First published: March 29th, 2019
Status: Putting out ideas

I have encountered plenty of ideas within the field of sexual selection that seem completely misguided to me, and I have an urge to retort. In particular, I have found such bonkers things in the wikipedia page of the same name and of which I had expected much better. Hereby are my own thoughts about sexual selection and the evolution of beauty.


As so often happens, people elevate concepts to unduly levels of idealization when discussing evolution. It is fine to contrast “natural selection” with “sexual selection”, for example when asking whether a trait X was a result of the former or the latter, as long as one remembers and considers that both of these are but shorthands. Alas, not uncommonly people discuss these as if they were completely different principles or even distinct forces of nature, like gravitation and the electromagnetic forces are.1

For the sake of order I shall review things from the basics:
Let us say we have different life forms in an environment. They are all capable of reproducing. As they reproduce, some progeny exhibit a variation in traits as a result of mutations in the zygote they developed from, and these variations are heritable, that is, they pass on to their own progeny. As far as these variations have differentiable effect on survivability, individuals with the variation that confers more survivability would tend to survive better, on avereage, all else being equal, and therefore reproduce more, and since the variations are heritable, these variations would increase in their frequency amidst this population. We say these variations are “adaptive” and to the principle that adaptive variations increase over time in frequency in populations we call “natural selection”.
We skip the evolution of sex for the moment and jump to assume that we have in our hands a particular species that reproduces sexually. Consequentially, for a member of the species to reproduce it is not enough for it to merely survive, but it must mate with a conspecific. In other words, it must either find or be found by such a conspecific, copulate with them, and have the offspring reach sexual maturity (and so on and on). We could say that to the degree that a trait is beneficial to bringing about this result of sexually mature offspring via sexual reproduction is (sexually?) adaptive, and that the tendency of such traits to increase in frequency within a population is the principle of “sexual selection”.
It is common to regard “natural selection” and “sexual selection” as distinct forces (originating already in Darwin’s writing?), but really the latter is a special case of the former. The traits whose shaping is attributed to the pressures of “natural selection” are those which facilitate survival at an environment, that is, render effectively the ability to gather food, escape predators, resist pathogens, resist parasites, and so on. We could have just as well had “food selection” and “predator selection”, narrowly referring to the differential survival-promotion of variable traits affecting a member of a species’ abilities to gather food and escape predators, respectively. The reason, of course, why these are lumped together and “sexual selection” stands out is that sexual reproduction adds a complexity of analysis that stems from (species-) self-referentiality. In non-sexually reproducing species the ability to (survive and) multiply is marginally greater than the ability to merely survive. A creature avoids predators, finds and eats food, and when sufficient energy and nutrition surplus had been acquired it either divides or lays eggs. The extra margin of ability necessary for multiplication refers to the ability to successfully divide or lay viable eggs which is distinct from the ability to, for example, gather food. The ability to multiply depends on the environment (for example, different kinds of eggs could be differentially viable at different humidity or ambient temperatures, or require nutrients that might be present in one environment and absent from another) and might be even affected by other conspecifics (for example, if they cannibalize eggs), but it does not require and therefore not dependent (in the strict sense of the word) on other conspecifics. This is in contrast to sexual selection. Not only does the “margin” responsible for multiplication is greater now as it encompasses not just the ability to successfully create a gamete/ zygote but also a behaviour that would lead to a successful copulation, but, more important to the complexity, the traits which affect and promote one’s success of reproducing are not merely present at the one individual, but also ––and increasingly so over time–– in the other conspecifics. To put it differently, (1) in order to sexually reproduce one must have conspecifics in the environment, (2) conspecifics in the environment of one individual are part of the latter’s environment, and, therefore, (3) when a species (that is, its members) evolves, so does that species’ environment, because the species is part of its own environment to which it adapts. And thereby lays the complexity.

To illustrate what I mean through an example, imagine that one member gains a reproductive advantage by somehow taking advantage of their mate. Since this ruse is advantageous the genotype responsible for this phenotype of this member spreads in the population until it becomes a common phenotype. Increasingly this phenotype “meets itself” and since the advantageous was exploitative, it is not possible that both sides reap the advantage. Perhaps their subterfuges “cancel each other”, but is it also possible that their efforts of mutual undermining result in a reproductive success that is lower than whenever two of the “old cooperative phenotypes” copulated. In this case it might be even advantageous to “be exploited” than to (try to) exploit another exploiter.2
This is an example of a negative frequency-depended selection. Were it a positive frequency-depended selection there would not be much complexity, but, On the other hand, one could also imagine more complex examples. Of course, in this example, since the exploitative phenotype could mate both with the non-exploitative phenotype as well as with itself, it means that either the phenotype is not sex-specific, or the members of the species are hermaphrodite.
When a species has two strictly-distinct sexes, the members of each sex would coevolve with those of the other sex. That is, how adaptive a genotype of one sex is would depend on the genotype of the other sex. As with “more general” natural selection, members would be in competition with each other, but in this case the competition would be within the sex (males competing with males, females competing with females) and never with members of another species, such as happens in natural selection when two or more species are “fighting” over the same niche, for example when predating the same prey. That is not to say that there is no conflict between the sexes. While the competition occurs within each sex, the terms of the competitions are set “between the sexes”, so that the females set the environment in which males compete with each other, while the males set the competition for the females. One could imagine that had diverging sexual strategies evolved within one sex which were responded to by divergent sexual strategies of the other sex, speciation could occur on basis of that.

Rendezvous and mutual recognition

Before I touch upon other theories, I’d like to march out my own theory about what’s behind “sexual selection”. First of all, to say the obvious, what drives sexual dimorphism is the different roles that each of the two sexes take in reproduction. More concretely, given an existing dimorphism (and generally, genotype and phenotype of a species), the traits that would be selected for are these that facilitate the reproductive function of a given sex and to the degree that they are are phenotypically restricted to that sex (i.e. appearing only in females when they are adaptive in females) or not maladaptive in the other sex when it exhibits them. The traits which I think sexual selection works on, other than these that are responsible for sexual reproduction proper (production of gametes, copulation and rearing behavior instincts and so on), are those that “solve” one of these two problems: location (finding) and recognition of sexually mature members of the opposite sex (contrasexual conspecifics, or concons, from now on). Solving the problem of location means being able to arrive to the same place at the same time as a concon –– to be able to find it or be found by it. Solving the problem of recognition means evolving a motivation for a behaviour vis-à-vis concons which leads to fertilization/conception, which often necessitates evolving a phenotype (behavioural or morphological) that elicits an analogous behaviour in a concon. The traits that solve either of these are those which, one could say, determine how “attractive” an individual is.
Why these problems? On the one hand, sexually reproducing creatures must be in a certain proximity to each other in order to mate. On the other hand, it is beneficial to spread out in space in order to avoid competition over food. Since they do spread out, in order to mate they have to (1) be able to find each other, that is, arrive at the same place at the same time, and (2) recognize members of their species of the opposite sex. These problems are not trivial, and they are solved through the utilization of auditory, visual and olfactory signals as well as through behaviour, such as the synchronised movement of salmon and of migratory birds to a special location in order to mate.
Both of these problems could be solved to a large degree by making one more conspicuous, whether visually, auditorily, olfactory or through any other signal that is perceived by members of the species. Such traits are otherwise often naturally selected against, as they make one more susceptible to predators and less capable of sneaking on prey.

I’m going assume that, all in all, if any member of a species simply mated with any other mature concon, that is, the first encountered concon that survived into maturity, the species would fare rather well. Surviving to adulthood is a clear proof of being adapt at surviving in the given environment.
In this case, not assuming monogamy and assuming an individual can bear children more than once in a lifetime, it would be adaptive to be able to find a mate as fast as possible once sexually mature and each time the member is ready to reproduce, as that would yield (everything else being equal) more begotten children in one’s lifetime. In this case, sexual selection would drive conspicuousness up, whether by making one more loud, more smelly or more strongly contrasted with one’s visual environment.
When the two sexes have different mating frequency capacities, as is often the case, for example when females have bigger and more expensive gametes, and/or when they need to expend time and energy post-conception in order for the offspring to survive to maturity, the sexual selective pressure to be conspicuous acts differentially on the two sexes. Assuming no paternal care, it is adaptive for males to seek and mate with as many females as possible (assuming cheap sperm and that males mate with less females than energy and time would have allowed them had they had infinite amount of female available to them), while it is adaptive for the females to discriminate mates in order to mate only with the fittest one. If a female became (through evolution) more conspicuous she would get more attention from males, but as any male mating with her beyond the first one would affect very little her reproduction, this conspicuousness wouild add little to her fitness. However, as it would also get the attention of predators, and the attention of any one predator (or prey being sneaked upon) would put her at a great existential risk, conspicuousness would be overall a disadvantage, and indeed in many species the females are inconspicuous.
On the other hand, while the same costs of attention from predators/prey apply to males, they do get an advantage by being more salient to females since mating with any additional female greatly increases their expected number of offspring. This creates a competition: at an environment with males that vary in their saliency, whenever a male is being found by a female, even if he mates with her, the lower a male is in his conspicuousness, the more likely it is that, on average, another male that was more salient than him had been already spotted by her and copulated with her, presumably making it less likely that the late-comer would impregnate her (though here comes in sperm competition).
And thus the females get to become choosy. Not merely because they do not mate indiscriminantly like males, but because being camouflaged (and so protected both from predators but also from “sexual predation” of conspecific males) they are the ones having an easier time finding concons, and therefore probably the sex which searches for the other. Once a female finds a male, she can decide whether to mate with him or not based on strictly “naturally selected” characteristics, that is, traits by which also a male would have judged females had he faced the opportunity to woo more than a single one at a single time.
As these secondary sexual characteristics (promoting conspicuousness) evolve, so would evolve the recognition of concons. Other than finding them, females also must be able to recognize males as concons, that is, their perceptive faculties must initiate a copulatory behaviour upon finding them. Failing to do so would result in no offspring. That recognition does not have to rely on the evolved secondary characteristics and could rely on primary ones, but perhaps as dimorphism grows between the sexes the recognition faculties must adjust in order to recognize concons as conspecifics at all. “Recognition” here does not refer to any cognitive process. Females do not have to “know” anything about the biological relation between themselves and the concons; they merely need to properly respond to them upon an encounter. After a shift has occurred whereby females recognize males by their secondary rather than the primary sexual characteristics the male-male competition intensifies as now these traits are not merely important for being noticed, but to be recognized as males at all.

My theory, therefore, if I may, is as follows. In species in environments where location of conspecifics is challenging and where predation renders a pressure to be inconspicuous (which I think is true for most species in most biomes) “sexual selection”, that is, natural selection that acts through one’s success in mating, would act to increase the conspicuousness of males vis-à-vis conspecifics3 in correlation to the difference in offspring-expenditure costs between females and males and in anticorrelation to the survival risks they confer upon the male such as greater risks of being predated on or greater difficulties in predation. My theory makes the following predictions:

  1. The greater the problem of location is, the more conspicuous males would be. When the problem is smaller males would still compete against each other, but the competition is then more likely to be manifested in ways that do not put them in risk of death due to external causes such predation, but rather through confrontation, whether it is intrasexual aggression or sperm competition.

  2. In social animals the difference in conspicuousness would be small. This is somewhat of a corollary of (1). When members of a species breed within their group the problem of location is not a problem at all. If they breed across groups then location of a mate is not a problem of finding an individual but a group, which is a. easier to find, the more so the bigger the average group is and b. depends on the conspicuousness of the group as a whole. A conspicuous male (or female) puts his whole group at risk (if it is preyed upon) and would also gather little advantage for himself if other forms of male-male competition is going on such as aggression.

  3. The easier predation is, the greater the conspicuousness of males. This is stated somewhat ambiguously on purpose: it is the case both when the species in question is the predator, and when it is the prey. The easier it is to hunt prey (or when conspicuousness does not hinder it) as a predator, and the less predators there are as a potential prey, the more conspicuous males would be. I’ll only note that while this may sound trivial, some theories predict otherwise.

  4. The greater the difference in investment between the sexes, the greater the conspicuousness of males. In particular, species that are monogamous or serially monogamous and rear their young together would diverge little in conspicuousness as being noticed by several mates is no longer an advantage to males, and so being noticed by conspecifics is as a big of a challenge to both sexes.
    Further, on the other hand, I would suppose that when the environment exerts a strong pressure against conspicuousness, males would tend to rear their youngs, but only if the problem of location is big enough that a male is more likely to increase his number of offspring this way rather than by finding another female.

  5. Increased conspicuousness in predators is more likely to be enacted than static, such as an auditory call or sprayed smell as opposed to vivid coloration. Conspicuousness thus being a behaviour they can remain inconspicuous when hunting prey and so interfere little with their fitness in that regard. Of course, if they have no prey which could detect some static conspicuous trait, they could evolve it without bearing costs.

