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June 07, 2003
African American Beauty
Whiter is brighter & righter?
June 06, 2003
Individual genetic engineering => social change?
Randall Parker addresses the long-term social implications of genetic engineering in the context of altruism. It's a very good post, I encourage you to read it! Of course, you don't need to bring up genetic engineering either to discuss individual vs. group costs & benefits, most educated Americans have only a few children because of their individual priorities, but probably end up short-changing "society." Genetic engineering only adds another wrinkle.
Jews are returning to Germany! One thing that the writer notes is that most are on welfare because they can't speak German, but an influx of Jewish immigrants is almost certainly a net long term positive economically as their German fluent children will ascend into the professions (many of the immigrants are mathematicians). For some reason the article seems to underemphasize the fact that some on the Christian Right (CDU, CSU) have been grumbling that there are too many Jews in Germany and that "enough is enough."
Too bad the Germans didn't have that attitude, that enough is enough, between 1940-1945.....
As everybody knows, the Eskimo have dozens, if not hundreds, of different words for snow, which proves the cultural relativity of knowledge, perception, or whatever.
Except that they don’t. I have occasionally seen sceptical comments about the Eskimo snow words, but I have only just found an authoritative reference:
Laura Martin: “Eskimo words for snow”: a case study in the genesis and decay of an anthropological example. American Anthropologist, 1986, vol. 88, 418-22.
Laura Martin traces the origin of the great snow myth to a book by Franz Boas, where he mentions four Eskimo snow-related words to illustrate a point about the structure of Eskimo language. But the story really took off when Benjamin Lee Whorf used the snow example in an essay on ‘Science and Linguistics’. Unlike Boas, Whorf (who actually had no expert knowledge of Eskimo language) was vague about the number of snow words, but claimed that they showed the way in which language structures perception and thought. After Whorf, the example spread, and (sorry!) snowballed out of control, until in 1984 a New York Times editorial could confidently assert that the Eskimos distinguished 100 different types of snow.
So how many different words do the Eskimo have for snow? Well, it depends how you count them, but according to Martin, ‘There seems to be no reason to posit more than two different roots that can properly be said to refer to snow itself’.
Mind you, English slang does have at least fifty words for penis...
June 05, 2003
If you're fat-it's cuz you're going to have a boy!
Two articles on the black-white academic gap that persists through socioeconomic levels. This one is about Dr. Ogbu's work in Shaker Heights and is rather detailed, while an article in The NY Times is much less meaty. Interesting reading, but I will add one thing that the articles don't mention, regression towad the mean (a point always brought up by Steve Sailer when I mention this topic). Jensen in The G Factor noted the importance of this, for instance, "gifted" black students (IQs above 120) were far less likely than gifted white or Asian students to have siblings who qualified for enrichment programs.
What I am curious about though, what about Americans who are members of the old black upper class, the individuals profiled in Our Kind of People. These are families with generations of high achievers who quite often tend only to marry "their own." I suspect this population regresses toward a different mean, that of W. E. B. Du Bois' "talented tenth," then the nouveau bourgeois that forms the majority of the black middle class.
The futility of universal love
Note: This post has been a while in coming. I am going to start and approach issues that touch upon political philospopy and the possible implications of evolutionary psychology & behavioral genetics. It has been stated-by me at least-on this blog that politics is something we can argue about once we agree on the basic facts that serve as the substrate for our norms. I am a strong believer that ought does not follow from is, but I also must acknowledge that the bounds of ought are constrained by is. Reader input is encouraged!
