This paper has been all over the news recently. The 2D:4D ratio is the ratio of the length of your second finger to the length of your fourth finger. This ratio, on the right hand, is found to be lower in males on average, and is correlated with prenatal testosterone levels. It has been found to predict incidences of autism, and to predict success in competitive sports. (The lower the ratio, the higher the rates of autism and of sporting success.) The authors of the paper studied the 2D:4D ratios of London traders, and found that trading success correlated significantly with low 2D:4D ratios, in keeping with the findings for sport. But they went beyond measuring just this one correlation. I thought I’d highlight a couple more of their supporting experiments that weren’t reported in the mainstream news.

A separate study had shown that traders with high levels of testosterone in the morning traded more successfully in the afternoon. It has also been found that prenatal androgens sensitize the body and brain to postnatal testosterone. One would therefore expect that traders with high levels of prenatal testosterone (low 2D:4D ratios) would be more sensitive to fluctuations in their postnatal testosterone levels — they would respond more to day-to-day differences in their morning testosterone levels. And indeed, it was found that that for those with lower 2D:4D ratios, the difference between their earnings when they had high morning testosterone levels and their earnings when they had low morning testosterone levels was larger.

The authors also tested another prediction of the hypothesis that prenatal testosterone levels are a significant cause of trading success later in life. Other studies have found that high prenatal testosterone correlates positively with the ability to ignore distractions, maintenance of visual attention, search persistence, and visuomotor skills like scanning and speed of reactions. It is natural to expect that people with such abilities would be better at what is known as high-frequency or noise trading. The authors therefore looked for correlations of success in noise trading with low 2D:4D ratios, and found a significant one. Tellingly, prior trading experience did not significantly correlate with success in noise trading (it did correlate strongly with success in less volatile forms of trading).

The fuel efficiency of a motor vehicle is popularly measured by miles per gallon (MPG). The ubiquity of this measure is such that the price people are willing to pay for a car is linearly correlated with the car’s MPG value. But, if you want to save the environment or reduce spending on fuel, the better measure is GPM — gallons used per miles travelled. The price you are willing to pay for a car should therefore be linearly correlated with GPM, and hence not linearly correlated with MPG, its reciprocal. In this short paper, the authors conduct a few experiments to establish the linear correlation of perceived environmental unfriendliness of the car with its MPG value, and suggest that we really should not be too leery of incentives like giving tax breaks to SUVs that use hybrid engines — for the absolute amount of fuel saved by changing your vehicle’s MPG value from 14 MPG to 12 MPG is actually, contra the linear interpretation, more than that saved by you switching from a 28 MPG vehicle to a 40 MPG vehicle. A small increase in MPG for a fuel-inefficient vehicle is, in environmental terms, as beneficial as a large increase in MPG for a fuel-efficient vehicle.

The authors of this study analysed a cross-region and cross-restaurant chain sample of fast food for specific carbon and nitrogen isotopes. The carbon isotope in question, ¹³C, is known to occur more commonly in corn-fed beef than in grass-fed beef, and also more commonly in corn-fed chicken than in cereal-fed chicken. Their analysis of beef patties bought from Burger King, McDonald and Wendy’s outlets across the US showed that all the beef patties, save for 12 samples from West Coast Burger King outlets, came from corn-fed cows. All of the chicken sampled had levels of ¹³C consistent with a completely corn-based diet. Their analysis of levels of ¹⁵N in chicken samples revealed a signature of uniform confinement and high exposure to heavily fertilized feed for all three restaurant chains, more markers of factory farming. Finally, their analysis of fries showed that Wendy’s used corn oil exclusively, while BK and McD’s use other vegetable oils.

Why should you care? Well, corn agriculture is heavily subsidized by the US government. Yet it requires more fertilizers and pesticides than crops like grain sorghum, rice, soy and wheat. Fertilizers and pesticides in turn require fossil fuels in their production process. Corn diets exacerbate the production of methane, a much more potent greenhouse gas than carbon dioxide, in cow burps and farts. Because cows are not adapted to eat corn, antibiotics are mixed with cow corn feed to reduce the flowering of e. coli in their guts that would occur otherwise. More antibiotic-resistant bacteria strains is not good news for anyone.

Intuitively, it seems that a larger number of alternative routes in a traffic network would reduce traffic congestion. This PRL paper, though, suggests that the removal of some roads would actually reduce congestion. This comes about because the presence of these roads can create a game-theoretic situation in which the Nash equilibrium is less optimal than the socially optimal solution. When the choice of using these roads is removed, so is that Nash equilibrium, and road users end up in a more socially optimal state.

A toy example illustrates how the Nash equilibrium is easily an undesirable outcome. Suppose two points are connected by a short but narrow bridge and a long but broad freeway. The narrowness of the former means that the delay on it is proportional to the flow, while the delay on the freeway is flow independent. For a fixed number of users, the social optimum would be obtained by a mix of users on the bridge and on the freeway — even though the delay on the freeway is higher for the individual user, because fewer users on the bridge reduce the delays on the bridge for others, the total social cost is minimized if some people ’sacrifice’ their time to use the freeway. (See the paper for the exact parameters of their equations.) However, the Nash equilibrium, in which all individuals choose the option that minimises their own marginal costs, is one where all users take the bridge.