Aposematism

Aposematism (warning-coloration) could evolve from this mating-promoting conspicuousness, I claim. That is, a sexually reproducing species where males are more conspicuous might develop a poison that is aversive to predators. Over time the predators learn (or evolve) to avoid these colored males. At this point the conspicuousness becomes an advantage rather than a disadvantage, driving the males to become even more conspicuousness; while before the evolution of the poison predators rendered a pressure against conspicuousness, now they rendered a pressure in favour of it, since they are more likely to eat the less conspicuous animals. In turn it makes it a disadvantage for the females to be camouflaged which thence evolve to have the same conspicuousness.
I went through the category page of aposematic animals on wikipedia, looking for non-sexually reproducing animals. I didn’t find any. However, there was one species that might if not “contradict” than at least be an exception for the idea above, Acanthodoris lutea, a brightly colored sea slug, and perhaps more generally, its clade Nudibranch. I say an exception because while they do have eyes, it seems like they are only sensitive to light/dark and so they cannot be using color to recognize each other (unless, that is, the their brightness per se, as opposed to their particular color, is a source of mutual attraction). On the other hand, they derive their toxicity from the toxic sponges that they eat. Since these sponges themselves are often vividly colored I wonder if the chemical compounds that give them their colors might not simply end up in the sea slugs (introducing the toxins and the warning coloration concurrently). However, that simply moves the question about the coloration to the sponges. These are, too, sexually reproducing, but they release sperm cells into the water and so they do not even need perception to reproduce, let alone find and recognize each other, so the color is not used for intraspecies communication. However, from a brief review I’ve made, it seems like the sponges that are brightly colored live at abysmal depths of the ocean to which light scarcely penetrates and so color would scarcely be an observable phenomenon. I cannot say much more of this and so I’ll leave it at that.

This here is in contrast to what seems to be the prevailing theories of the evolution of aposematism, or at least as far as I can tell based on the wikipedia page. It seems they all assume that the toxic defences evolved first, followed by coloration, while I suppose that coloration evolved first, followed by the toxic defences (though coloration does intensify and spread to females after the evolution of the defences).
There was one study cited there4 which advocated sexual selection as the driver of warning coloration in several populations of Oophaga pumilio, the strawberry poison frog. However, I’d say that they got “sexual selection” wrong, and that made their analysis confused and full of contradictions. In their discussion they expressed their awareness of those contradictions, but they couldn’t square them together. For example, on the one hand they mentioned that bright coloration ––– which females prefer –– would make males more conspicuous to predators, thus treating it as a handicap-principle trait, while on the other hand, on another paragraph, they say that the color deters predators, and so the less bright females are more susceptible to predation. While I agree with the coda of their conclusion section that “[…] sexual and natural selection must be jointly considered in the study of aposematic evolution”, I think their study mostly failed to show the relationship of the two ––– given their orthodox views of sexual selection ––– if only because in 4 out of 5 of the populations they studied the females were as bright or even more so than the males,5 making this trait not sexually-dimorphic or even dimorphic in “the wrong direction”.

On Beauty

It has been known for a while that averaged faces, that is, face images produced by “averaging” a multitude of face portraits, are more attractive than most or all of the faces being averaged, even after correcting for “skin smoothening”. The common explanation for that is that an average(d)-looking face is an honest signal of the developmental stability of its owner, that is, of health and resistance to pathogens. However, I think that it is something else.
First of all, as far as I know, these studies always averaged faces of people of the same sex, and I suspect that the result might be somewhat different had the faces being averaged had a sex ratio of 1:1. Would that be the case, this is not to contradict the common explanation per se, but one would have to admit that humans are, then, also sensitive to the proper/healthy development of sex-specific features (that is, sex-hormones-induced). That this is the case is suggested by different studies; there are vartiations in preference of faces with more or less feminine/mascluine features, for example intraindividually over the menstrual cycle of a woman6 (and particularly so among females with more feminine faces), and interindividually across people of different constitutions.7

Sexual characteristics of faces

But first, we need to take a step back. As psychometric investigations relying on self-reporting questionnaires, all of these studies suffer from the same problem, namely, that subjects were reporting their opinions about their own attitudes, rather than acting on them. This, first of all, matters, because people don’t always act the way they imagine they would. Furthermore, it makes the results depended on the interpretation of the subjects of what they are being asked. What does “attractive” really mean? Is asking how attractive a face is the same as asking how visually pleasant it is, or is it the same as asking how likely it is that we would appraoch such a stranger? There was only one paper that I have encountered in which subjects were shown faces subsequently, for a total period of time of fixed duration, and in which the subjects could either prolong or decrease the duration of exposure to any one face with a pressing of a key. The results are ostensibely ambiguous –– the researchers don’t know “why” the subjects wished to look longer or less long at any given presented face ––– but, at the same time, they are much more definite, since it was behaviour that was measured, not responses to questions. There were studies that made the question more precise, for example, asking not merely “how attractive a face is” or “which one is more attractive” but querying about how much a person(‘s face) is desireable for a short-term relationship and how much as a long-term relationship. On the one hand it makes things clearer, but on the other hand it casts doubt on the whole premise of the methodology. For example, the former differentiation was used in advnacing a theory about a so-called “mixed mating strategy” and the results were interpreted in that light, namely, that that non-single women in their fertile period of their menstrual cycle have increased interest in “short term relationship” with men with masculine faces is part of a strategy to get impregnated by a man with good genes while continuing to get support (for herself and her child) from the less-masculine and more care-giving partner she has. But that with the masculine man would not be a “short term relationship” but what one would call “a one night stand”. That questionnaires say “short term relationship” and not “hook-up” or “one night stand” or “no strings attached sex” is somewhat understandable; these are prying questions and the researchers want to get sincere responses by avoding affrontery to the defensive sense of decorum of subjects. But this “mild” articulation of the question changes the question itself, so researchers cannot really be sure of what the answers answer. As oppose to euphemisms that are indirect but have a clear reference,8 the blurry language used in these studies is simply unclear. What is a “short term relationship”?9 On first glance it seems to be referring to a real phenomenon, but I think it doesn’t really hold under scrutiny. Not really a proof as much as a suggestion, but searching for “long term relationship” on Wikipedia directs one to the “Interpersonal relationship” article, but “short term relationship” leads nowhere. Relationships can be “short” (though how long is “short”?), but that is a retrospective and not a prospective view, though in these studies it’s the latter that subjects were asked about (“how much is this person desireable as a short term partner?”). People engage in inconsequential sex with each other (though only 11% of women do so with no emotional involvement whatsoever, according to one study I cannot now find, that is, only 11% engage in sex that is really “inconsequential”), but I don’t think people enter an intimate relationship with a plan for it “not being long lasting”, unless they are aware from the getgo that it is unlikely to go very long e.g. because they are in the country for a circumscribed period of time or because they are terminally ill. Even if for whatever reason (idealogical, mostly, I suspect) they “plan” it to be “short”, I think they really are deluding themselves and that at the end the course the relationship would take is not any more dependent on that plan than the activity of a person at 1:15AM is on the decision to watch “one last youtube video” fifteen minutes earlier.

Nonetheless, I do not hold that these investigations are not at all informative. On this particular topic, however, I’m a little skeptical. One paper by Christine R. Harris10 that sought to replicate the findings about the changing facial preferences along the menstrual cycle failed to replicate the findings, and given Harris’ seemingly very organized methodology I trust her investigation. Beside her empirical results she also raises several interesting points, for example questioning whether the conditions that would have made such preference relevant existed in the relevant evolutionary times, namely, that an ovulating woman would get together with a “good gened man” in order to concieve a child with him and then the man would simply leave her alone and she would raise the child with a care-giving man, having the “origins of the child” in secret.
Her empirical results not only did not replicate the previous studies of Penton-Voak et al, but they showed the opposite trend, even, that is, that women preferred less masculine men when they were fertile, which somehow goes along with a review of Jones et al11 who generally held the opposite view, but whose introduced orthogonal theory is relevant here. They mention that in the “non-fertile” parts of the menstrual cycle progesterone is elevated, which is also elevated during pregnancy. During pregnancy a woman’s immune system is somewhat repressed, and, in addition, she is responsible via her health for the more sensitive health of her developing child, both of which should make her more avoidant of contact with sickly looking people lest she catches a disease. That is, when she is pregnant (elevated progesterone) it is sensible to be more attracted (approach, seek the company of) towards feminine looking faces (who are associated with more care-giving) and to faces that are similar to hers (a proxy for kin, which, again, are more likely to lend help than strangers), but these tendencies/ “restrictions” are relaxed when her progesterone is low (around ovulation) and she’d be less wary of contact with sick looking people (note that health here is not some sort of “developmental health” but can refer to a transient condition) and more masculine looking men. That being said, since masculine looking men are judged to be more healthy looking, the idea that women are avoidant of sickly looking people when their progesterone level are high goes along the Harris’ result showing a tendency towards preferring masculine looking men during the infertile parts of the cycle. Be as it may, Jones et al’s paper is important in that it points to the fact that “attraction” does not mean “sexual attraction” or, let’s say, “motivation to copulate with”, which seems to had been taking for granted as an assumption in studies where subjects rated faces of the opposite sex.

Just to touch on an additional point, the Jones’ paper cites a study12 that found that women had a preference for masculine faces on “days of their menstrual cycle when testosterone was elavated”, i.e. around ovulation. While I won’t contest their finding about the association between the elevanted testosterone levels and the preference, I’d contest their association of the elevation and the particular point of the menstrual cycle. First of all, in their own paper, they found that the mean (unsigned! which is suspicious) difference between the highest testosterone test session (these were conducted daily aruond the same time of the day) and the day of ovulation was 7.25 days. Even given the long period of time (~14 days) within a menstrual cycle where the probability of conception is elevated,13 7+ days within an estimated cycle of 28 days is a rather big deviation, where we would expect a synchronisation given the proposed theory. In fact, an unsigned difference of 7 days within a bell-shaped window of 14 days would mark either the very beginning or the very end of the fertile period, so that testosterone either decreases as conception likelihoold increases, or vice versa. In addition, the mean unsigned difference between the session with the lowest testosterone and ovulation was 9.38 days, which according to their paired t-test testing was significantly different. Nonetheless, a 2.1 day difference between polar values of testosterone (min and max) within a 28 day cycle seems very minute. A paper that specifically studied hormonal changes along the menstrual cycle found no regressional model that significanly fitted testosterone levels to the day of the cycle nor changes in its irregularity,14 though another paper –– which didn’t look for a regression model –– did find a significant rise of testosterone in the pre-ovulation (“fertile”) period.15

The Immunocompetence-handicap hypothesis

There is the Folstad and Karter’s immunocompetence-handicap hypothesis16 which has gained a lot of traction. The hypothesis is that, since testosterone inhibits the immune system and is responsible for masculine secondary traits, a masculine face is a honest signal of health: only healthy/ vigurous males could sustain the burden of elevated testosterone. I think the hypothesis is utterly wrong. First, out of the same grounds that I think that the handicap-principle is generally wrong.
Second, it assumes that masculine faces have to be a developmental response to raised testosterone levels, and I think this is false, too. The long-tail of the peacock or the big antlers of the deer are themselves the handicap. In the immunocompetence-handicap hypothesis the actual handicap is the immunosuppression, not the male face. Had the male face signaled vigour, one would have expected an evolution of a development of a male face that is independent of immunosuppression.17
Third, the immunocompetence-handicap hypothesis postulates that the masculinity of the face is responsive rather than intrinsic. That is, a male would develop a masculine face in response to faring well vis-à-vis parasaties, so that the development would depend on the environement (presence of parasites) and on his immune system. However, it seems like this is not the case. One study18 took photos of male and fmale siblings (identical and non-identical twins and non-twin siblings) at ages 16 and 18. They develop an algorithm that calculated a metric of “masculinity”. It seems to me that the paper erred about the assumptins that the immunocompetence-handicap hypothesis makes (which might be due to the kind of research that had been conducted in support of the theory, discussed below)) and therefore also on its conclusions, but these interpretations stand beside the study per se. However, regarding the study itself, they made some odd decisions which leads me to take the results with a grain of salt. Their algorithm calculated the metric based only on the shape of the face (texture and so on were not involved), but the number of landmarks on the face that they used was very sparse, 16. While it did successfully separate female and male faces into two distributions, they overlapped considerably and it correctly classified the gender of merely 80% of the faces, which seems rather low to me. On the whole, while I do not think that the algorithm/metric they had used did an excellent job, I do trust that it did what it claimed to do.
What they found was that the correlation of face masculinity was very high for identcal twins (r=0.5), lower for non-identical twins and siblings of the same sex (r=0.2319), and, most importantly, that it was rather high (r=0.25) for non-identical twins and siblings of the opposite sex. That is, more masculine faced males had more masculine faced sisters, which also correlated with lower attraction ratings (based on human rater) for the sisters. What this suggests is either one of two scenarios, both of which go against the immunocompetence-handicap hypothesis. One scenario is that face-masculinity is an intrinsic feature and not a developmental response, which goes against the premises of the hypothesis. The second scenario is that the masculinity is indeed a developmental response and that the correlation in masculinity of faces is a by product of the correlation of the strength of the immune system. However, if this is the case, it means that females’ faces are likewise responsive, that is, develop masculine features in response to successful coping with parasites, which goes against the whole premise of it being a strategy employed by men, especially since facial masculinity is regarded as less attractive in females. One could perhaps suppose that this strategy is “still evolving” and didn’t reach the optimum point of sexual-segregation, but perhaps that’s giving too much leeway to the hypothesis, and I don’t know whether it is likely to be the case ––– given that support for the theory is given by mentioning other species, as remote as fish and lizard, one can suppose that segregation would have been reached already.
Fourth, the hypothesis would predict that males in societies in environments with low parasitic load (e.g. urban Western societies?) would have on average significantly more masculine faces than those that are in environments with high parasitic load (e.g. modern hunter-gatherer societies, such as the Tsimané; rural communities?). I couldn’t find any papers of studies that looked into this, which leads me to suspect that there isn’t such a difference. Also, looking at footage of hunter-gatherer societies I don’t get the impression that their males are particularly feminine looking. Looking at the correlation between males’ facial masculinity and the parasitic load of the environement they live in could shed some light, though one must keep in mind that it is not the parasitic burden per se that is important, but also how well the males cope with them (hence the “immunocompetence”).
Finally, a meta-analysis of studies where testosterone levels were experimentally manipulated in animals did not find much support for the hypothesis, in particular among mammals.20