This is clearly illustrated in the case of ancient China-for one can look toward the Mohists, under the leadership of Mo Di, as exemplars of the idea of "universal love," set against the teachings of Confucius, who acknowledged the importance of tradition and the "natural order of things" (in contrast to forward thinking constructed ideals), giving great weight in particular to the need to accept the paramountcy of family above all other institutions and loves . Unlike the messy and often cantankerous Confucians, Mohists were in many ways a laudable group of individuals, driven by a genuine desire to do "good." Not only did they preach that one must love all human beings equally, they organized defense militias that aided weak principalities against the strong, putting into their practice the principles of justice and egalitarianism as goods that could be achieved within their lifetimes. Not surprisingly Mohists were utilitarians who inveighed against wasteful "music" and other fripperies, objecting to excessive bending toward tradition, even in time-hallowed areas like mourning for the dead, when misery and suffering was the staple of much of the human condition for the living . In a fashion they presaged the ideas of Jeremy Bentham, who asked to have his skeleton preserved to show how little he cared for his flesh emptied of cognition. In contrast to the Mohists, the Confucians, and in Bentham's day Burke, emphasized that human beings have natural inclinations to care for their parents, to spend inordinate time on rituals, art and religion, and though these were not necessarily rational and easily justified when set against the material short-comings of their fellow man, they were constants of the human condition that could be channeled usefully to maintain the greater good short of turning men int automatons who were cost vs. benefit calculation machines. The ultimate end was the same for both camps, the greater happiness of the human race, but while the Mohists assumed that abstract concepts of justice could actualize Heaven-On-Earth, the Confucians argued that there were pre-ordained predelictions that had be accounted for and made the foundations upon which a political order was grounded-for man did live for more than bread or water.
Though the Chinese dynastic system that began with the Former Han owed much to the harsh Legalistic reign of the Chin dynasty, its spirit was still Confucian, and it was the ghost of the philosophy of Confucius, Mencius and Hsun-Tzu that animated it for 2,000 years. Historians have long marvelled at the fact that where the blind law and later military autocracy of ancient Rome was not resurrected in the Middle Ages, the Chinese system of governance recapitulated itself time & again for 2,000 years-bouncing back from repeated chaotic interludes.
Why was this? I believe that part of the answer lay in the fact that the pre-industrial mind did, as some historians intuit, have difficulty with internalizing abstracts such as Roman Law, while personal rule by the Mandarins of the Confucian system was not difficult to grasp because in some ways its paternalism resembled the natural family organization that served as the center of Chinese culture (to be sure, any human culture, as the family is a biological as much as a cultural unit of organization). Ultimately the Emperor was the Son of Heaven, but he was Father of China as well, the common-folk his "children," just as foreign potentates were also viewed as lesser relations and subordinates in the family superstructure. Chinese legal tradition even granted some legitimacy to the heirarchy of priorities, during some periods sons could not be prosecuted for aiding & abetting a criminal father, because it was natural that a family would aid and shelter their own (of course, there is also the tradition of executing whole family lines because of the treason of one member).
On the issue of "music," costly and time-consuming mourning traditions and the like, Confucius freely allowed one to dissent as to whether there was any direct utility in these things, but he and his followers simply asserted that no matter the root cause, the impulse to love and honor family and parents in particular were natural feelings, to mourn was a reaction to a genuine and universal emotion, and these facts of life had to be assimilated into any coherent theory of humanity that could be applied to governance. Additionally, filial piety and these natural inclinations toward "goodness" could be harnassed to shape a better individual who could serve the good of the whole, the state. Utlimately, the complex emergent structure of the Chinese state was rooted in truths about human psychology and basic atomic familial structures, rather than created de novo with engineering efficiency in mind. Idealists driven by the force of human perfectionism might demand that their followers renounce preferential love, such as Mo Di did, or raise their children in a communal setting, such as on the Israeli kibbutzim, but such waves of fervor and universal world-shaking altruism tend to run up against the parameters of human nature.
Elaborated by W. D. Hamilton, the idea of kin selection indicates the thinking of philosophers such as Confucius who believed it natural that human beings favor close relatives over those who were distant from them by blood. The fact that anti-kin selectionist thinkers like Mo Di could arise points to the power and influence of higher level cognition and abstraction in the human psyche, but it still must run up against the more deep-seated instincts inherited from ancient mammalian forbears. As I have noted, Confucianism, unlike Mohism or Legalism, was based on the idea that family, and cultivation of filial piety, "good-heatedness" (jen) and "ritual" (li) would ultimately produce a better society at the top by percolating character upward from the gentry to serve the rulers. Though bastardized and bowlderized Confucianism did serve the Chinese Empire well for 2,000 years, an admirably successful mode of political governance and organization if longevity is to be used as a criteria-a good clue as to whether the initial axioms of the philosophy were valid or not . Almost certainly the unconscious leveraging of the idea of kin selection, hard-wired into human beings, was a part of this success. In contrast the principate, the early pagan Roman Empire, the dominate, the militaristic late pagan Empire, and the Christian Roman Empire, were not animated by any similarly durable political philosphy. Rather, the Empire spent its capital over time, husbanding it in the east until after 1100 it became but a small petty kingdom slowly wasting into obscurity .
