Math Ph.D. student here.
1) The model is not good.
2) The author shows a failure to have properly consulted the literature by redefining existing terms (my memory fails me, but the concept of "more variable" in this paper is known by another name to probabilists…)
3) The results are absolutely trivial to prove. I'll give that this isn't a serious problem in this flavor of paper, though - the meat of the paper is the model.
Specific Model Criticisms:
1) The model assumes a very, very rigid homogeneity of sex A's selection criteria.
2) The model assumes that sex A never "settles down" - that is, mating is only ever done by "the best" members of sex B. This is not what we observe - less fit members of both sexes mate in real life, even among selective species.
3) The model ignores selectivity by members of sex B.
The upshot is that the model is too simplistic, and the results are too trivial. It's the "cannonball being fired in a vacuum" problem: we don't ever fire cannonballs in vacuums.
This isn't a paper that should've been published in a journal. Although my gut reaction is that >>12122729 is a shill (they have not *explained* why the paper is shit), I am forced to concur with them on this point. It is a good undergraduate honor's thesis paper (and is arguably an acceptable Master's thesis paper), but it is not journal-worthy… to respond to >>12123171, even *with* heavy revisions.
The arxiv exists for a reason. Mathematicians are the ones behind a somewhat large push to move to the arxiv, which is not paywalled. Although much other science is still under the heel of journal paywalls, it is becoming standard practice to publish papers in the arxiv before they hit a journal. (Journal publications *look better* on a CV, but a paper that is only on the arxiv can be very good even despite a failure to publish in a journal.)
This paper got published to the arxiv. This is a paper that perhaps belongs on the arxiv - if this person is an undergraduate or master's student, then this is still going to help their career later on: "Oh hey, this person's capable of doing very basic research-ey type things. Sure, the paper's trash, but at this particular level this is not bad…"
Unfortunately, the author has made a bit of a fool of themselves by pushing that article as they have, and people might second guess hiring him for an academic position…but if not for that article, I see absolutely no reason that this paper should harm his career as it stands, so long as he is not at the Ph.D. level…