Could we support a variant of the hypothesis by assuming that the masculinity is intrinsic and not a response? Even disregarding the results mentioned two paragraphs above, I think the answer is no. First, the responsiveness in the original formulation is a critical component that makes a big difference; it being there, and had empirical findings supported it, I’d say that my general reservations about the handicap principle (which postulates predetermined, that is, unresponsive, development) would not apply. Second, it would make very different predictions. From the point of view of the interaction of the scientific community with the theory it seems like it would make little difference, since as it is seems like researchers predict whatever they find (rather than find what they predict), always finding an explanatinos of their results ––– like good conspiracy theorists ––– which doesn’t make for a very good science, as the theory is rendered unfalsifiable.21 I’ll demonstrate how the predictions would be different if the morphology of the face is intrinsic and not responsive with one paper. In a paper by Rhodes et at22 they write, The immunocompetence-handicap hypothesis predicts that the expression of secondary sexual traits should be negatively associated with parasite burden, because individuals with good heritable resistance to parasites can afford the immunosuppressive costs of secondary sexual trait expression. This is correct, though I’d have changed the formulation to “[…] because individuals with good heritable resistance to parasites will develop secondary sexual trait expression despite their immunosuppressive costs, affordable due to higher immunocompetence”. However, if the facial morphology was intrinsic and not responsive we would have predicted either no association or the exact opposite; which of the two would have depended on our assumptions in regards to the linkage equilibrium between immunocompetence and facial morphology genes. Nowadays we would have assumed a linkage equalibrium; given modern hygiene and health care, including medication and vaccination, the impact of parasaties and disease on humans in Western societies is greatly diminished, child mortality is very low, and some tradeoff between facial masculinity and immunocompetence would hardly affect one’s survivability. This would mean that also men with masculine faces who wouldn’t have been able “to afford it” at former times now can reach maturity and reproduce, so that the association between masculine faces and immunocompetence would decouple. Nonetheless, one could expect that men with facial masculinity they cannot afford, while not at a real risk of dying, would be less healthy. Assuming, again, linkage equilibrium, that is, that concurrence of facial masculinity and immunocompetence is random, we would expect that, on average, men with more masculine faces would be less healthy than those with less masculine faces, a prediction that is opposite to the one made in the study. What if there was no linkage equilibrium? I think in this case we would expect that on average men with masculine faces would have the same level of health as those with less masculine faces. The environment exerts pressure on humans in the form of parasites and other pathogens so that only individuals with an adequate immune response would survive. This is irrespective of their facial masculinity; the immune system of masculine faced males simply has to be better to reach an adequate level to compensate for the immunosuppression, but at the end they would have on average the smae level on health.
In the study, the pictures whose masculinity was judged by subjects were of adolescents born in California between 1920 and 1929. During that time child mortality was still decreasing23 and life expectancy increasing, so that communicable diseases (and presumably parasites, too) were a factor that led to the death of people prior to maturity, so one could suppose possiblly a linkage disequilibrium. Nonetheless, this disequilibrium cannot be total. Genetic recombination was still at play and one would expect immunocompetence, even when developed in mascunine faced men, to “leak” to the less masculine faced men. Supposedly an above adequate level of immunocompetence is not harmful. Being below adequate level was significantly more harmful reproduction-wise than the “loss of some children” to extramarital affairs that non-masculine-faced husbands supposedly suffered. So it seems that, on the whole, one would still expect a somewhat diminished health among masculine=faced men ––– again, if face morphology is intrinsic and not a response. But what the study found was a (small, but significant) positive correlation between health and facial masculinity ––– in accordance to the original formulation of the hypothesis.

Intrasexual communication

What I think is much more plausible is that facial masculinity is a part of intrasexual adverserial communication. Let’s first briefly discuss communication. When it goes on between adversaries it often facilitates a reduction of costs. During mating season, deer stags would fight each other. However, before they do so they assay each other, and often one would concede defeat without a fight, presumably knowing that he was very likely to lose. This pre-fighting assessment is a mutual communication where each of the males communicates his vigour to the other, and assesses that of the other.24 When the difference in vigour is discernible and the oonflict is resolved without physical engagement, this mutual-assessment is beneficial to both. Both parties, the obvious would-be-loser and would-be-winner, save themselves the damages and energy expenditure that they would have incured fighting, whether to lose or to win. While the “unchallanged” winner gets a “free win”, the “unchallenging” loser suffers a defeat with no “overhead loses”. Both therefore benefit by making predictions on the outcome and “agreeing on it” by letting the probable loser fleeing unscathed instead of going at it head-to-head.
Facial expressions such as anger work similarly. When two humans interact with each other and one expresses anger at the other, what he communicates is a threat. He communicates that the other has done something that is not to his liking, suggesting that had he done it again it would not be without consequences. Expresssion of anger is used to manipulate the behaviour of the recipient without incurment of much costs in the form of energy or bodily damage. It’s a mutual arrangement; one party agrees to forgo a behavior and the other agrees to forgo the employment of violence. While people can coordinate behaviour in harmonious, eye-to-eye, ways, making consessions and reaching a mutually understood agreement, when someone expresses anger they essentially push some behavioural equilibrium to move in their favour; the concession they make is refraining from being violent, which is hardly a concession at all.

Facial masculinity in young adult males is correlated with testosterone levels.25 Testosterone levels are correlated with aggression26 as well as with dominance.27 Could I suggest that a masculine (dominant) face is akin to a permanent angry-like expression? A masculine face would be dominant in a sense that it communicates (1) strength and (2) a certain relentlessness, an inclination to not cooperate.
Of course, an angry attitude (or facial feature) is not absolutely a winning strategy, and is not without its costs. If it was, we would all look very aggressive and constantly behave angrily. While acting and seeming dominant (tall, muscular, strong, unyielding, relentless) would benefit a person in any interaction –– so long it is not contested –– by letting the person have things their way, it affects negatively others’ willingness to interact with that person, both people who interacted with the dominant person before, and other people who haven’t interacted with him but got a whiff of his dominance from afar. Having a choice and all else being equal, a person might choose to turn to and interact with a cooperative person with whom he could get “a better deal” than to turn to a person he knows from experience or reputation (or appearance) to be domineering. Being aggressive, therefore, is a trade-off between gaining more at a given transaction and being let in on future transactions; by extention, having a dominant look is a general shift of the trade-off ––– on average people would be more yielding to avoid confrontation with the dominant looking person, but they would tend, on average, to be less inclined to interacting with him.
This trade-off is not completely “either-or”. The Frankish Merovingian kings who did not hesitate slaying their siblings and other relatives, as well as misbehaving subordinates, come to mind, but their use of violence alongside them being the beneficiaries of continuous cooperatinon is merely more explicit, or, rather, frank,28 than the violence employed by contemporary authoritarian regimes. The power held by rulers extends the units of agency in the aforementioned “transactions” and alters the nature of the space/timeline along which agents make their decisions regarding interactions:
First, the agency of the leader goes beyond the single person. Even when “authority” has that leader as its locus of power, authority itself is somewhat abstracted and in a way involves the entire population as a component.29 Partially it is a problem of information; even if all or the great majority of the population (including the government) finds the leader to be overly domineering as well as inadequate, unless there is a free flow of information e.g. through free press, the pepole of this majority would not be privy to this information, and would act therefore as if the leader is well supported ––– as it seems to be the case ––– or, in other words, cooperate with him and his authority, thereby rendering in behaviour an undesireable reality for themselves and others.30
Second, while I can avoid interacting with a person I regard to be overly domineering by ceasing to meet up with him, I cannot avoid interacting with the state at which territory I reside, other than by leaving the country or by successfully bringing about the replacement of the regime, both of which are no easy operations.

On the other hand, one does not always have the freedom to choose or avoid interactions with another concrete individual. Undoubtedly many of us heard of stories of abusive people, such as employers or spouses, who would terrorize others to the extent that not only the victims feel compelled to cooperate, but they are afraid to seek help, for example by reporting the terrorizer to the police. I’m not referring here to an interaction that is circumscribed in time and place, but where one person would have control over others over the span of many years or even decades. That is, the person, by employing aggression, does not merely gets things his own way at the present, but dictates the pattern of future interactions. He manages to have it “both ways”; to eat the cake and have it too.31
How come? One way to subsume this case under the “trade-off rule” is to extend it by having it refer to non-atomic interactions, that is, with interactions that do not have to be localized in space in time. Indeed, many times the decision whether to interact again with a person is not availabe between “atomic interactions”,32 if only because of the way people associate with one another, whether it is shaped by compliance with social norms or innate “social instincts”. We could now look backwards and even use these concepts in order to define what an abuser is: a person who employs tactics in order to force another to come in interaction with them, and uses coercion in order to define the terms of any transaction. I suppose that often those people get things their way and die peacefully, but other times when the (non-atomic) interaction ends the abused party not only would cease to interact with the abusing party, but take measures in order to retribute.
This extention of the theory would subsume the example above of tyrranies, where the interaction between the leader and the led is non-atomic. And while some tyrants get away with it, some eventually get their due, such as Nero, Maximilien Robespierre or Nicolae Ceaușescu. This is true not only among humans, but also at least among chimpanzees. Alpha males rise to power not merely through strengh and the application of sheer force, but also through their ability to form “alliances” with others. Undoubtedly the alphaness of one chimpanzee is variably good for the rest of the group, and there have been accounts of former alpha male chimps being murdered after they had fallen from their mighty positions.33

Honest signal

The biggest flaw of the immunocompetence-handicap hypothesis is its assumption of a necessary causal link between testosterone levels and facial musculinity. Had facial masculinity been absolutely attracive to the opposite sex and sexually selected for, human males would have evolved to develop such facial features independently of their immunosuppressive testosterone levels. However, I claim, the association between facial masculinity and testosterone level is adaptive when we regard the former as communicating dominance.

Assuming that testosterone levels correlate with dominant behaviour, and that facial masculinity correlates with the perception (by others) of being dominant, what I’d like to claim is that it is advantageous to seem dominant if you act dominant, to seem cooperative if you act cooperatively, or, in other words, that the development of facial masculinity in response to testosterone levels is adaptive. I’ll treat the behaviour and appearnace as binary features, which I think does not lead to a loss of generality.

Seeming dominant when dominant is advantgeous over seeming dominant when cooperative

Seeming dominant would generally speaking, on average, decrease other people’s willingness to approach and engage with the person. A person who just looks dominant incurs the costs of the appearance without utilizing the advantage their looks could confer if they used aggression/intimidation to get things his own way. If you seem dominant, its advantageous to act dominant.

Seeming dominant when dominant is advantgeous over seeming cooperative when dominant

Seeming dominant would generally speaking, on average, increase other people’s willingness to yield to unfair propositions made by the person. A person who acts domineering without seeming the part would not be taken as seriously (not being perceived as dangerous/ strong). However, by acting domineering he would decrease the willingness of those he tried to dominate in the past to engage with him again in the future. He asks for more than people would have been ready to give him, which possibly makes him seem even more unfair of a person than someone who demands the same but also looks domineerig. Possibly. Maybe becuase people have a general sense of what is right/ just as far as allocation of resources is concerned, and with a person who doesn’t seem domineering the gap between “what he demands” and “what he deserves” seem wider. Or, perhaps more likely, the dominant person, seeming more powerful (and able?), seems like a better person to appease, in line with his potential to hurt/contribute. That is, like a person who is more important to reckon with than the submissive looking person. If you act dominant, its advantageous to seem dominant.

Seeming cooperative when cooperative is advantgeous over seeming dominant when cooperative

Seeming cooperative would generally speaking, on average, increase other people’s willingness to approach and engage with the person. A person that seems cooperative would attract to himself the engagement of others, thus forming cooperative relationships faster and easier than the cooperative person who looks domineering. If you act cooperatively, its advantageous to seem cooperative.