In the end, familial love served as the glue for Chinese civilization, while the universal love of Mo Di sailed over the horizon of historical memory, only to be ressurected now and then and trotted out by Maoists or Christian missionaries for their own ends . Of course universal love and preoccupation with individual salvation, two extreme antipodes against the norm of the Golden Mean of family and kin, manifest themselves in many other cultural traditions. The original messages of Christ and Buddha for instance were rather anti-social and difficult to reconcile with worldliness. And yet both of the faiths that sprung from these charismatic teachers quickly adapted to themselves to the powers that be and tempered their messianic tendencies and lived with compromise. In fact, the Buddha is said to have almost turned his back on the world, and only entreaties from his disciples brought him back to engage with the masses and teach him the way to salvation and nirvana. In contrast, Christ unequivocally brought his message to the masses, and preached a radical spiritual doctrine that seemed to break out of the narrow sectarianism of Pharisaeic Judaism and taught a rejection of current order of things in anticipation of a new kingdom of God upon the Earth . The idealistic, pacificist, and anti-government message of "primitive" Christianity became transformed into the militaristic "muscular" faith that peaked during the early Crusades and later emerged once more during the Victorian Era. Buddhism flourished in societies as militaristic as Tokugawa Japan and Oiyrat Mongolia. The axiomatic points & principles of the faith were superseded by the practical decisions made by prelates and abbots who had to live within a system where temporal figures wielded great power over religious folk. Additionally the elite religious clerisy were easily able to sway the masses of the faithfull to break with axiomatic points because the latter were not literate or sophisicated enough to comprehend the historically unorthodox application of religious principles.
Today, with the spread of literacy and the decentralization of power, the force of religious texts and the basic theological axioms are rising to the fore in many places (Islam for instance). This has happened before, the Reformation was in part a reaction against the quasi-paganism and worldliness of the Catholic Church heirarchy of the time. While in past periods of dissension the heretics were absorbed or eliminated, the existence of information technology in the form of the printing press meant that the wildfire of dissent coud not be extinguished. Martin Luther's conception of Justification by Faith alone was in large part motivated by his reading of the scriptures, and each iteration of the Protestant Reformation (Lutheran -> Zwinglian -> Calvinist -> Noncomformist) became progressively more "primitive" in orientation, turning against the temporal powers and withdrawing. The idea of "unviersal love" permeated the early Church, and its non-pragmatic concern for all individuals (rather than just the powerful), was clear to even pagans. As St. Augustine had noted, from fair-haired Angles (Germans) and dark-skinned Ethiopians, all were possessed of an immortal soul. The Wars of Religion in the 16th and 17th century, though partially motivated by venal intentions by the princes of the day, were also giving vent to universal love and concern for their fellow man. Those who found the Gospel in its most unadulterated form wanted to spread this to others, to the whole world if need be. By the sword did Protestantism spread in much of Europe, while Catholics re-converted many others also by force, for the love of their fellow man, against the follies of heresy and eternal damnation. The volatile balance of the Medieval Age, where a "universal church" accepted de facto paganism among the masses so long as there was lip-service to the strictures of the Christian faith, were gone. Christian creed now soaked into the heart of Europe, rather than enforcing hollow outward forms and rituals that served as scaffolding for political institutions.
And yet a peculiar consequence of the Protestant Reformation and its world-changing zeal was that it too was subborned and underminded, the last iteration of the Reformation saw the emergence of narrow sects that rejected practical universalism, accepting that in truth most of humanity was doomed to hell-fire. Of course the principle of universalism remained, the Good News would be spread by word, but the Wars of Religion had disabused many even among the state supported denominations of the idea that universal salvation could be coerced. Only so much were they willing to do for universal love.
And yet after the de-centering of Christianity from the Western identity, the whithering of Christianity, other forms of universal love replaced the messianism of radical/primitive Christianity. Marxism, Fabian Socialism and other "Left" movements made strong claims about justice, the universal dignity of man, and the importance of spreading the world from shore to shore over the face of the world. Within the modern Left there still exists tensions over the various levels of universalism, nationalist labor leaders disputing with transnational Leftists who wish to attack globalism and bring "power to the people," all people, not just kin & kin, fellow citizen or subject.
