's word would justifiably carry more weight?

1. Does Fischer predict ratios at birth or ratios at puberty or ratios of reproducing males and females? Each is potentially distinct.

The first two, not the latter. The argument is about sex ratios at the moment of control - say conception. If one of the sexes has a higher mortality rate during the period of parental care (when parents are supposed to incur the costs of raising their offspring, say by allocating resources to their offspring that could have benefitted their own future survival), then that sex becomes relatively "cheaper" in a sense because if it dies the parent cannot invest in it anymore. Since boys have a higher mortality rate than girls in humans, this tends to make sons relatively cheap. Fisher then predicts a slight excess of sons at conception and because of the sons' higher mortality a slight excess of daughters near the end of the period of parental care. This pattern tends to equalize investment in sons and daughters. This is exactly what we observe in humans. The problem is, Fisher's argument presupposes that parents have a way to manipulate the sex ratio of their offspring somehow. So far, no plausible mechanism has been identified. It could be that the human sex ratio bias is not an adaptation at all, but an accidental result of physiological mechanisms. There is some evidence that male embryos grow faster in very early development and that this gives them a higher chance of being succesfully implanted in utero, thus causing a slight male excess at birth.

Meanwhile, over on another thread, Zachriel stated:

I had suggested "surviving children per couple that go on to themselves reproduce". While the birth ratio is somewhat skewed to males, it tends to equalize by puberty, which is the expected result.

This raises some questions.

1. Does Fischer predict ratios at birth or ratios at puberty or ratios of reproducing males and females? Each is potentially distinct.

2. Isn't "the expected result" dependent on the relative costs of raising males vs. females? Fischer makes an economic argument related to limited resources.

3. There any number of non-genetic reasons why the ratio of males to females could change between birth, puberty, and reproduction. Should these be considered relevant to affecting Fischer's arguments? For example, if it is cost based, the net average cost of raising males to successful reproduction can be increased by the number of males that die in any type of fighting any time before reproducing. Should we expect that routinely sending unmarried young men off to war could affect the birth ratios? Would sending men and women in equal numbers and in equal danger also change the birth ratios?

BTW, thanks to Raevmo and keiths for their patient answers.

To more clearly express myself, I'm not just trying to pick in order to disagree. If Fischer is right, I would have no trouble with that. I'm not inherently opposed to the idea.

Fischer's ideas (as presented by Dawkins) do not yet appear to hang together and make sense logically. To me it has instead the appearance (so far) of one of the narrative gloss explanations that can be attached to something after the fact. But that could be simply because I don't grok it correctly yet.

I also find it odd that they don't seem to enter into mysterious questions about why birth ratios are changing. When real scientists are doing real science on birth ratios, do they turn to economists and measure relative costs of raising males vs. females? If not, how is this not just a narrative gloss?

"Devra Lee Davis of the University of Pittsburgh and her colleagues gathered data on U.S. birth ratios from the National Center for Health Statistics. From 1970 to 2001, they found, the number of boys born for every 100 girls dropped steadily from 105.5 to 104.6. Male births among U.S. whites dropped even more steeply, from 105.9 per 100 girls to 104.7. The researchers found similar declines in Japan.

"The cause remains a mystery. Davis and her colleagues suspect that much of the shift is because of exposure to gender-bending pollutants."

The Washington Post

Hmm. So why is it that "the cause remains a mystery"? Haven't they studied Fischer? Apparently they didn't get the memo that the answer is due to changing costs in raising boys vs. girls.

Raevmo: Finally, it may seem trivial that in diploids all males contribute an equal number of autosomal genes to posterity as females, but the important implication is that an individual of the minority sex contributes on average more genes to posterity than a member of the majority sex. This is the crucial ingredient.

Hope this helps a bit.

OK, yes this does help a bit, although I think it needs to be tightened just a bit. One can imagine a case where males are in the majority, but nearly all of them are excluded from mating and a dominant male acquires a large harem. So the fact that males are in the majority by virtual of gender ratios at birth would be immaterial to their individual contributions. The non-reproducing males are effectively indistinguishable from being dead or never born.

So if we are talking about average individual contribution, that still isn't necessarily connected to ratios (avoiding that other filtered word ) ratios at birth.

So, it might be significant that individual reproducing males (for example) might have an average contribution that is far greater than the average for reproducing females. Thus, in some sense their genes might carry more genetic "weight" in future generations. However, that does not yet seem to have any necessary connection to gender ratios at birth. There could be wide variance to how many born males are excluded from reproduction.

I noticed something else just this evening that seemed interesting. I'll put it in a separate post.

3. "the total male contribution to posterity must equal the total female contribution".

The "must" in the last statement is inherent to the nature of sexual reproduction. One could just as well have said "sexual reproduction must be sexual reproduction" or "P must be P" or "if P then P', which becomes a tautology. The only way it could not be true would be something like a virgin birth, i.e. a case of non-sexual reproduction.