Seeming cooperative when cooperative is advantgeous over seeming cooperative when dominant

Seeming cooperative would generally speaking, on average, decrease other people’s willingness to yield to unfair propositions made by the person. A cooperative appearance would attract others to engage with a person, but if he acts domineering in response to their approach they’d feel like they had gotten the wrong address and gradually disengage. The domineering person, on the other hand, would not get what he asked for, and, worse still, would get less than what he would have gotten had he made a cooperative approach, since the others reject him. If you seem cooperative, its advantageous to act cooperatively.

Cooperativity vs. Dominance

This goes beyond the question of the association between testosterone (dominance) and masculine faces, but the above calls for the missing comparison in order to complete the picture, namely, a comparison between being and seeming cooperative and being and seeming dominant. However, while the former comparsions were between a “stable” and an “unstable” strategy, here we want to compare between two “stable” strategies, and as for the answer which is advantageous we must reply that “it depends”. For one thing, it depends on the strategy employed by others, in a manner that is akin to the negative frequncy-depended selection that was mentioned above. In tribal societies, as well as among kin and to an extent friends in societies with a central authority, if everybody else employs a “cooperative strategy” it would be advantageous to be dominating. If everyone else is a pushover, much is to be gained by being a bully, as the latter will never face resistence and will thus reap much benefit for himself. On the other hand, if everyone else is non-cooperative, it might be advantageous to be cooperative; it is better to get the shorter end than getting no stick at all. While the rest of (non-)society keeps on fighting with each other, the submissive person gets a little bit here and there by yielding instead of promoting conflict to the end result that ––– all else being equal ––– he has a little more than average.

In the modern world, however, we interact with many people who are complete strangers, and our interaction is affected to a very large extent by existing institutions, such as the government, police, law, economic system and so on, which altogether shape how adaptive any one strategy (cooperation or dominance) is. It would be futile for a person to try and squeeze a lower price for cucumbers out of a cashier in a chain-supermarket. Any kind of aggression that would have any effect is a robbery, and that would provoke a response from the police and therehby very likely a costly outcome that would greatly exceed what had been gained with violence. In general, law and the police together discourage the utilization of dominance for the purprose of taking advantage of others in interpersonal interactions, and even “discourage the appearance” of being dominant as this attracts the attention of the arm of the law. On the other hand, a lassez-faire market economy encourages dominance in vertical relationships from above down; the system leads all economic activity towards an ever increasing productive efficiency which gets the cooperative non-squeezers out of competition.

Attractiong to dominance

I used the expression “intrasexual communication” above as a reference to the existing hypothesis that facial masculinity is part of an intrasexual competition. However, the dominance of a face is of course also communicated to members of the other sex. Moreover, a dominant face could be selected for, that is, it could be affected by a process of sexual selection, though here this terminology becomes unhelpful.
As mentioned above, whether being cooperative or dominant is more adaptive depends on various environmental (social and otherwise) variables. The appearnace and behaviour on the cooperaton/submission-aggression/dominance spectrum affects interaction both with potential mates and potential competitors, e.g. other males, though this competition is not exclusively over mates but also over other resources, which makes it perhaps more accurate to say that this trait undergoes social selection. Given a degree of monogamy in humans, the “choice of strategy” of a mate is relevant when mating (1) to the degree that it is heritable, (2) in the way that it affects resource acquistion and (3) distribution between partners and their children.

Some evidence for the above can be seen in one study that found a strong correlation between a preference of masculine faces in mates by women and the gini coefficient of the country the women were from.34 That is, in countries with greater economic inequality women have a stronger preference for masculine-faced mates.
This makes sense from a strategic point of view. The stronger the pattern of inequality in a society is, the more there is to gain by being aggressive and the more there is to lose by being complacently agreeable; cooperating is unfortunately remunerated by being taken advantage of. It therefore would benefit a woman to couple herself with a man who knows how to advance himself in society and thereby provide resources, for her and her children’s sake. On the other hand, in a country with greater economic equality there would be less variance in how much a husband earns, and so what determines how much resources reach the wife and children is his degree of cooperativity.35 Moreover, it might be the case that an increased dominance would not be viewed positively in an egalitarian society, thus decreasing rather than increasing how much a man can gain in resources. In either socioeconomic scenario the assumption is that women more or less correctly perceive the degree of economic inequality in the country and adjust their behaviour accordingly.36 It is therefore that the intrasexual male-male (signaling) competition becomes an aspect, via monogamy, of intersexual male-female (male to female signaling) competition. Without monogamy males would be solely selected for their (presumably heritable) ability to survive in the social environment, such as their ability to seize resources at the expense of other conspecifics, independently of how they might have shared their resources had they stayed, and without the male-male competition males would have been selected only on the amount of investment they were expected to bestow upon the family (which does not necessarily mean selecting the one who maximises investment; see here). In either case, of course, the mate is also judged based on “general fitness”, the ability to survive in the non-social environement.

Face Averageness

What I’d claim is that the averaged face is more attractive because it fits better one’s internal schema of what a concon looks like. When selecting a mate or even being merely attracted to another concon one relies on more than a face, but when only a face is available one is attracted to the degree that the face looks like a member of the opposite sex (or of the same sex when one is attracted to these). In other words, one is attracted to a face to the degree that one recognizes that face as belonging to the opposite sex. Perhaps, even, to the degree that it does not look like the face of a member of the same sex while still looking like a face of a human. And to put it in the terms formerly laid, to the degree that the face “solved” the problem of recognition.
Why humans rely (also) on faces to distinguish the sex of other humans is a separate question. I can hypothesize different reasons, such as the loss of perception acuity of cues such as olfactory ones, or females evolving to have more infantile features37 in order to look younger and therefore more fertile, altogether evolving a dimorphism of the face that one could rely on. It could also have to do with humans being social creatures with an elaborate interpersonal communication that utilizes the face as a central medium: the eyes are an important source of information, and while body movements are too, the signals of body language are large, and one can follow their expressiveness without directing attention away from the eyes. Attention on the face (via the eyes?) allowed for a communication to develop which relied on minute changes of the face, further making the face an attention-worthy locus of a conspecific body.38 This necessitated the development of a perceptive faculty that could detect and distinguish these minute dynamic differences, which had to rely on the evolution of a precise perception of static facial features, which allowed us humans to, among other things, recognize each other through this medium.39 This acuity could have been then leveraged for extraction of information about conspecifics through their face.40 That information could have been related to fecundity and sexual relation, in turn creating a sexually selective pressure that shaped the faces of both sexes in their respective stereotypical directions, leading to dimorphism.

What I hypothesis the case to be is that humans have an innate (“geneticlaly encoded”) but rough visual schema of the human face, which allows them to correctly direct their attention to face-like looking things shortly after birth. I think that that is the case is rather well supported by the fact of the human tendency to “see faces” where they are not. Running an internet search for “things that look like faces” says it all; we merey require two dots above a horizontal line or blob to “see a face”. However, what faces “really” look like is learned through exposure throughout a person’s life. That is, a basic schema orients a person’s attention, and the attention leads to the learning of what a person’s face looks like. This learning, through some averaging, creates a detailed schema that allows a person to differentiate humans from non-humans, kin from non-kin, and males from females.41 It’s simpler to have this kind of information learned rather than being “hard coded”: it’s more efficient, since morphologically-evolved changes (of others) do not require a repsonsive evolution of the perceptual faculties, and it’s more effective because a species does not need to go through the failed experimentations of persons being born with “the wrong facial detailed schemas”, that is, detailed schemas that do not match the “facial environment” she is born into. Had such detailed schemas innate and not learned, it would have been less likely that the simple schema (two dots and a line) would persevere. Interestingly enough, there were studies that found that chimpanzees are able to learn, through exposure, to differentiate individual human faces.42 Moreover, there’s some research that suggests that humans are not the only species that can read emotions off human faces. For example, one paper showed rather convincingly that dogs (mainly Border Collies) can distinguish between happy and angry human faces.43 Conversely, humans rely on the same auditory features of vocal expressions to assess the intent of the calls of humans and dogs.44

This idea that preference for regular –– averaged, symmetrical – faces is due to the perceptional faculties’ design rather than an evolution responding to an adaptive advantage accrued through mating with developmentally-stable concons is not new; studies have suggested animals would prefer a novel averaged stimulus over non-novel non-averaged stimuli (as well as other novel stimuli).45 It is important to note that as far as there is a preference to faces with low “flactuating symmetry”, it is a learned rather than an innate preference. That is, the symmetry to which there is an emergent preference is a result of averaging of faces one has been exposed to. Therefore the paper, for example, that found no preference for symmetrical over non-symmetrical upturned faces,46 constitutes no evidence against this hypothesis (as the upturned faces constitute a set of unfamiliar stimuli). It is also important to note that for this all to work, individuals need to be able to correctly differentiate conspecifics from non-conspecifics, as to not average the latter into the image of the former. Other than relying on cues from other faculties (auditory, olfactory, when aveaging visual stimuli), supposedly one might not consider individuals whose appaerance is far enough from the existing image of what a conspecific looks like.
How could one disassociate the percetpual hypothesis from the developmental stability one? On the one hand, one could design an experiment where an animal, which recognizes conspecifics visually, is exposed only to one-sided asymmetrical conspecifics, and see how it affects its mate selection. It seems rather difficult to pull off. Perhaps one could apply colored stickers on one side of others’ bodies, but for this experient one would have to have the assumption that these colorations are attended to. One the other hand, one could look whether there really is a correlation between health and face averageness. Had there been one it would not have provided evidence for or against either of these two alternatives, since the preference might still be a product of the perceptional faculties rather than of selection,47 but a lack of such a correlation would have been a strong evidence against the developmental stability hypothesis.

First, let’s consider a paper that sought to show a correlation between health and face normality. A 2000 paper by Rhodes et al.22 used black and white photographs of 17 year old individuals born between 1920 and 1929 in the USA whose health records were available and who were judged for asymmetry and non-avergeness (“distinctiveness”, in the study described to the raters as “the ease with which a face could be picked out of a crowd”) by contemporary subjects, as well as measured for asymmetry based on geometrical feautures of the pictures. While their report mentions some evidence for a correlation between ill-health and rated non-avergeness, their findings are not so convincing. First, their statistics are rather sloppy. They mention a “marginal correlation between midadult health and measured facial asymmetry at 17 in females”. They add that this should be interpreted with caution given the small sample size, but they ignore the glaring fact that the p value for the correlation was p < 0.1, found in two statistics out of 24 statistics derived for “measured asymmetry”. That is, at a rate of 2/24 = 0.083 < 0.1. Furthermore, given that in total they looked at 72 statistics, the three p < 0.01 and one p < 0.001 statistics they are found are somewhat unremarkable.
These significant statistics were found for a correlation between childhood ill-health and current (17 years old) rated non-averageness in males, and between adolescent and current ill-health and current rated non-averageness in females. The fact that there are gender differences in these correlations over developmental times is very suspicious. Perhaps something in development would give rise to different correations between face avergeness at 17 and health at different periods in life, but that it is variable between the two genders is extremely peculiar. Could it be explained?
Let us assume that the face is generally planned to develop symmetrically (further discussed below). We could make an assumption but this is almost a corollary of a definition: on average faces are planned to develop in a typical, that is, average, non-distinct, kind of way. We’ll assume that a failure to develop a averageness is a failure to develop “as planned”, and that being ill is a disturbance of the proper functioning of the body which might then lead to disturbances in proper development and therefore in developed averageness. How do we explain correlation between childhood ill-health and non-averageness at 17 (as seen in males)? The skull and face are formed in childhood so perhaps the “scars of development” at that time are strongly engraved into the shape of the face such that deviations from the plan “stick” onto adulthood, while disturbances later in life are less critical since the face had already formed. But, then, why would the females not exhibit such a correlation too? One could have explained this difference if, for example, the faces of females underwent a strong development later in life (adolescence and late-adolescence), that is, a stronger development than that which male faces undergo, but the reverse is true: female faces experience a decline in growth at 13 and stop growing at 15, while males exepience an extended facial development that starts at pubetry and continues until at least 18.37
On the other hand, a paper by Pound et al.48 with a large sample size (n=4732) of South West England individuals and a well conducted statistical analysis, found no correlation between fluctuating symmetry and a myriad of health conditions.49 They suggested that the attraction to low-FA faces might be an overgeneralization of an adaptation that avoided mating with individuals with gross facial asymmetries. That is, small fluctuations are irrelevant to health but great fluctuations are, and the avoidance of the latter led to the avoidance of the former. I’d in turn say that the avoidance of gross asymmetries in mates is an overgeneralization of the avoidance of mating with individuals of others species.