While modern Leftism tends to emphasize the higher emergent properties of cognition, free choice, abstract system building, much of the Right has unwittingly taken refuge in our biology, from libertarianism with its individualism to social conservatives who emphasize family & tradition. Conservatives freely admit that if they could have a just world by fiat, they would do it, but argue powerfully that there are parameters and limitations on the level of perfection, on the goodness, that exists within individual human beings. Of course, conservatism is by nature a shape-shifting ideology, one generation's abstract systems giving way to another-one generation's "progress" and "fad" becoming the status quo wisdom of the later years.
On a contemporary note, I believe Islamism is a partial expression of universal love, though rooted and co-existent with other urges and tendencies. The conservatism of one age is the progress of the days of yore, and it will be perhaps true that "Islam" as a culture will transmute as it goes through the same cauldron that Christianity did, that individual Muslims will one day wake up, one at a time, Islamists, moderates and seculars, see that the world is sloppy, that though God is perfect, his creation is flawed. The Koran might be Uncreated, but it is holds a different promise to the hearts of each man, that a universal message to mankind is futile.
 The great exception being John Rawls. His seminal work in Theory of Justice and its point of initiation, "the original position," have been criticized as being excessively abstract and to my mind seem not to take much account of our biological predispositions as opposed to our cognitive pretensions.
 Chinese politico-philosophical schools were complex and multi-faceted, so for instance, Mencius and Hsun-Tzu both effected latter-day Confucianism at least as much as St. Paul or Augustine shaped Christianity, if not more. But as general camps I believe one can distinguish Mohists and Confucianists, for though leaders of both groups had their differences, they were held together by a certain spirit of opinion.
 A strange fact the Mohists were the one school of ancient Chinese philosophy that most closely approached the theist concept of a God. Also, it might be important to remember that Mohism rose to the fore during the "Age of Warring States," when social disorder had mostly likely reached a crescendo in ancient China.
 See the book The New Chinese Empire for an argument that Confucianism and Legalism still serve as the mode of governance for the Communist dynasty.
 The Roman/Byzantine politico-historical entity did experience mild cycles of growth and collapse. For instance, the climax of the principate during the Antonine Age (~100-180), gave way to militarized chaos that peaked in the mid-3rd century, only to usher in the centralizing tendencies of the dominate under Diocletian and the Tetarchy. But these patterns are harder to discern and much more attenuated than the clear cycles that characterise Chinese dynastic patterns.
 Communists liked Mo Di's egalitarian orientation and contempt for excessive ritual, tradition and "old ways," while Christian missionaries saw a kindred spirit in the Mohist conception of Heavan as a beneficent spirit.
 There is much dispute over what Christ preached and what his followers attributed to him. Current research and scholarship seems to indicate that Christ did not have nearly as expansive a conception of the Christian message and his successors such as St. Paul.
June 04, 2003
Will be at the Gramery Park Hotel for 2 days (Thurs. & Friday). E-mail me if any of you know of a cafe with a good WI-FI connection nearby....
(have high-speed in my room, but I like freedom)
CUCKOLDRY AND CORRELATION
DNA testing shows that many children are not the biological offspring of their supposed fathers. The incidence of misascribed paternity in present-day western populations has often been alleged to be over 5%.
This has implications for estimates of heritability. These usually depend on a comparison of observed correlations for some trait (height, IQ, etc.) with those predicted by a genetic model. If genetic inheritance is purely additive, and there is no assortative mating, then the correlations between relatives should reflect the average proportion of genes they share by inheritance from a recent common ancestor: 50% between individual parents and offspring, 50% between full siblings, 25% between half siblings, and so on.
If there are significant levels of cuckoldry in a population, the proportion of genes shared by relatives (except those related solely through the female line) will on average be reduced. If the rate of cuckoldry is k, the average proportion of shared genes attributable to a particular line of relationship will be diluted by a factor of (1-k) for each step at which cuckoldry may have broken the link (assuming that the probability of cuckoldry in each case is independent, and that the same male is never the true father of more than one offspring of cuckoldry.) In the case of full siblings, the line of relationship through their mother is unaffected, giving them an expected correlation of .5 x .5 = .25 from this source, but the line through their father presents two opportunities for cuckoldry. The expected correlation will therefore be .25 + .25(1-k)(1-k) instead of .5. If k is 10% this gives a correlation of just over .45 instead of .5. Other cases, such as cousins, are more complicated, and each line of ancestry needs to be carefully traced.