Good thinking. There are species, such as all wasps, bees and ants that are haplodiploid: males come from unfertilized eggs and are haploid, while females come from fertilized eggs. In other words, males do not have a father. The sex ratio argument of Fisher applies to diploid species (but by a more complicated argument it can be shown that the stable sex ratio of haplodiploids is also 50:50, if the sexes are equally expensive and the sex ratio is controlled by the mother. Here's something to think about: what's the stable sex ratio when the worker bees control it?). But whats more, the argument also assumes that sex ratio is under control of autosomal genes, that is, genes not on the sex chromosomes (the X and Y chromosomes). Because genes on the sex chromosomes violate the principle that total male contribution equals total female contribution. Females contribute no Y chromosomes to posterity, hence a gene on the Y chromosome would "like" to be part of an all-brother family because sisters do not carry a copy of the father's Y. In fact, Y-chromosomal sex ratio distorters are known. They typically "poison" X-bearing sperm. Such Y distorters can very quickly go to fixation in a population, driving the population extinct (since no females are born).

Finally, it may seem trivial that in diploids all males contribute an equal number of autosomal genes to posterity as females, but the important implication is that an individual of the minority sex contributes on average more genes to posterity than a member of the majority sex. This is the crucial ingredient.

Hope this helps a bit.

(Raevmo and) keiths: By the way, now that Raevmo and I have explained it, do you see why the equilibrium sex ratio will depart from 50-50 when the cost of raising female vs. male offspring is unequal?

I've been meaning to respond about Fischer and sex ratios, but other things took priority. A recent post by keiths motivated me to at least give this response.

I still have issues with some mathematical aspects, but I won't respond on those until I given the mathematical aspect of your answers the careful consideration they deserve. But there is one other aspect I will respond to.

This might be the fault of Dawkins' description more than Fischer, but I remain amazed to find this declaration.

"Fisher's own solution made no appeal to species advantage. Instead he pointed out that, since every individual born has one father and one mother, the total male contribution to posterity must equal the total female contribution."

Disregarding virgin birth, all of these statements are true about sexual reproduction and are essentially equivalent in content:

1. "every individual born has one father and one mother"

2. In sexual reproduction, a sperm (from the father) fertilizes an egg (from the mother).

3. "the total male contribution to posterity must equal the total female contribution".

The "must" in the last statement is inherent to the nature of sexual reproduction. One could just as well have said "sexual reproduction must be sexual reproduction" or "P must be P" or "if P then P', which becomes a tautology. The only way it could not be true would be something like a virgin birth, i.e. a case of non-sexual reproduction.

It follows that no other consideration, including no consideration about sex ratios, could possibly make these equivalent statements false regarding sexual reproduction. Given any ratio of males to females, the statements remain unaffected and true.

Thus, the essential meaning of sexual reproduction exerts no causal power over sex ratios. It cannot affect sex ratios because it imposes no constraint whatsoever on sex ratios, apart from the minimal fact that you must have both at least one fertile male around and at least one fertile female to continue reproduction.

As a supposed foundation for reasoning about sex ratios, it is vacuous and ineffectual. No sex ratio can violate this truism. All sex ratios we find or could find are compatible with it, regardless of relative costs.

I find it amazing that this should be presented as a foundation for what follows, as if it could have some relevance.

What might need to be shown is something else entirely, perhaps that the costs involved in the contributions need to be equal, or some other idea. But that does not in any way proceed from restating the meaning of sexual reproduction. The real claim might be true or it might not, but to try to derive this from the meaning of sexual reproduction is a non sequitur and not a promising or encouraging reflection on the line of reasoning employed.

That leads to a second, separate consideration that I'll just briefly mention here. On the face of it, there is no evident reason why evolution should prefer to make the costs equal. Why should it? I would have supposed it would lean instead toward greatest efficiency. Even if bulls and cows are equally costly, why should there need to be one bull for every cow? Yet, according to the Fischer conclusion, that is what we should expect from equality of cost.

Pregnancy takes a long time, fertilization does not. One bull can potentially fertilize many cows, as dairy farmers and others know. To suppose that evolution has an egalitarian streak, rather than ruthless efficiency is not prima facia obvious. (That said, it could be true. I'm not claiming here that it could not be true.)

In any case, to return to my main point here, it does not follow as a logical consequence of restating the meaning of sexual reproduction.

But that it works on the whole does not explain why it works, why the world is predictable that way.

Just to be clear, the question wasn't "why it works", but whether it works.

A woman claims that the Sun will always rise in the Eastern Sky rather than the Western Sky. The tribe gathers to watch and see. The Sun rises as predicted! They repeat this experiment day after day, year after year, generation after generation. Is this a reasonable case of induction?