  • the recognition was earlier suggested
  • However, it concentrated on the symmetry of stimulus, however:
  • Can one decouple these?
  • symmetry not associated with health.
  • brain development is not symmetrical, and brain developmetn affects the face. (fluctuatings vs directional assymetry). THe autistic faces

  • for fluctuating symmetry to indicate bad development, symmetry (as a whole) had to first evolve anyway Why do we have symmetry? symmetrical functionality But the shape/morphology of the brain, like other oragns, is not interfacting the outside (though the constraints on it ARE, such as the room it has). Brain affects face morphology, so FA/DA that is adaptive could evolve (autistic faces). Assmetry of external organs (hands, legs) could evolve becuase the brain is asymmetrical and employs them differently (perhaps the asymmetry is “phenotypical only”; are lefties asymmetrical in the same way?).

«also: recognizing faces of other animals. Recognizing expressinos of other animals: apes(?), dogs. Dogs recognizing our expressions.»```` «allowing us to quickly discern and decode the facial expresions of groups we had never encountered, even of creatuers we havn’t seen before?» «how sexual orientation arises? The notion of the gender to be attracted to»

«mention the other studies that postulated the recognition aspect, but criticize their assumption that it is due to symmetrical input being easier to process. And, indeed, that paper about the upside down faces»

« average because of developmental stability or because of a schema of an idea? –– decouple. Maybe seek some inspiration from the idea of the Platonic idelas. Is average really always better? no. Things about objects, tools, averageness there. Mention how extremes can be selected for (dimorphism) while averageness is selected for at the saime time. (one answer: the extreme is a product of seeking averageness elesewhere. For example, one can have an idea of the averagped child, having a schema of youth. Then females are selected for for looking young, which creates an “extreme selection” because they are not necessarily young. Nonetheless, the “direction” in which there’s a selectino is within the repertoire of human morphology.»

Dimorphism in the body might stem from exaggeration of functional differences and from intrasexual competition. A wider hip might be necessary for women especially in order to accommodate the big head of human newborns (the bottleneck of delivery as anyone who ever tried to move through a school fence even as a child or adolescent –– with smaller head to body ratio –– knows), but sex-specific accumulation of body fat in that area is presumably not “functional” but aimed to increase their perception (by others) as female, or at least avoiding decreasing that perception. Stronger skeletal muscles and, perhaps?, wider-shoulders might assist males if they often engage in physical fights between each other, but it also makes them, in turn, be recognized as such, males, to other humans. (voices): https://www.sciencedirect.com/science/article/pii/S0960982209020491

Alternative Sexual Selection theories

I’d like to hereby criticize a few existing theories. I quote some definitions from a 2008 paper:

Sexual conflict: Sexual conflict refers to intersexual conflict. It describes the diverging interests in males and females to optimize their fitness. From the point of view of one sex, this is done best if the mate cares for the young thus freeing resources (e.g., time and energy) that can be invested in additional offspring. Regarding to polygynous mating systems, sexual conflict means the optimization of male reproductive success by having mated with multiple females although reproductive success of a polygynously mated female is reduced.
Good genes: Good genes refer to the assumption of an additive indirect genetic benefit that increases offspring quality. Offspring quality, that is, viability, leads to a compensation of any inferior direct reproductive success, that is, fewer offspring.
Fisherian runaway selection: Fisherian runaway selection assumes indirect genetic benefits in mating decisions. This process assumes that sexual selection for a specific trait was at first correlated with a small increase in viability. During evolution, the female preference for this trait becomes exaggerated while the good genes effect loses its importance. At the end, sexual selection is driven only by the attractiveness of this trait and not by any additive genetic effect that is relevant for natural selection.
Sexy son hypothesis: The sexy son hypothesis (SSH) is closely related to the good genes assumption and the Fisherian runaway selection process. SSH, too, assumes indirect genetic benefits that are able to compensate any inferior direct reproductive success, that is, fewer offspring. The main difference between good genes and SSH is that SSH assumes an indirect effect due to the attractiveness of the sons whereas good genes focus on viability in sons and daughters. However, attractiveness is not specified and can be every trait that increases a male’s probability to become polygynous.
Compatible genes: Compatible genes also belong to indirect genetic benefits that increase the genetic quality of offspring. Whereas good genes generally lead to positive effects, compatible genes are beneficial only for specific individuals. That is, a positive effect depends on the interplay of the individual genetic architecture of both mates.50

Regarding the Fisherian runaway selection. As stated above, my own theory is that traits which are sexually dimorphic and seem maladaptive from a natural selection point of view are traits that aim to solve the problem of mate location. But what about Fisher’s idea? The idea is that first there was the appearance of a trait T which was adaptive. At some point it got to be recognized by females, a recognition that was adaptive because they could choose mates that would lead to more adaptive offspring (all else being equal; presumably how fit a male is depends on more than a single trait). Because the trait was now “recognized as adaptive”, that is, it became sexually attractive, there was evolutionary pressure to exaggerate it in order to attract mates, only this exaggeration loses the benefit of the original trait.
I’d expect a stabilization of a trait. That is, the “runaway” part seem to me unsound. Imagine a population where virtually all males exhibit trait T, and that many or all have had this trait “run away”, that is, it surpassed the point in which it is adaptive and either lost its adaptive power or even became maladaptive, that is, worst than not having the trait T at all. We could expect –– by the very same theory –– that a male that exhibited a diminished version of the trait (T-), or even not exhibit the trait at all (T0), would start the same process but “in the opposite direction”. His offspring would be more adaptive than those of the T males, and those females who would recognize that would have their offspring better adapted, and so on until the trait would “run away” back. Or, perhaps more likely, the trait would oscillate until its optimal degree becomes the average phenotype of the population. Both “more than” and “less than” are really qualitatively symmetrical around the optimum. The Fisherian runaway principle is not consistent with itself.

The sexy son hypothesis is much more problematic, partially because it seems like the concept has evolved in meaning since its inception. The term first appeared on a 1979 paper by Partick J. Weatherhead and Raleigh J. Robertson, Offspring quality and the polygyny threshold: “the sexy son hypothesis”. They discuss bird populations and put forward a mathematical model. The premise is that there are males who are monogamous and males who are polygamous. The behaviour of the males is heritable, i.e. sons of polygamous males are polygamous, likewise for monogamous fathers and sons. Females who mate with monogamous males have more offspring than those who mate with polygamous males (thanks to paternal parental support), but polygamous males have more offspring than monogamous males. Doing some algebra they conclude that even though on the short-term the mates of polygamous males suffer in terms of lower offspring number, in the long term this coupling is advantageous to them because their sons are polygamous and so will have more offspring –– the mate’s grandchildren –– hence the “sexy sons”. The problem with the model is that it doesn’t hold water. The math is wrong.51

However, the sexy son hypothesis is often evoked by saying that sometimes females would prefer an attractive male that would not invest in the offspring over a less attractive male who would, because their offspring would likely to have sexy sons which in turn would have, being promiscuous, a large number of offspring that would compensate for the loss. That is, they’d have less children but more grandchildren. But as Huk and Winkel block-quoted above mention, often it is not specified what attractiveness is, and it really makes the model rather hollow. You might as well say “magic”. Why are they attractive? The words of the evokers often make it sound like the trait is arbitrary, that is, it is desirable and attractive because it’s attractive, it’s attractive because others find it attractive so the sons would be attractive and sought after. As if all females colluded and decided on a standard by which to judge males. But this is, of course, nonsense. One could imagine some evolutionary glitch that would make females be attracted to an “arbitrary” trait, but that would be the evolutionary equivalent of an economic-bubble, and we know what happens to economic-bubbles in the long run, which is the only run that evolution cares about.52

I’d like to propose a variation on the hypothesis. I could have called it the “selfish son hypothesis” had it not had the same acronnymm, but then again “selfish” is also misleading. It could be called promiscuous son in times of plenty hypothesis (PSTPH), though it doesn’t quite rolls on one’s tongue. To use the same register as in the original, I’d call it the douchy son hypothesis (DSH). First, it assumes that females are strongly limited in the number of offspring they can produce at any given time period. That is, we are concerned here with animals that gestate or lay eggs that are of a size comperable to the size of the female, as oppose to animals that spawn in the hunders or thousands. Second, it assumes that males’ rearing style (monogamous, non-monogamous) is heritable. The hypothesis is that if the environment is “easy”, that is, not harsh, with plenty of availabe food and little predative danger, females would prefer as mates males who are promiscuous because, again, they would then have more grandchildren. If the mother can bring her offspring on her own, the father’s lingerilng presence confers no advantage. It could confer a surplus of time, but the mother has little to do with it. It could have spared her energy, but since energy is freely avaiable, nothing is really spared. Since the reasing style is heritable, mother of sons whose father is monogamous would at most mate with one female. However, if the female mates with a male who is promiscous, that is, one that would go and seek other females to mate with after he mates with her, her sons (which would reach maturity at the same rate as if the father stuck around, given the giving environment) would likewise be promiscuous and would mate, on average, with more females than the sons she could have had with a monogamous father, and therefore she would have more grandchildren. Therefore, in such conditions, if females could at all discern “monogamous” males from “promiscuous” males, it would benefit them to reject monogamous males and mate only with males who are promiscuos.

Another suggested principle is the handicap theory of Amotz Zahavi. To put it in his own words,

My interpretation of sexual selection implies that sexual selection is effective only by selecting a character which lowers the survival of the individual. [An argument along this line was given by Emlen (1973) among several other arguments.] It is possible to consider the handicap as a kind of a test imposed on the individual. An individual with a well developed sexually selected character, is an individual which has survived a test. A female which could discriminate a male possessing a sexually selected character, from one without it, can discriminate between a male which has passed a test and one which has not been tested.53

That is, a handicapped animal, usually male, proves through his displayed handicap (bright and large plumage, antlers &c) that it had managed to survive despite the handicap it has. The handicap is a sort of compromise; on the part of the females because they have to choose a mate who is disadvantaged (by the handicap) in order to be sure that he is otherwise “fit”, and on the part of the males as they have to handicap themselves in order to advertise their fitness. I must say that the theory is rather attractive, and that the paper presenting it is generally well put. However, it has some problems.
Shortly after the Zahavi paper was published, a paper by John Maynard Smith54 was published which set to make a mathematical model out of Zahavi’s model, and found it to be implausible.55 Though I think Smith might have incorporated erroneous assumptions into the model which left me less than convinced by it, it’s a good step in the direction of investigating the plausibility of the hypothesis, and I’d like to rerun such a model with the corrections I think it deserves.
That being said, I don’t imagine the handicap principle would emerge triumphant. As opposed to Smith’s model where you had a genotype that led to females mating only with handicapped males and another which led females mate randomly, imagine the genotype separated females to those who mated only with handicapped males and to those who mated only with non-handicapped males. Then we’d have two separate populations who only interbreed, but with some trickling of offspring from one group to the other (though I suppose that over time this crossing would go to zero). All else being equal, it seems clear that the non-handicapped population would grow faster ––– assuming there’s no “population size cap” (rendered by scarcity of resources or predation, or both). That is, on average, members of the non-handicap population beget more offspring that reach maturity than those of the handicapped population. That is, the former population is fitter. If we introduce a new female that can freely choose which population to belong to, she’d choose the non-handicapped one. Same with a newly introduced male. Which brings me to the one graph presented in the Zahavi paper:

Zahavi 1975, figure 1

We have here an abstraction, a quantification of traits of animals, that is, a mapping from an animal wits its set of attributes to a number that represents its quality, its “fitness”. That quality is on the y-axis, while the degree of the handicapped trait runs on the x-axis from the left where it’s at its ideal natural-selection-wise. We have two curves, representing respectively the “worst” and “best” members of the species as a function of handicap degree, and an additional curve that is simply the averaged quality of these two curves. There are a few problems with this graph.
Presumably the quality measured on the y-axis is an “exclusive quality”, that is, the quality of the animals without including the handicap, which, as Zahavi mentions, is a compromise and which makes the animals worse off in terms of surviving. In this case the lower curve should indeed go up: animals that otherwise have already a not such a great genotype who in addition grow the handicapping trait would simply not survive, leaving the “last place” to animals of higher quality. The top curve of “highest quality”, however, should be flat. Presumably an animal can both have a very fit genotype AND grow the handicap. Unless, that is, we think of it in terms of the phenotype of the creature and only include part of the handicap on the y-axis. For example, while an animal of the highest-quality can grow or not grow a handicapping trait (long tail, large antlers), there’s an energy cost that makes it impossible for it to be as fit as it could be without the handicap. Perhaps one cannot both grow and maintain strong legs and bones, efficient lungs and heart, keen perception and so on AND put the resources into growing the handicap. Notice, however, that the decline of the top curve would affect the slope of the “average quality” curve”. Either way, a flat top curve would still keep the average curve rising as a function of the handicap degree, which is Zahavi’s main point in presenting the graph: females that choose more handicapped males would be going for a higher quality mate on average. However, it’s important to put this in the right context; as Smith briefly mentioned in the paper above, the inheritance of the traits is important, and Zahavi doesn’t speak about it.
That the averaged curve in this graph goes up would be relevant only if (1) the traits responsible for the high quality of the male are heritable, and, in particular, heritable by the daughters, and (2) the daughters do not inherit the handicap. Both of these are very likely, but then we have to add that the incline of the average curve is only relevant as far as the daughters are concerned. Presumably the sons would inherit the handicap as well, meaning that the female is choosing “worse excepted sons”. She might have as well chosen a male with crooked legs and inborn blindness.56 The graph we would care about when we consider the sons is with an “inclusive quality” on the y-axis, that is, a measure that captures the total natural-selection-relevance, that is, a measure of the fitness that takes into consideration the handicap. In that case, the curves would look different. The top curve would indeed decline–– the otherwise best animals get hindered by the additional handicap, making it more difficult for them to survive. They lose fitness. The bottom curve, however, would be flat, assuming a “survival fitness-threshold”; if your fitness score is below that threshold you are very likely to not survive into maturity. Animals of low quality who had also grown horns would simply not survive, but animals that are just fit enough to make it with their handicap would be just as good at survival as the animals of lower quality without the horn, and hence the flat curve of “worst quality”. In this case, of course, the “average quality” would decline as a function of handicap degree, in which case the females would get the best mates, on average, by mating with males without the handicap.