Twins are a special case. Monozygotic twins always have the same true father. Dizygotic twins could in principle have different fathers, but this must be comparatively rare. The standard ‘twin method’ for estimating heritability is therefore not seriously affected.
The most obvious implication of cuckoldry is that we would expect correlations between offspring and their mothers to be higher than between offspring and their supposed fathers. The evidence on this is mixed. It has generally been accepted that maternal and paternal correlations are equal. This is notably the case for IQ, which has been intensively studied [ref. 1]. However, it has also been claimed that in some psychological traits mother-offspring correlations are slightly higher than father-offspring correlations, which has been ascribed to the greater role of women in child rearing [ref. 2] This overlooks the possibility of cuckoldry. Another implication is that the correlation of ordinary siblings would be lower than that of DZ twins. This has been sometimes been observed for IQ, but this has been ascribed to the greater similarity in upbringing of twins.
It may be doubted whether the incidence of misascribed paternity is really as high as often alleged. High rates have not yet been confirmed in published peer-reviewed studies. Some ten years ago a survey of the literature [ref. 5] showed a wide range of different rates in different communities. For example, in 1957 J. H. Edwards made an estimate of 5% in the UK based on blood groups. In 1963 a study in Michigan showed a rate of 1.4% for whites but over 10% for blacks. A more recent study [ref. 4] in France has found a figure of 2.8%. Over the longer term, Bryan Sykes has concluded from Y chromosome evidence that in England since the late Middle Ages cuckoldry did not average more than about 1% per generation [ref. 6]. It seems likely that the rate of cuckoldry in European and American populations in recent decades has averaged somewhere between 2% and 10%, but with much variation.
Even with a rate as high as 10%, the departure from predicted correlations would usually be small enough to fall within the range of uncertainty due to assortative mating and other complications. However, this would not apply to those cases where misascribed paternity is actually identified from DNA testing. In these cases the predicted correlation based on assumed relationships would diverge widely from those based on true genetic relationship. In the case of father-offspring, the true genetic correlation would be zero, except to the extent that assortative mating correlation between husband and wife, or between husband and true biological father, raised the expectation somewhat. I presume however that this would not raise it above, say, .2. In fact, the offspring of cuckoldry can be regarded as a natural experiment in adoption, with the difference that there is no problem of ‘selective placement’, and no ‘Pygmalion effect’, since the cuckolded fathers do not even know that the experiment is taking place. Admittedly, cases of misascribed paternity are not a random sample of the population, but they are probably closer to a random sample than many other categories studied in behaviour genetics.
All of this should be fairly obvious, but I have not seen it discussed in the literature on kinship correlations (e.g. refs. 1, 3) If anyone knows of relevant discussions that I have missed, I would be interested to know.
June 03, 2003
Who's Zoomin' Who?
Genes are at your mercy, says Matt Ridley in this short essay, which appears to be an extended abstract of his recent book, reviewed infra by Razib.
Affirmative action & mongrelization
A pot-shot against affirmative action in The Nation! My how the times-are-a-changin'. Of course the perpetrator is Michael Lind, ex-neocon, and neo-class-warrior. Lind has long wanted to shift the focus of debate on the modern Left away from race and back to the old standard flag of class. This article is a clear case of this, and ironically he makes many arguments that one can find in the conservative press. Lind seems to mimic the likes of Ward Connerly in arguing for the importance of race-blindness as an organizational principle of our society.
Lind focuses on interracial marriage to highlight the general issues. He brings up some important statistics-showing that "mongrelization" has greatly increased in the past generation. Of course he can't hide the fact that rates between blacks & whites are still low and emphasizes the importance of assortive mating-socioeconomic equality is an important variable, though one could argue that affirmative action is the only path to this end . Lind brings up the interesting statistic that though the majority of blacks have dated non-blacks, only about 5% seem to marry someone of another race. This pattern also surely shows up with other minorities, though to a lesser extent, highlighting that though the situation on the ground might seem racially amicable, when the important decisions in life are made, race still matters.
 I think more importantly affirmative action enables economic, not social, equality. Rather, to recognize the power structure tends to crystallize it in place.
THE RIGHT TO BEAR WHAT?