That example simply illustrates how the Nash equilibrium can deviate from the socially optimal solution. For such a simple example, it is clear that removing the bridge, and leaving only the freeway as an option, isn’t going to improve things. But in a more complex network of roads, it is possible that removing a road might shift the Nash equilibrium in such a way that it is closer to the socially optimal solution. The authors studied the road networks of Boston, London and New York City to find such scenarios. For Boston, they considered journeys from Harvard Square to Boston Common. They then plotted the ratio of the cost of the Nash equilibrium to the cost of the social optimum (they called this the POA — price of anarchy), for varying rates of vehicular flow. Except for very small flow rates, this ratio was always above one — the Nash equilibrium is almost always more costly than the social optimum:

POA is the ratio of the cost of the Nash equilibrium to the cost of the social optimum. Note that it is more than one for almost all values of the flow.

After obtaining the initial POA versus flow graphs, they then experimented with eliminating certain roads from the networks. Most roads increased the POA when cut, but 6 out of the 246 roads in the Boston network actually reduced the POA when cut. Similar results were obtained with the networks of London and NYC. So it seems that as a general rule of thumb, removing roads does increase delays, but there are certain roads for which the reverse is true. (One wonders if these roads have anything in common.)

One severe limitation of these results is that they were obtained by considering only travel from one origin to one destination. The authors claim that they remain robust for several origin/destination combinations, but it is nevertheless the case that for any one simulation, the costs are calculated by assuming that all drivers are going from a common origin to a common destination. In a real city, other directions of travel have to be thrown into the mix, and it’s not clear that similar effects will necessarily be found then.

Cute results, but why did this paper appear in PRL? At the end, the authors suggest possible applications to systems like electrical circuits, which have to satisfy Kirchoff’s Laws but do not necessarily minimise the dissipated energy in the process. They point to a couple of papers which show that removing wires can increase the conductance of a circuit.

References:
Cohen, J. E. and P. Horowitz (1991). Paradoxical behaviour of mechanical and electrical networks. Nature 352 (6337), 699-701.
Penchina, C. M. and L. J. Penchina (2003). The braess paradox in mechanical, traffic, and other networks. American Journal of Physics 71 (5), 479-482.
Youn, H., M. T. Gastner, and H. Jeong (2008). Price of anarchy in transportation networks: Efficiency and optimality control. Physical Review Letters 101 (12).

Label one end of a straight line 0, and the other end 100. Ask a person to place the number 10 at some point along the line. Where would the person choose to place the number 10?

This study finds that while Western adults tend to place small numbers at the ‘correct’ position along the scale (in the above example, that means 1/10 of the way to 100 starting from the 0 end), the relatively uneducated and uncontaminated (by Western civilization) members of the Amazonian Mundurucu tribe tended to place 10 about halfway between 0 and 100. And Westerners tend to do similar things with large numbers — they tend to place it much ‘higher’ up the scale then we’d expect if we mapped the number line linearly to the spatial line. Remarkably, this systematic ‘error’ is found to closely resemble a log relationship. It’s also been known for some time that children in Western countries commit the same ‘error’.

To eliminate the possibility that the error is caused by some special characteristic of the representation of the stimuli, the researchers repeated the experiments with varying kinds of stimuli — with numbers presented in the subjects’ native language, in the subjects’ acquired language, in pictorial form, etc. The log relationship remained. So came the tempting conclusion that this is in fact an innate characteristic, and Western adults fail to display it for small numbers only because they have been schooled to place numbers linearly along a spatial line (the schooling tends to use examples involving mostly small numbers, so they fall back on their logarithmic intuitions for large numbers).

A possible explanation for this log relationship is the ‘compressed numerosity code’ the brain uses for mental arithmetic:

Research on the brain mechanisms of numerosity perception have revealed a compressed numerosity code, whereby individual neurons in the parietal and prefrontal cortex exhibit a Gaussian tuning curve on a logarithmic axis of number (27). As first noted by Gustav Fechner, such a constant imprecision on a logarithmic scale can explain Weber’s law—the fact that larger numbers require a proportional larger difference in order to remain equally discriminable. Indeed, a recent model suggests that the tuning properties of number neurons can account for many details of elementary mental arithmetic in humans and animals (21). In the final analysis, the logarithmic code may have been selected during evolution for its compactness: Like an engineer’s slide rule, a log scale provides a compact neural representation of several orders of magnitude with fixed relative precision.

Reference:
Dehaene, S., V. Izard, E. Spelke, and P. Pica (2008, May). Log or linear? distinct intuitions of the number scale in western and amazonian indigene cultures. Science 320 (5880), 1217-1220.