At the end, what the handicap-principle suggests is that given female choice, as far as discernible traits go (whether visible, smelled, audiable..), males would tend to evolve them as suboptimally as possible without killing themselves, thus advertising how fit they are otherwise (in non-discernible ways). But we don’t see dimorphism that leads males to have crooked legs, asymmetrical wings, maladaptive mouths, smell that attracts predators and so on. Instead, I claim, these traits that puzzled Darwin and many after him are functional, not dysfunctional. Plumage, as I wrote before, is used to solve the location and recognition problem. I want hereby to address some points from Zahavi’s paper:

It is probably more difficult to discriminate quality among mates with cryptic plumage.

I don’t see it as the case. A plumage is “cryptic” as far as it blends in with the environment, but is essentially not any different from other plumage. A bird of paradise might be cryptic inside a busy neon-light district.

Species which have environmental conditions allowing for prolonged periods of pair formation, or others which cannot put males to a high predation risk probably, choose such a strategy [of cryptic plumage]. This may explain Lein’s (1973) finding that monomorphic species of warblers take longer to pair than sexually dimorphic species with colourful male plumage. This may be the reason why northern duck species, whose short breeding season demands a short period of pair formation, evolved striking male plumage. Where time for breeding is short and where males do not participate as much in parental care, males evolve the colourful plumage as a result of female preference. The male’s colourful plumage then serves as a mark of quality and helps females choose good quality males.

My answer to this, of course, is that the shorter the breeding time, the greater the urgency of the solution of the location problem is. If everyone is cryptic then some might not find a mate within a proscribed amount of time. With female choice, if you are a male, by making yourself colorful you guarantee that you would be found. Zahavi tries here a sleight of hand and lump several things together. He wrote “Where time for breeding is short and where males do not participate as much in parental care”. It is the latter, the lack of paternal care, that gives rise to female choice and therefore to the colorful plumage of males. Had this plumage followed the handicap-principle the “time for breeding” should have no effect whatsoever on the dimorphism.

Zahavi also mentions antlers. While not the first to attest the usefulness of antlers, one 2018 paper by Metz et al57 exhibits several points nicely. First, antlers are clearly serving a protective function against predators. As opposed to horns, antlers are temporary structures and are shed and regrown. Among elks, antlered males (as opposed to those who had shed them) were less likely to be attacked by wolves, and less likely to be killed by them. Second, big strong antlers are evidence for their carrier’s fitness, but in a way that is completely opposite to Zahavi’s model. Elks shed their antlers annually between breeding seasons, but not immediately after one –– a further evidence that they are not only as good as female-magnets; they retain them for up to 6 months after their rut. Those who shed their antlers earlier increase their risk of predation, but, on the other hand, since they have more time to regrow their antlers, they would have bigger antlers by the time of the next breeding season. Metz et al found out that early antler shedders were more healthy and fit than those who did so later on. This makes sense: being fit these males have a chance to survive despite being without antlers; presumably the not so fit males, had they shed their antlers early on, would not have survived confrontation with wolves, while the fit ones are able to make up for their lack of weapons with their vigour. It then follows that the bigger antlers of the next mating season are a direct and honest evidence of the fitness of their carriers. But it is so not because the antlers are a handicap as Zahavi suggested, but, on the very contrary, because they are an asset. The bigger antlers are evidence that their carriers got rid of their previous set earlier, attracting a disproportional attention from predators. And, third, elks do use the antlers during male-male competition (for females), and so the securing of females comes about through a functional utilization of the antlers, rather than them standing for a conspicuous handicap. If elks could shoot down rivals with eye-lasers they would have done it and gained all the ladies, even if the latter couldn’t detect their weaponry. In short, Zahavi’s handicap-principle certainly does not apply to elks, and probably not to other antler or horn wearing animals.


  1. There are theories that seek to put under one principle all of the fundamental forces, so called Grand Unified Theories. Whether they succeed or not, that it is a major challenge suggests that they are distinct in a meaningful way. Either way, I hope this is not much to detract from the analogy. 

  2. Thinking about this I constructed a little “fecundity payoff table”, not unlike the table used to discuss the prisoner’s dillema. There are two types of members, one that puts more investment into the offspring, and one that puts less. For simplicity I thought of these as females and males, and had the following table:

    \ f m
    f 10/20 \ 10/20 4/20 \ 4/1
    m 4/1 \ 4/20 0.1/1 \ 0.1/1

    Not the best formatted table, but the idea is this. Fs put investment into the progeny, which leads to the greatest litter of 10, every 20 time units. When an m mates with an f, he puts minimal investment (one time unit) while she invests just as much, 20 units of time. The litter is 20% less than half of the litter of fxf mating, 4. When ms mate they have merely a single viable offspring every 10 “pregnancies”. Therefore, on average, the different copulations have the following number of offspring per unit of time (from the perspective of the capital letters):
    F x f: 10/20 = 0.5
    F x m: 4/20 = 0.2
    M x f: 4/1 = 4.0
    M x m: 0.1/1 = 0.1
    As you can see, the greatest number of offspring is seen by a male mating with a female, 4 per unit of time, while the lowest is seen by a male mating with another male.
    This is not something I originally considered and I don’t know what is there to be made of it yet, but an FxF pregnancy happens to be the most efficient one. If we look at number of units of time invested on each offspring, we get the following numbers for the three types of pregnancies:
    FF: 40/10 = 4.0
    FM: 21/4 = 5.25
    MM: 2/0.1 = 20.0

    I was curious to see how such a system would behave, so I programmed a simple simulation. My setup was as follows: at time zero there are 10 males and 400 females. Mortality rate is 1/80, that is, every time unit about 1/80 of the population dies. The 20 units of time necessary for the females were broken up int he following way: they “gestated” for 16 time units, and needed 4 units of time before mating again. A pregnancy between males always produced males, a pregnancy between females always produces females, and a pregnancy between a female and a male produced 10 females and 10 males.
    At every unit of time each member that is free to mate (females who are not gestating and are not in the inter-pregnancy period, and all males) mates with another member “randomly”. That is, each such member gets a mate, and which type the other member is depends on the proportion of males and females in the population.
    The results were pretty much as I had expected. I hadn’t really thought about the dynamic aspects of this system, but I think that if I had thought about how my results would look like, I would have expected the proportion of males to grow until it reaches some equilibrium, and then stop. Instead, what we have is a growth of the male frequency which then diminishes to a steady equilibrium level (this is how I described it in the “main text”, but I did so only for the sake of clarity), and oscillations all throughout. In other words, the proportion of males first “overshoots”.
    male proportion
    The same can be seen, however, when the initial proportions are reversed, and we start with 400 males and 20 females (one “per state”). The proportion of males falls down to an unstable dynamic equilibrium, and after a while longer drops to oscillate around the same value as in the first scenario (notice that the values on the y axis are different:
    male proportion


    The ratio between the “gestation time” and “inter-pregnancy” time had also an effect. If you wonder what difference it makes, then it is this one: while either way males mate every unit of time and females mate every 20 units of time, the gestation period sets how long it takes from begetting until the introduction of new members into the population (the offspring). For simplicity’s sake, all offspring are born mature, only that newborn females must wait the “inter-pregnancy” period before conceiving. This means that, really, it affects the system only by affecting the number of males; since newborn females must wait before waiting, ““receptive females”” are introduced after the same interval post parents copulation, whether the gestation was short or long. On the other hand, since males can mate immediately, the shorter the gestation time is, the quicker new males who can reproduce are introduced.
    If gestation was shortened to one time period (at the expense of elongating the inter-pregnancy time to 19 units) we get roughly the same result, only the magnitudes are different and the oscillation has a different shape. On the other hand, setting gestation to 19 units of time and the inter-pregnancy interval to 1 unit (at which case new sexually active males, born out of a FxM pregnancy, are introduced into the system at the same speed at females), we get something different: the growth in male proportion in the beginning is part of an oscillation, while generally the trend is for the oscillation to dampen such that the ratio slowly approaches zero. The growth in this ratio, however, is not due to the increase in numbers of males, but the decrease in numbers of females.
    Overall perhaps a better model can be made by adding a carrying capacity, to it, that is, have a factor that limits the growth of the population, for example, by having the death rate increase as the total population size increases. 

  3. Predators and their prey can have different perceptional faculties, and other theories regarding “sexually-selected” traits make different prediction. What I want to stress is that the saliency-increasing traits are conspicuous to conspecifics and not to predators, which is what, for example, the handicap principle (discussed below) predicts. Of course the trait must be to some degree perceptible to conspecifics, otherwise they cannot make mate-selection based on it. But I claim that the inverse is not true, and that a trait that increases conspicuousness towards conspecifics and not to predators would still be selected for.
    The case that could have properly spoke against my own theory but in favour of the handicap principle might be so artificial that it would not be found: an animal might have some trait that is observable by conspecifics but is much more salient to predators. Imagine seeing but deaf animals with a hearing predators. Males could have evolved bells on their tails. These would be perceived by conspecifics upon a meeting but would otherwise not be detected by then. Predators, on the other hand, could hear them from afar whenever they moved, so having those bells could be an “honest signal” of being capable of evading predators and nothing else ––– or at least until some male evolve a tail that looks like the noisy ones but it actually silent. The difference in perception could be not so absolute but simply rely on differences of acuity, for example if males employ a scent that is detectable by females but is significantly better detected by predators, but one would imagine that detecting the scent would be adaptive for this species such that the females would evolve better acuity. However, it would also be advantageous for the predators to detect that smell so perhaps they would also have their acuity increased and faster than those of females. 

  4. Sexual dimorphism and directional sexual selection on aposematic signals in a poison frog, Martine E. Maan and Molly E. Cummings, 2009. 

  5. though the one population where males were brighter was the only population where the difference was statistically significant. That being said, there were still three populations with no “significant” sexual dimorphism.
    The paper however differentiated between “brightness contrast” and “color contrast”, and in one population the females had a statistically significant greater color contrast. 

  6. Menstrual cycle alterns face preference, I.S.Penton-Voak, D.I.Perrett, D.L.Castles, T.Kobayashi, D.M.Burt, L.K.Murray and R.Minamisawa, 1999. 

  7. Context-dependent preferences for facial dimorphism in a rural Malaysian population, Isabel Scotta, Viren Swamib, Steven C. Josephsonc and Ian S. Penton-Voaka, 2008. 

  8. Euphemisms are ambiguous as a language, but the context of their employment disambiguates them so they point to a specific meaning. This is achieved by using metaphorical langauge where the literal meaning of the expression is meaningless in the given context, and the suspicious hearers would look for analogy in the realms that are rarely spoken about directly and thus decipher the reference. Yet, despite referring to something accurately, the indirectness by which euphemisms do so makes them less harsh. However, one ostensibely cannot employ them in such research: first, euphemisms are informal as a language and therefore might undermine the gravity which researchers undoubtedly ascribe to their work. Second, euphemisms lose their mitigating effect when written, since the latter depends on the quick rhythm of spoken language; on paper where a reader can stop and ponder it would either look like a cheap trick, or simply be cringy, and either way would no be taken very well. You know what I mean? 

  9. One paper mentioned after “short term relationship”, in parenthesis, ‘e.g., an “affair”’. It wasn’t clear to me whether this elucidation was also presented to the experiment subjects or not, but either way it doesn’t make the question any clearer. For one thing, “being an affair” alludes more to the relationship’s status within a socioeconomic context than it does to its duration. After all, some affairs can be long, longer than marriages, and even lifelong. 

  10. Menstrual Cycle and Facial Preferences Reconsidered, Christine R. Harris, 2011. 

  11. Effects of Menstrual Cycle Phase on Face Preferences, Benedict C. Jones, Lisa M. DeBruine, David I. Perrett, Anthony C. Little, David R. Feinberg and Miriam J. Law Smith, 2008. 

  12. Raised salivary testosterone in women is associated with increased attraction to masculine faces, L.L.M. Welling, B.C. Jones, L.M. DeBruine, C.A. Conway, M.J. Law Smith, A.C. Little,D.R. Feinberg, M.A. Sharpe and E.A.S. Al-Dujailif, 2007. 