American readers may be amused by the following as an example of cultural diversity between genetically similar populations.
Here in Britain, there has recently been a survey of a major group of public employees on their attitudes towards guns. 78 per cent of the group said they would be opposed to routinely carrying firearms during their work. 59 per cent said they would actually resign if required to carry guns.
So who are these pinko cheese-eating pacifists?
Why yes, of course, the Police!
June 02, 2003
The Universal Church no longer?
Surely, times have changed, when a online magazine with the title Beliefnet could publish an article titled Should Catholics Proselytize?. Personally, I prefer Opus Dei to the trashy mega-churches that dot the landscape of Americana. As someone who once had the Diderot quote "Man will never be free until the last king is strangled with the entrails of the last priest" as their email signature, I am no friend of the papists, but better an enemy with class & cognitive capacity than the drooling fools that pass as the soldiers of God in this day and age....
ARE MEN DOOMED?
I mentioned that I have been reading Steve Jones’s book Y: The Descent of Men. It’s brilliantly written, often very funny, and full of fascinating information, most of which is probably true.
I’m not going to give a detailed critique, but as a general weakness, the book doesn’t present much in the way of systematic theory, compared with e.g. Matt Ridley’s Red Queen or Genome, or the other Ridley’s Mendel’s Demon. A notable example of this weakness is Jones’s treatment of the Y chromosome itself. As everybody knows, the Y chromosome is a degenerate little thing. It is much smaller than other chromosomes, and most of its DNA is useless junk. Jones brilliantly describes the oddities of the chromosome, but he doesn’t say much about why it got the way it is. In so far as he gives an explanation, it is that because the Y chromosome doesn’t recombine, it has no way of getting rid of harmful mutations, so these accumulate. But he doesn’t explain that this is a controversial view (it is tantamount to accepting the Kondrashov theory of sex), nor that there are alternative theories. One theory is that the Y chromosome is the target of attacks by the X chromosome, and as there are three times as many Xs as Ys in the population, Xs have more opportunities to produce successful mutations. On this view, the Y chromosome and its genes have shrunk in order to present a smaller target to attacks from Xs. On another view, the Y itself is the aggressor, always trying to bias the sex ratio towards males, even if this reduces the overall fitness of the individuals who carry it. This is against the interests of all the other genes in the genome, and since these greatly outnumber the Y, they have succeeded in largely shutting it down, except for its limited function of triggering male development. I don’t know which (if any) of all these theories is true, but they ought to be properly discussed.
However, I don’t want to dwell on Jones’s book (which is a must-read). The rest of this post will be devoted to refuting a number of arguments that are floating round in the meme pool to the effect that men (the male of the species) are degenerate, parasitic, or doomed to extinction. (These arguments are not necessarily found in, or endorsed by, Jones’s book, though such phrases as ‘men are wilting away’ (p.241) do give encouragement to this line of thinking.)
So here, in no particular order, are the arguments, followed by my comments:
Females are the ‘default option’ in the development of an embryo: in the absence of the trigger provided by a Y chromosome, it will develop as a female. The female form is therefore more ‘fundamental’.
The (male-determining) Y chromosome is small and degenerate.
The Y chromosome will eventually disappear altogether.
The male gamete (sperm) is essentially parasitic, exploiting the larger egg which provides all the nutrition for the embryo.
Most males are a ‘waste’, as reproduction would be more efficient if there were a small number of high-quality males ‘serving’ a large number of females.
Females do most of the hard work of reproduction, providing nutrition and
With the prospect of cloning, etc, males are unnecessary and could become
E. O. Wilson interviewed
Steve Pinker introduces E. O. Wilson as he is interviewed in The Edge. It is titled "A United Biology."
June 01, 2003
Out of Africa cont.
Interesting new study:
"Human beings may have made their first journey out of Africa as recently as 70,000 years ago... Writing in the American Journal of Human Genetics, the researchers estimate that the entire population of ancestral humans at the time of the African expansion consisted of only about 2,000 individuals.
SEX RATIO FALLACIES
I’ve just been reading Steve Jones’s enjoyable book Y: The Descent of Men. More on that some other time, but first I want to comment on one passage: “In China, with its one-child policy, the ratio of boys to girls has risen from about even to a 20 per cent excess of males. Much of this comes from abortion and infanticide, but many farming peoples follow the same rule in a less murderous manner, as they continue to have children until a son is born. All over the developing world a last child is more likely to be a boy than a girl, which again biases life in a masculine way” (p. 33).
