[quilletteThrow]

The paper doesn't have a conclusion, really. It describes a model and is supposedly intended to spur greater discussion. This is probably part of the reason the paper is written as it is: meant to be simple and easily accessible to people in other fields. The parent will need to work harder to dismiss the author...

[thraway180306]

What the parent charitably didn't stress is that this proof is the totality of mathematical work in this paper.

The rest is a stream of words.

As such it is a work of social science. It might even have been respectable in social science journal. Economists input a lot of assumptions into calculus 101 level equations and call that a "mathematical proof" of an economic theory.

If the author wanted this to be a interdisciplinary discussion, why drag it into a mathematical journal where actual mathematical truths are published?

Author says himself he was unable to formulate actual mathematical idea and recruited help. Why ask Tabachnikov, who is a geometer specializing in classical mechanics, instead of someone with like a clue about statistical modeling? He then compares his experience to one he had fighting in Vietnam... which only makes me wonder if that wasn't the point: to either succeed with a flag-planting diversion or be able to make that comparison and hero of himself anyways.

[leiroigh]

I am not trying to dispute the paper's (implied) greater point: Larger variability of reproductive success favors larger variability of phenotype (in so far as phenotype is related to reproductive success); this can obviously apply to different sexes of the same species [1]; and it is trivial to cook up a toy model for this.

I am just saying that (1) this paper does not belong into a mathematical journal, and (2) the point looks almost too trivial to state.

I am a mathematician; I cannot say whether the paper belongs into a bio journal and whether its points are common knowledge in the bio community. I can only say that, had the arxiv-paper landed on my desk for peer review, I'd have recommended to reject it.

[1] By the conservation law that each offspring has one male and one female parent, differing "effective selectivity" and differing variability of reproductive success are kinda equivalent in the model; casting it in terms of "desirability" looks like a weird choice to me.