  13. Likelihood of conception with a single act of intercourse: providingbenchmark rates for assessment of post-coital contraceptives, Allen J. Wilcox, David B. Dunson, Clarice R. Weinberg, James Trussell and Donna Day Baird, 2001 

  14. Salivary testosterone, cortisol, and progesterone: Two-week stability, interhormonecorrelations, and effects of time of day, menstrual cycle, and oral contraceptive useon steroid hormone levels, Scott H. Liening, Steven J. Stanton, Ekjyot K. Saini and Oliver C. Schultheiss, 2010. 

  15. Pituitary–Adrenal Hormones and Testosterone across the Menstrual Cycle in Women with Premenstrual Syndrome and Controls, Miki Bloch, Peter J. Schmidt, Tung-Ping Su, Marie B. Tobin, and David R. Rubinow. 1998. 

  16. Parasites, bright males, and the immunocompetence handicap Ivar Folstad and Andrew John Karter, 1992. 

  17. For example, by being independent of testosterone, or by being very sensitive to testosterone (small levels leading to a strong degree of masculine face development) but suppressed by estrogen (to avoid manifestations in females). 

  18. Genetic Factors That Increase Male Facial Masculinity Decrease Facial Attractiveness of Female Relatives Anthony J. Lee1, Dorian G. Mitchem, Margaret J. Wright, Nicholas G. Martin, Matthew C. Keller and Brendan P. Zietsch, 2013. 

  19. However, the 95% confidence interval for the correlation for non-identical male twins and siblings was around 0, which is odd and suspicious. 

  20. Testing the immunocompetence handicap hypothesis:a review of the evidence M. L. Roberts, K. L. Buchanan and M. R. Evans, 2004. 

  21. Stress, testosterone, and the immunoredistribution hypothesis Stanton Braude, Zuleyma Tang-Martinez and George T. Taylor, 1999.

    While Folstad and Karter’s hypothesis offered an explanation for higher parasite loads in males than in females, it has been used to explain both correlation and lack of correlation between testosterone and reduction in indices of immunity. Specifically, if males with high levels of testosterone have higher indices of immunity or lower parasite loads, the interpretation would be that those males have such high-quality immune systems that they can overcome the immunosuppression of testosterone (Zuk, 1996). On the other hand, if high-testosterone males have higher parasite loads, the interpretation would be that those males are of such high quality overall that they can display and attract females despite higher infection due to immunosuppression (Salvador et al., 1996; Weatherhead et al., 1993). And if no relationship is found between testosterone and parasite loads, the argument is that the high-quality males “are reliably signaling their resistance to parasites since they are still able to fend off parasites in the presence of high circulating levels of androgens” (Saino and Moller, 1994:1331). The invocation of the immunocompetence handicap to support such contradictory trends undermines the utility of the hypothesis.

  22. Do facial averageness and symmetry signal health?, Gillian Rhodes, Leslie A. Zebrowitz, Alison Clark, S. Michael Kalick, Amy Hightower and Ryan McKay, 2000.  2

  23. Infant Mortality in the United States Robert M. Woodbury, 1936. 

  24. The “passivity” of this activity might give us the idea that it is very different from what we commonly think of as communication, but really it is not much different. Both parties refrain from action in order to establish a timeframe within which information can be exchanged. They use this time to collect information about the body of the other, while adjusting their own stance in order to appear as intimidating as possible. 

  25. High salivary testosterone is linked to masculinemale facial appearance in humans, Ian S. Penton-Voak and Jennie Y. Chen, 2004.

    Another study, Second to fourth digit ratio, testosteroneand perceived male dominance, Nick Neave, Sarah Laing, Bernhard Fink and John T. Manning, 2003, found no such relationship. However, they didn’t mention collecting saliva samples at a speific time of the day, so intradiurnal intrapersonal variance in testosterone levels might have blurred interpersonal differences if the sampling time differed between subjects. They did find an anti-correlation between masculinity and dominance ratings of photographed faces and the second and fourth digit ratios of the photographed, the former being thought to be an (inverse) indicator of prenatal testosterone levels. 

  26. The relationship between testosterone and aggression:a meta-analysis, Angela S. Book, Katherine B. Starzyk and Vernon L. Quinsey, 2001. 

  27. Testosterone and cortisol jointly regulate dominance: Evidence for a dual-hormone hypothesis, Pranjal H. Mehta and Robert A. Josephs, 2010.

    More specifically, they found that this effect of testosterone ~~ dominance is modulated by cortisol, such that high cortisol level either block the effect or even reverse it. They seem to have found an important cofactor in the relationship between testosterone and dominance, the oversight of which might have led to ambivalent results in the past.s 

  28. Apologies. 

  29. This is of course why we would get candidates on democratic elections who advertise themselves as “strong leaders”. Their appeal is not that they would oppress the population once they are incumbent. Rather, the population, as constituters of the state, sees itself as an extention of the leader, and with a strong leader they could all together cooperate to deal with the problems of the day with the clout they deserve. 

  30. Simply a case of the so called Abilene Paradox 

  31. The starkest example I know of this is the horrific story of Steve Raucci, the head of a school maintenance department(!).

    This American Life, episode 419. From here 

  32. On the other hand, sometimes the option to stop an interaction in medias res is availabe. 

  33. The Brutal Elimination of a Rival Among Captive Male Chimpanzees, Frans B. M. de Waal, 1986.

    Intragroup Lethal Aggression in West African Chimpanzees (Pantroglodytesverus): Inferred Killing of a Former Alpha Male at Fongoli, Senegal, Jill D. Pruetz, Kelly Boyer Ontl, Elizabeth Cleaveland, Stacy Lindshield, Joshua Marshack and Erin G. Wessling, 2017. 

  34. National income inequality predicts women’s preferences for masculinized faces better than health does, Robert Brooks, Isabel M. Scott, Alexei A. Maklakov, Michael M. Kasumovic, Andrew P. Clark and Ian S. Penton-Voak, 2010.

    One reservation I’d have concerning this study is that the researchers whose data was used in this study didn’t seem to collect information about contraception usage. Hormonal contraceptives seem to affect facial-masculinity-preference among women, and the pattern of contraceptive methods usage varies greatly from country to country. As there’s publicly available data about he latter from the UN Department of Economic and Social Affairs, I have hopes to take a look at whether there are confounds to be found there, but I am yet to have done such an investigation. 

  35. One might wonder how gender gaps in economic opportunities and compensation would figure into this. When women have less potentcial for economic independence than men they have to financially rely on their partners to a larger degree, giving them less power in negotiating their relationship. In addition, it gives the financial standing of the mate a stronger relative importance among his attributes as the finance of the family rests to a greater degree on him as a provider rather than on the earnings of two adults (assuming a nuclear family).
    If in addition the gini coefficient is high (high inequality) I’d expect a stronger competition among women over hige earning (presumably dominant, on average) mates: males are the core providers and the amount of money they can bring in depends on their dominance, and as livelihood depends on it, other attributes become less important. However, if the gini coefficient is low, then I’d expect an even stronger preference for cooperative looking (less masculine faced) males than in societiies with greater gender financial equality. Males are the core providers but how much they earn varies less with their dominance. That means that what matters as far as provision goes is not so much what the mate earns, but how he distributes his earnings between himself and his family; presumably a more cooperative male would give more to his wife and children. 

  36. However, the assumption that people have an accurate sense of their country’s income distribution or their own relative position within this distribution seems to be quite wrong, as can be seen in Misperceiving Inequality, Vladimir Gimpelson and Daniel Treisman, 2015. However, as far as evolved strategy goes (or evolved development of strategy), one would assume that the mind became adapted to choosing a strategy within a small, comprehensible (and sensually experienced) group rather than reckon distribution within an abstract entity as the modern state. The figures in the paper refer to actual and stated perception of state wide inequality, but one can imagine that there is variability within the country as well. For example, it might be that the gini coefficint within one country is different within its big cities and within its rural communities. The country with the worst gini coefficient (higest in value, lowest equality) appearing on figure 2 is South Africa, where apartheid ended only 20 years prior to the publishing of the paper, and where one can imagine it is the economic differences between communities (white/ black) that makes the largest impact on this index, while it is less clear how distribution appears within the communities.

    Even if people are bad at this kind of estimation, the question is how bad they are. Figure 2, showing actual vs. perceived gini for several countries, shows a correlation of .37 between the two. The chosen strategy needs only be correct “on average” to be adaptive. But of course we ignore many complexities here. 

  37. Ontogeny of facial dimorphism and patterns of individual development within one human population., E. Bulygina, P. Mitteroeckerand and L. Aiello, 2006.  2

  38. Really to such an extent that we don’t think of the “face” as part of the “body”. 

  39. in addition to other identifying features such as smell, voice, body shape and gait. 

  40. Such as personality:

    Using composite images to assess accuracy in personality attribution to faces, Anthony C. Little and David I. Perrett, 2007.

    This study sought to find whether people could discern a person’s personality from their face. They assembled participants, administered them the (Costa and McCrae) personality test, and took photographs of their photos. Then, for each sex and for each of the five traits, they created two averaged face images, one composed of the 15 highest and one of the 15 lowest scorers. A different group of participants rated each of these faces for each of the five traits. The investigators looked at interaction between the criterion trait, averaged face, sex of face and sex of rater. While this was not true for each trait and sex, generally an ability to correctly extrapolate trait from a static face image was found. While it agrees with one’s intuitive notion of being able to read the personality of people off their faces, the findings of this invesetigation –– I find –– are quite astounding.

    They offered a few possible mechanisms that might be behind the correspondence of face and trait, including hormonal composition (affecting face development and behaviour), behavioural adaptation/ “self fulfilling prophecy” (people matching in their behaviour the expectations of others) and muscular/jaw developmet (facial expressive habits leading to differentially developed features). One mechanism that they didn’t mention is others-mediated self-perception. That is, it might be that the way other treat one affects the way one sees oneself. This is similar to the second article on the list, but different. Rather than affecting the personality per se, the perception is affected. Since the personality traits in this study were meassured through a self-report questionnaire, it makes a difference. Nonetheless, the study is rather convincing about there being such a faculty of discernment in humans. 

  41. At the same time, it seems like people rely not so much on the rich input that the vision of a face provides, but on simeple relationships between geometrical elements such as the relative lenghts and position of the mouth, nose, eyes and so on. I say it on the bassis of the human ablity to recognize individuals even from “simplle” line caricuates. Likewise, people can easily differentiate male and female factial representatinos rendered only as a line drawing, and presumably to an extent people who are similar to them or their family (same “ethnical group”, i.e. kin) from those who are not. Cats can be similarly distinguished from dogs and birds and so on. Perhaps, then, the “detailed schema” emerged not from the inclusion of all perceived content (texture, color &c) but the fine-tuning of the innate schema. This also makes adaptpable sense: there’s presumably more intra-individual variation overtime of texture (skin condition changes, different light conditions giving a different impression thereof &c) than interindividual variaton (as individuals from the same ethnic group have similar skin &c) while the facial structure that gives rise to the visual impression of the geometrical relationships of the face are rather constant intra-individuallly and variable inter-individually. 

  42. Human and Chimpanzee Face Recognition in Chimpanzees (Pan troglodytes): Role of Exposure and Impact on Categorical Perception, Julie Martin-Malivel and Kazunori Okada, 2007.

    Their primary aim was to investigate conspecific and nonconspecific recognition as meditated by exposure, using chimpanzee cohorts from two research centers with different kinds of human and chimpanzee exposure. As far as analysis goes, I find that their reliance of “exposure” is lacking, and really one should looka at “attention”. That is, I think what matters is not so much the “sheer amount” of “exposure” (perceptional encounters), but the degree to which differentiation has been important/ useful. Each time I go to the supermarket I encounter tomatoes, but I never needed to distinguish them in anyway, ans so no effort is put into rectifying the fact that “they all look the same to me”. If you’d tell me that the city I live in utilizes traffic-lights that come from three different manufacturers with distinct characteristics, I’d believe you. I have never paid attention to how traffic light look like, only to the signal they show, and so my experience/memory has nothing to contradict you. However, if I start paying attention to them, especially if you suggest that there might be some benefit to me from doing so, I’m sure I’d be able to do just that.

    Also their algorithm for the computation of “face similarity” is rather weak, but I’d say it is not so to a degree to cast doubt on their results. The biggest problem of their research ––– which they were aware of ––– was one of the cohorts they used and its “exposure history”, but that was mainly a function of the cohorts available to them, presumably. 

  43. Dogs Can Discriminate Emotional Expressions of Human Faces, Corsin A. Müller, Kira Schmitt, Anjuli L.A. Barber and Ludwig Huber, 2015. Supplamentary material 

  44. Humans rely on the same rules to assess emotional valence and intensity in conspecific and dog vocalizations, Tamás Faragó, Attila Andics, Viktor Devecseri, Anna Kis, Márta Gácsi1 and Ádám Miklósi, 2014.