Now, I hesitate to accuse the great Professor Jones of a fallacy, but it certainly looks as if he thinks that the practice he describes - continuing to have children until a son is born - leads to an excess of males in the population. I have also seen similar assumptions elsewhere, so it is worth pointing out the error.
Suppose the probability that a birth is male is K. I assume that the probability is the same for all births in all families (I’ll come back to this point). Now consider the total number, A, of first-born children in the population, the total number, B, of second-born children, and so on. The probability K applies independently to all births, so the expected number of first-born males is KA, the expected number of second-born males is KB, and so on. The total expected number of all males is therefore K(A + B + C....). But the expected total number of all children is simply A + B + C...., so the ratio of all males to all children reduces to K. There is no ‘excess’ of males. This reasoning applies quite regardless of whether parents ‘stop at a boy’ or follow any other such rule.
If not convinced by this, consider a population of N families, all of whom apply the simple rule: ‘have children until a son is born, then stop’. For simplicity I will assume that the probability that a birth is male is exactly 1/2. We therefore expect half of the families (N/2) to have a son at the first attempt, half of the remainder (N/4) to have a son at the second attempt, and so on. The total expected number of male births is therefore N(1/2 + 1/4 + 1/8...), and the expected number of all births is N(1/2 + 2/4 + 3/8 + 4/16 + 5/32....). It can be proved that the ratio of male births to all births converges on 1/2 as these series are extended (proof available if required.)
The probability of male births is of course, like any probability, a long run expectation, and there will be stochastic fluctuations both above and below the expected levels. And in practice, in a finite population all families will either terminate with a boy or reach their reproductive limit with no boys at all. But these factors produce no bias one way or the other. More seriously, in reality the probability of a male birth will not be exactly the same in every family. It is likely that some families have a tendency to produce more girls, and some to produce more boys (though the evidence suggests that such variations are slight). But note, the effect of any such tendency is in the opposite direction to ‘male bias’. If families keep ‘trying for a boy’, and stop when they have got one, then those families with a tendency to produce girls will, on average, have to keep going for longer, and will have more offspring (mainly female) than those with a tendency to produce boys. The ‘stopping rule’ will therefore tend to produce a female-biased population.
While on the subject of sex ratio fallacies, it may also be worth mentioning infanticide. Obviously, selective infanticide of one sex produces an immediate distortion of the sex ratio, but it is sometimes argued that it it also produces a selective pressure on the sex ratio at birth. For example, Darwin’s Descent of Man included a discussion of the sex ratio. Following the publication of the first edition, Darwin received a letter from an anthropologist, Colonel Marshall, in which Marshall tried to account for an excess of male births by the practice of female infanticide. Darwin appears to have been impressed by his argument, and included an extract from Marshall’s letter in the second edition of Descent. Unfortunately, Marshall’s argument is not so much fallacious as unintelligible.
Viewing the matter from the perspective of R. A . Fisher’s theory of the sex ratio, one’s immediate thought is that female infanticide will produce a female-biased sex ratio. Since infanticide occurs before parental investment in the offspring is complete, selective mortality of females will reduce the total investment in females below that in males, and by Fisher’s well-known argument, the proportion of females at birth will tend to rise to restore equilibrium.
However, on second thoughts, there are complications. Fisher’s argument (which concerns natural mortality, rather than deliberate infanticide) implicitly assumes that the risk of increased mortality falls equally on all members of the disadvantaged sex. But it is possible to imagine patterns of infanticide where this is not the case. To take an extreme scenario, suppose the practice is to kill all female offspring in the family until at least two sons have been born. The selective mortality would then fall disproportionately on families with a tendency to produce females. These families would produce fewer surviving offspring in total, and possibly even fewer surviving females, than those with a tendency to produce males. So maybe Colonel Marshall had a point after all.
None of the above takes account of W. D. Hamilton’s theory of ‘extraordinary sex ratios’. Notably, where there is close inbreeding, selection may favour a female-biased ratio. In the extreme case where females mate exclusively with their brothers, and males exclusively with their sisters, selection would favour production of the minimum number of males capable of fertilising the females. However, this assumes zero effects of inbreeding on fitness, and zero parental care, so it is largely irrelevant to humans.