Darwin was puzzled by exaggerated traits. (Aren’t we all, really?) For example, why would a widow bird male have a tail so long that he could scarcely fly away from predators? Indeed, speaking of birds:

What a contrast is presented between the sexes by the polygamous peacock or pheasant, and the monogamous guinea-fowl or partridge! Many similar cases could be given, as in the grouse tribe, in which the males of the polygamous capercailzie and black-cock differ greatly from the females; whilst the sexes of the monogamous red grouse and ptarmigan differ very little. Amongst the Cursores, no great number of species offer strongly - marked sexual differences, except the bustards, and the great bustard (Otis tarda), is said to be polygamous. With the Grallatores, extremely few species differ sexually, but the ruff (Machetes pugnax) affords a strong exception, and this species is believed by Montagu to be a polygamist. Hence it appears that with birds there often exists a close relation between polygamy and the development of strongly-marked sexual differences. On asking Mr. Bartlett, at the Zoological Gardens, who has had such large experience with birds, whether the male tragopan (one of the Gallinaceæ) was polygamous, I was struck by his answering, “I do not know, but should think so from his splendid colours.”

Darwin, C. R. 1871. The descent of man, and selection in relation to sex. London: John Murray. Volume. 1. 1st edition. Pages 269-270

I don’t want to give a comprehensive (or bullet proof) “definition” of sexual selection. Instead, I want to lay out a few key ideas and suggest a way to think of models of sexual selection.

Darwinian Sexual Selection.
Females possess a built in aesthetic for a certain trait or form of trait found among males. The aesthetic drives selection of the feature in the male. This of course can work the other way (a male aesthetic) but most examples are female aesthetic and male trait in a co-evolutionary pattern.

Fisher’s runaway selection idea.
The trait being selected for is driven to such an extreme that fitness is reduced. One version of this is that the trait (such as really really large antlers on a moose) does not necessarily reduce fitness, but under changed conditions does. So all the male deer in a clade within a region are driven to have larger and larger antlers, then the region shifts from an open habitat to a more closed habitat, so in those species with the most extreme antler size get tangled up in the bushes and extinction ensues (note: This is an intentionally comical and absurd characterization of the idea so don’t rag on me.)

Fisher’s Sexy Son hypothesis.
Runaway selection and exaggerated traits in general don’t seem to make sense because they are so, well, non-sensible. But this hypothesis lends credibility to the idea. Simply put, a female has a choice: She can mate with a male who lacks the absurd trait and have a son who, lacking that giant tail or enormous antler, will survive longer. Or she can mate with the male with the most extreme version of the trait and thus have a son who has a chance of getting laid. Get it? Sexy son.

Zahavi’s Handicap Principle and Honest Advertising.
These are separate yet linked ideas. How separate or linked you think they are depends on what you think of the ideas. The Handicap principle is that a female selects a male with a handicap that proves that he’s a real mensch. “If this guy has survived to sexual maturity with that giant tail, he must have some qualities that I want in my son,” the female is thinking. Or, “If this guy has fought his way to the middle of the Lekking Ground (a breeding place where males display), and I know this takes years, he must have survived many assaults by predators, many diseases, etc. so yea, he’s a good one.” And so on.

The honest advertising part of this is the first time we really see females becoming part of the picture in a way other than the idea of being impressed with extreme male behavior or extreme male assets. Here, imagine two kinds of traits displayed by males, both seemingly indicating a quality via the handicap principle. But one of them is easy to fake. In version A, the male has a long tail that he grew and with which he survived the slings and arrows of multiple negative selective forces. In version B the male does not have an excessively long tail, but whenever he senses that a female may be looking, he hangs a long branch of a certain tree from his butt so he looks like he has a long tail. (This is like sucking in your gut at the beach whenever a cute chick strolls by.)

The female that does not distinguish between the two (a trait that really does indicate quality and a trait that indicates nothing in particular) will sometimes mate with the “inferior” or “wrong” male. Thus, females that can’t choose between the “honest” and “dishonest” trait will have lower fitness. In other words, females are selected to detect honesty in the trait, and thus, males are selected to display traits honestly. Honest advertising is selected for.

Trivers: Selecting Good Genes for Daughters.
I first heard this theory from either Irv DeVore or Bob Trivers, and it was attributed to Trivers. He did publish it in “Selecting Good Genes for Daughters” which can be found in Natural Selection and Social Theory: Selected Papers of Robert Trivers.

The story I heard and will relate here with only minor embellishment to cover up my bad memory of it is this: Trivers was in a waiting room at a dentist office browsing through a copy of Field and Stream magazine when he came across an article that claimed (apparently correctly) that the amount of calcium … a rare and sometimes limiting nutrient for mammals … that it takes to produce a large, pretty antler rack on a deer is almost exactly the same amount of calcium it takes for a female deer to bring an offspring to full term.

Thus, when a female deer selects a larger-antlered male, she is “hoping for” genes (from that male) that she will confer on her female offspring, increasing the chance that her daughter will have the ability to produce grandchildren. This is different, obviously, from selecting for sexy sons. It is selecting for a daughter who will be a real mensch.

Laden: Fragile Males.
This (as the header suggests) is my own idea. Here, females drive males into a state of fragility by selecting for traits that reduce survivability and longevity. This allows the female to get what she needs from the males (a mix of genes) with a greater chance that the male will fall out of the picture sooner than later. This would apply to species where males do not provide any sort of useful investment into offspring or benefit to the female other than his seed. In the absence of some redeeming quality, males are generally a pain to have around. They eat your food, they attract predators, the harass you sexually, and they may commit infanticide. The most extreme example of this may be salmon where the females make the males swim up stream and die. This may apply to cases like Elephant Seals where the females get into sufficiently large groups to force strong male-male competition so she is mated by only one male while other males are kept off the beach where all they would do is squish the pups in their efforts to mount as many females as possible. I like this hypothesis mainly because it is so deeply insidious that it must be true.

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How does one distinguish among these hypotheses? It is possible to model them all out and decide among them which strategy would be dominant in a hypothesized “game” in which each is a strategy competing against all the other strategies. The result would be to identify one of these as the “evolutionary stable strategy.”

However, it is more likely that which of these (and possibly other) models would be operational in a given species in a given context may change over time. However, some things can be said of the overall pattern among these explanations.

First, forget about the simple female aesthetic. There is no reason that females would develop an aesthetic for no reason! The sexy son is cool but a sensible female will have higher fitness. The simple Darwinian model has to be modified into one of these other models because a female with a random aesthetic would benefit less than a female with some sort of sensible strategy.

Second, something like Fisher’s sexy son and Trivers good genes for daughter may work in concert. You get both if you select for antlers. This may be why there are antlers instead of some other trait that would select for sexy sons OR good daughters. There may be a number of ways in which these ideas will interact to produce strategies that meet multiple needs.
Along these lines, one would expect honest advertising to always be in play.

Another way to approach this problem is to test it empirically. Any given instance of sexual selection can be viewed as a test case. While looking at the real life data, there may be very important variables that are hard to detect, or if ascertained, to measure accurately. In the end it may be impossible to sort out which of these compartmentalized models works generally for a certain clade, or even a certain species.