    Looking at the spread of data points it seems like the relationship between the auditory features and emotonal content is rather flimsy, but I’ll take their analytical results as given.

    Either way, it is hard ot see these reults as supporting the “pre-human origin hypothesis of affective prosody” which holds that “the acoustic cues of emotions in human vocalizations are innate and have strong evolutionary roots”. They looked at perception rather than expression. The faculties responsible for the deciphering of auditory calls could have evolved after the split of humans from other species, subsequently being applied to the interpretation of vocalisation of other species. Even assuming that the vocalisation of the dogs was “correctly” deciphered, one could imagine that as a domesticated companionship animal there was a selective pressure on dogs to evolve vocalisation that was meaningful to humans. 

  45. In these studies the “averaged” is a symmetrical stimuli. In the former, theoretical, paper, the orientation (right/left) is really an arbitrary choice, such that it could have been any other trait so that the averaged would not have been “symmetry”. Indeed, the empirical studies they mention include studies that used non-orientational stimuli, such as the one with the pigeons and the colors. In the latter, well conducted, study of starlings, it is possible that the results would have been different had the “averaged stimulus” been anything other than a symmetrical stimuli. It seems to me that they could have easily tested it with a slight adjusment of their procedure. Namely, they had birds that were trained on asymmetrical “left stimuli” (“left birds”), on “right stimuli” or both of these, with the latter prefereing at the test phase symmetrical stimuli while the former two prefered the respective asymmetrical stimuli. As it happens, their preference was for averaged asymmetrical stimuli (5% assymetrical, while they were trained on 2.5% and 7.5%) over symmetrical stimuli. However, on the test phase they were choosing between these aveaged asymmetrical stimuli and symmetrical stimuli. Had they were choosing also between the averaged asymmetrical and non-averaged asymmetrical (2.5% and 7.5%) one could have seen whether really it was a preference for averageness.

    Generalization and the evolution of symmetry preferences, M. Enquist and R.A. Johnstone, 1997.

    Symmetry Preferenceas a Cognitive by-product in Starlings, John P. Swaddle, Judy P.K. Che and R. Earl Clelland, 2004. 

  46. Evidence Against Perceptual Bias Views for Symmetry Preferences in Human Faces, Anthony C. Little and Benedict C. Jones, 2015. 

  47. This really rests on evolutionary history. What would stop us from saying, given the advantage of averaged faced mates (being developmentally stable), that the “preference of the perceptional faculties” evolved in order to detect these? One would have to show that this was the case. Beyond the identification (and assessment) of mates, the construction of “averaged stimuli” (something like the Platonic ideals) is an important cognitive feature that allows learning. When we see a new tomato that looks a little different from all tomatoes that we have seen before we still recognize it as one of the kind, since in appearance it resembles the average of all other tomatoes and is distinguished from the averages of other known entities. Presumably for any creature to take advantage of its senses by interpeting complex stimuli (that is, non-simple ones such as perception of light/darkness, oxygen and other chemical levels &c) it must be able to generalize from stimuli that have been experienced in the past. This kind of generalization through averaging, then, must be an old cognitive feature.
    The evolution of species is prone to be directed by external pressures, but the way that a creature evolves has constraints, the more so the more complex a creature is. If that kind of averaging that goes into classification happens when an individual recognises conspeficis, then one cannot claim that it evolved in order to differentiate stabily-developed concons from those that developed less stabily. One might say that this former evolution (former since it solved an older and more general problem of recognition) is adaptive for this situation, but not that this situation rendered any directed pressure therefor. 

  48. Facial fluctuating asymmetry is notassociated with childhood ill-healthin a large British cohort study, Nicholas Pound, David W. Lawson, Arshed M. Toma, Stephen Richmond, Alexei I. Zhurov and Ian S. Penton-Voak, 2014. 

  49. They did find, however, an inverse correlation between IQ at age 8 and facial FA at age ~15. 

  50. Testing the sexy son hypothesis—a research framework for empirical approaches, Thomas Huk and Wolfgang Winkel, 2008. 

  51. The model is problematic in more than one way.
    First, a minor point. To avoid expressions such as “mates of polygamous males” I’ll call females that mate with polyamorous males “pollies” and those who mate with monogamous males “monas”. The authors first arrive to the number 0.85 as the minimal number of fledglings that pollies must have per fledgling of monas in order for it to be advantageous to mate with a poly-male. They arrived at this number after calculating the “fitness” (total number of offspring x genetic relatedness) of pollies and monas over two generations. However, what we (that is, they) care about is only the final generation so we should count only generation F2 (as they do later on, but with a different pretext) which would give us the number 0.77, which really makes the conditions for the advantage of polly behaviour looser. Unless, that is, we assume birds of one generation might mate with birds of other generations but that adds complexity that is beyond the formulated model and anyhow it won’t salvage the model.
    They made the following assumptions: (1) the sex ratio is 1:1; (2) females mate with males randomly, that is, the chance that a female is a mona equals the proportion of mono-males in the population (p), and otherwise (1-p) the female is a polly; (3) sons have the same number of mates as their fathers.

    I’ll follow their own particular demonstration of the model. First they supposed that the “harem size”, that is, the number of mates that poly-males have, is two, so that they are bigamous. Monogamous pairs have two fledgling. Then they delineated two scenarios. In the first one there’s a one to one ratio between mono-males and poly-males, that is, p=0.5. Let’s suppose pollies have 0.85 fledglings per mona fledgling (in the paper they wrote it should be greater than 0.85, but the math gives a smaller number so that really it’s “greater than or equal to”), or 1.7 fledglings in total (0.85*2). For convenience, let’s suppose that there are in total 200 males, 100 mono-males and 100 bi-males.
    First of all, note that to continue from here we already must break some of the assumptions. In order to give our males the females they deserve we must have 300 females ––– 100 monas and 200 pollies ––– thus breaking assumption (1) of the sex ratio, but we’ll squint our eyes and continue.
    The birds do what they do and in the next generation the “mono side” didn’t change: the 100 monas and 100 mono-males have 200 fledglings, 100 females and 100 males. On the polyside the next generation has 340 fledglings, 170 females and 170 bi-males. In total, the fledgling population has 270 females, 100 mono-males and 170 bi-males. In order to couple the males of our new generation according to assumption (3) we must have 100+170*2 = 440 females, but we only have 270 females. Oops.

    Now, later in the paper they wrote, “However, assigning a value of 1/2 to p in the example given above would certainly not be valid if one considers the polygynous mating system at the time that it first evolved. At that time the proportion of monogamously mated individuals would essentially be one”. They mention that in that case, with p=1, the threshold remains the same.
    Let’s suppose that there are 101 males, one of which is bigamous, and 102 females. Each of the two polies would have 1.7 fledglings, so that the bi-male would have 3.2. Let’s say he has 3 fledglings.
    Suppose these are 2 sons and one daughter. The offspring generation has therefore 101 females and 102 males. If the females mate by chance, then each one of them would mate with just one male, or very slightly less since there’s a surplus of one male. That is, giving even a single female per next generation bi-male is slightly generous. But, either way, the bigamous sons would have no more mates than average and therefore confer no advantage to their mother. “Sexy but alone” if you will. Their mothers had less than average amount of fledglings, and if the polygamy is behavioural so that these males would expend energy to search for mates instead of taking care of their offspring, then they’ll have as many, that is, as little fledglings as their single mate, 1.7 instead of 2. But even explanation aside, the point is that you cannot satisfy all the assumptions of the model at once.
    Even if we assume that that first generation bi-male had 1 son and 2 daughters, then the next generation would have 102 females and 101 males, that is, it would be the same as the parent generation. You can see that what would happen to the bigamous-males and their offspring would depend on the sex ratio among the 3.2 fledglings. If there are 0 sons then there would be no more bigamous males. One son keeps the status quo. Two or three sons means the sons will get as many mates as mono-mates, possibly with less offspring, and either way giving less grandchildren to their polly-mothers than they would have gotten as mona-mothers.

    I know little about the evolution of birds, but I’d assume that polygamy preceded monogamy, so that the starting proportion of mono-males should have been ~0. In that case it would have been even harder to satisfy all the assumptions, and if the poly-males wasted time chasing skirts then the few monogamous fathers would have more fledglings than the polygamous ones, having an advantage and growing in proportion within the population. 

  52. That being said, it is possible that a preference for a trait would develop such that females would “reconize” only males that have that trait, as described above. It is not that the trait is a marker of fitness, and the preference is only as good as it is successfully recognizes concons, even if it excludes those that do not have it. It is not associated (correlated) with any behaviour (such as promiscuity) –– if it did then we have a different phenomenon at hand. As cuch the preference does not confer any advantage, except, again, for possible assistance in locating conspecifics. If there are females that do not possess this preference then it is likely that speciation would occur, that is, either the species would “split” into two species, one with the trait and the preference for it and one without, or the one species would, in a sense, turn into another one, where you only have individuals with the trait and preference. Either way, within a species with a trait and the preference you won’t have variation on the trait –– it would become a fixed trait. 

  53. Mate Selection –– A Selection for a Handicap, Amotz Zahavi, 1975. 

  54. Sexual Selection and the Handicap Principle, John Maynard Smith, 1976. 

  55. To take Smith’s word for it, before he published his findings he met up with Zahavi to figure out why his mathematical model is not working, but nothing came out of it:

    The question to me was always: Can you formalise it? It’s very much as it was with George Price’s notion of retaliation, can you make a formal model of this which will show that the thing will work, because, for me, I can’t operate with verbal models. I have to have a… a formal mathematical model, essentially because if you make a mathematical model, you have to say what you mean. You have to define your terms. And even if you don’t, anybody else looking at the model can see what you must have assumed in order for the thing to go the way you say it does. And then the point of a mathematical model is really to make it absolutely clear what is being said. And after Amotz had published his original handicap model, I tried to formalise it. And I… in the context of sexual selection, which is the context in which he’d first talked about it, and I made a formal model of it, which didn’t work, did not lead to the conclusions that he claimed it did. And I sent it to him and said, ‘Look, Amotz, I’m in real trouble here, I’m obviously not modelling what you say I ought to be modelling because I’m not getting the answer you get. You know, where am I going wrong, where are the assumptions that I put into this model not what you think they ought to be?’ And actually, it’s… it was one of the worse weekends of my life. Amotz and I sat in the chairs that you and I are sitting in now, for a whole weekend, really, trying to come to terms with this. And when he left, Sheila said to me, ‘He is not to come again.’ And this is not because he misbehaved, but because I was in such an impossible mood at the end of it. I had… I felt, at the end of two days conversation, he hadn’t understood a single word I’d said. And I found this very frustrating, arrgggh, you know, I was really… but I’m sure he felt the same. I think at the end of two days conversation he felt I hadn’t understood a word he’d said, and I think we were both right. You know, information had not flowed between us. And it wasn’t personal dislike, it was just a complete inability to understand somebody who thinks totally intuitively and verbally, and somebody who has to have it all made easy with… with maths. And I was left persuaded that there probably wasn’t much in this, you know. I mean, that I could forget the handicap thing, if it couldn’t be made clear, I wasn’t going to bother with it.58

    I do find one issue with his mathematical model, though I cannot say whether its correction would have salvaged the model. I would have come midway towards the Handicap principle and set the all handicapped males to be of the fitter genotype and see how the populations propagate. Alternatively, I would have waited for more than 5 generations to see what was going on; presumably the males that are both less fit and handicapped would decrease in numbers, so that handicap becomes a “genuine” marker of fitness, making in turn the offspring of the females who mate with them more fit. Perhaps it’s a matter of how he implemented the mathematical simulation, but otherwise it seems odd that Smith stopped after 5 generations of simulation run. The reason he gave is that the population departs from linkage equalibrium, but he had also stated that the reason to run the simulation at all is “because linkage disequilibrium is an essential feature of the situation”, precluding an analytical solution. 

  56. John Maynard Smith mentions this in the paper though he doesn’t give an example; the handicap principle would apply in the case that the handicap is not heritable. Consider, for example, some erratic event that damages the male. Let’s say one winter is particularly fierce, there are very heavy rains with floods that dislodge boulders and large tree branches and a male gets injured during this time, for example breaks a leg. If he managed to survive for long after the event it would be a clear sign of fitness. Not only could he survive during “average periods”, but he managed to survive despite being accidentally damaged during extreme times. Since his offspring is not going to inherit his broken leg but will be likely to partially inherit his perseverance, he’s a good catch.
    I say “erratic event” and “accident” because the cause of the damage must not be a steady feature of the environment. In that case it would behove a female to find a male with traits that render him adapted to the circumstances of harsh winters, or of hunters, or of whatever it is that caused the handicap. 

  57. Predation shapes the evolutionary traits of cervid weapons, Matthew C. Metz, Douglas J. Emlen, Daniel R. Stahler, Daniel R. MacNulty, Douglas W. Smith and Mark Hebblewhite, 2018. 

  58. John Maynard Smith - Struggling with Amotz Zahavi’s verbal model of ‘stotting’