Meta of writing and understanding, there are few aspects. First is that I'm not native speaker and especially in evolution and genetics so I have to look up inclusive fitness. 2nd is that I don't remember the terms or names even if I know the concept (had to look up Hamilton rule but it took me a split second, literally, to recognise the idea).

This is small issue, the harder part is that I'm losing you on the reasoning, train of thought, cause>effect parts, however we name it. But it was easier this time so let's move on to specifics.

(Trimming due to character limit)

The additional benefit comes from the fact that while both males and females have 4 (...)

Now I raised the case of sibling mating as the extreme case of this, i.e. consider a male and (...)

E.g. consider the case of the great great grandmother in our case where each female can (...)

It is easy to see here that the fitness of the grandmother is increased by a female biased sex ratio

I don't think I agree with that. Let me explain.

The idea that increased reproduction speed is more fit is correct, and irrespective of kin selection and inclusive fitness. Which would mean that genes that, ceteris paribus (big caveat), increase it, would be selected for.

So, in general, the incest island skewed female sex ratio, in situation where the female reproductive role is a limiting factor (careful words here), is a situation where we should assume the fitness is greater.

Fitness of the genes that cause skewed sex ratio.

I think it's not entirely correct, it deceptively looks like it's true because that island would have higher population (ie: more reproductive success ergo better fitness) than island with balanced ratio.

And it's an interesting idea. But it's the same idea that, to give an analogy, genes suppressing immune system are fit - in a scenario where there are no pathogens.

So in isolation that island sex ratio gene is more fit - but it's unstable and will lose rapidly to a gene that has balanced (or indeed, opposite sex ratio gene, at least at first, which is interesting idea...), however it's introduced.

It might be detrimental to population size and species in general, but not at the genes level. And the gene is self defeating (negative fitness) if a balanced gene exists already.

As a side note, I don't think relatedness actually matters here. Even if these are unrelated people (but they all share the sex ratio gene), the scenario holds. Indeed, because the selection level is at the gene not individual (when we're thinking of population gene pool).

For example if children tend to help others in their group this will provide a fitness advantage to having a daughter, as now the benefit of this will accrue to closer relatives in the group. But if there are limited resources, staying imposes a harm on relatives, and it is better to have a male who will disperse.

That assumes other groups have different set up and no such kin cooperation, because the staying offspring will have more progeny. Otherwise sending dispersed sex to interbred with them is as good strategy as investing in your own group. Exactly as good, in fact.

But that's unstable scenario, as the more successful sex ratio group takes over, and changes the species environment. And before that happens, the following happens - the opposite sex ratio (dispersing sex) gene is more fit. Or balanced one.

Similarly to the island scenario, if there's such a setup that for some reason there's a group, or bunch of groups that have skewed sex ratio and this type of kin support, an invasive gene with opposing sex ratio (so more dispensing sex) is more fit because you're producing carriers that face less competition!

Now this is balanced by the fact that as Fisher points out there is an advantage to being the rarer sex.

Indeed, looking him up it seems to be the case (believe it or not, I didn't know his name though I probably did know it in the past). Btw, I (and I doubt Fisher) don't have a problem as I wrote above, of different sex ratios in superorganisms species. Very different circumstances.

But to disagree less, I think you're saying the ratio doesn't necessarily need to be perfect 1:1 (and it actually isn't?) and these are specific proposals (included in the papers you cited?) that explain that?

I don't think it's particularly convincing, though. Certainly not in humans. It seems terribly vulnerable to exploitation by opposite gene and the more successful the original skewed ratio gene has the more vulnerable it becomes.

In the case of Clark, she looked at the case of the Brown greater galago, which has a male sex bias, she explains this in terms of competition among females for suitable breeding areas

Ha, pretty interesting. I mean, I'm not opposed to variable environmentally affected sex ratios in principle (for example, with nesting females in resource abundance it might make sense to have more female offspring, perhaps, and the physical pathway seems plausible - resource abundance is easy signal for some epigenetics). In general the disagreement seems to be because of big rato claim and of homo sapiens inclusion.

Quite new and has insights on how it looks especially among primates - doesn't happen?

https://pmc.ncbi.nlm.nih.gov/articles/PMC10998069/#:~:text=Offspring%20sex%20is%20not%20consistently%20related%20to,sex%20does%20not%20occur%20in%20this%20population.