A new paper in Nature Neuroscience follows Benjamin Libet’s pioneering experiments in showing that the brain makes decisions before the mind occupying it is aware that a decision has been made. The experimenters had subjects decide to press either a left or right button. They found two brain regions that encoded ahead of time whether the subject was going to press the left button or the right button. This encoding could take place up to ten seconds before the subject made his/her conscious decision.

C. S. Soon, M. Brass, H, Heinze, J. Haynes. Unconscious determinants of free decisions in the human brain. Nature Neuroscience. Published online: 13 April 2008 | doi:10.1038/nn.2112

In this experimental paper, Acar et al find that yeast cells that have been engineered to randomly switch phenotypes at a faster rate fare better in quickly changing environments, whilst yeast cells engineered to randomly switch phenotypes at a slower rate fare better in more slowly changing environments. They construct a population dynamics model that verifies that fast-switchers have a higher fitness than slow-switchers in rapidly fluctuating environments, while slow-switchers have a higher fitness than fast-switchers in more static environments. The only difference between the fast- and slow- switchers in their model is the transition rates between the two alternative phenotypes available, suggesting that the difference in transition rates is responsible for the trend they found in their experiment. The differences in growth rate, both experimental and theoretical, are easily seen in the following graphs:

In figures (a) and (b), the model predictions are represented by the solid lines, while the experimental findings make up the data points.

The authors interpret their findings as an example of risk management by yeast populations:

Our data suggest that tuning phenotypic switching rates may constitute a simple strategy to cope with fluctuating environments. Following this strategy, an isogenic population would improve its fitness by optimizing phenotypic diversity so that, at any given time, an optimal fraction of the population is prepared for an unforeseen environmental fluctuation. The diversity is introduced naturally through the stochastic nature of gene expression, allowing isogenic populations to mitigate the risk by ‘not putting all of their eggs in one basket’.

Citation:
Acar, M., J. T. Mettetal, and A. van Oudenaarden (2008, April). Stochastic switching as a survival strategy in fluctuating environments. Nat Genet 40 (4), 471-475.

Now you have an excuse for why you can’t seem to stay on a diet. If this paper is right, the drop in blood glucose levels caused by dieting erodes your self-control and increases the likelihood, as your diet progresses, that you fail to follow it.

The authors designed nine different experiments to test each of the following hypotheses:

1. Completing a task that requires self-control causes a relatively larger drop in blood glucose levels as compared to completing a task that requires no self-control.
2. Low glucose levels after a self-control task impairs performance on further self-control tasks.
3. Impairment of self-control by previous exertion of self-control can be counteracted by dosages of glucose (but not by dosages of a non-glucose placebo).

All three hypotheses were confirmed. Now, it may not seem particularly surprising or significant that blood glucose levels affect self-control. All brain processes require glucose, and if self-control is a brain process, of course it’d require glucose. What is significant is that self-control apparently requires a substantial amount of glucose. So it’s not true that “it’s all in the mind” — sometimes physical factors can weaken your willpower. Nevertheless, some experiments revealed that some people were more depleted than others in their self-control after going through the same tasks, suggesting that differences in personality could be partly responsible for self-control.

Reference:
Gailliot, M. T., R. F. Baumeister, C. N. DeWall, J. K. Maner, E. A. Plant, D. M. Tice, L. E. Brewer, and B. J. Schmeichel. 2007. Self-control relies on glucose as a limited energy source: willpower is more than a metaphor. J Pers Soc Psychol 92(2):325-336.

Just read a speculative commentary by Stephen Stearns on whether the human species is ’stalled’ in a possible transition towards group-level selection as the dominant selective force.

First, Stearns makes the case for the existence of such a transition. For non-social animals, selection happens mostly at the individual level: traits of individuals are selected for/against on the basis of their costs/benefits (in terms of individual fitness) to the individuals possessing them. As [the ancestors of modern] humans became more social animals and began living and dealing in groups, group-level selection grew in importance. At first, most group-level selection would be really ‘just’ kin selection on groups of kin. But with the advent of language and hence culture, group-level selection was further strengthened by the possibilities of cultural evolution and gene-culture coevolution, and it became possible (probable?) for group selection to occur without kin selection ‘underlying’ it. (There is of course some controversy over whether all cases of group selection are ‘really’ ‘just’ cases of kin selection.^{2, 3}) The giants of the selective units are nations, whose members can and often are punished for not obeying the norms of the group, who can expand by assimilating new members, who compete with other nations for new members, and so on.

The problem with current social groups, though, is that it’s not clear that biological-cultural evolution on a group level can occur effectively with them. And, Stearns suggests, it’s due to modern changes in society that group selection may not be as strong in humans as it used to be (granting the already controversial claim that it was strong at some point). Stearns provides the following reasons to doubt the strength of group selection in modern human societies:

1. The increasing lack of coincidence between biological groups and cultural groups — humans increasingly belong to social groups that contain a biologically diverse mix of other humans.
2. With globalization, the weakening of the contrast between in-group and out-group mentalities — we are less likely to see people in other groups (biological or social) as ‘the other’ and hence less likely to respect group divisions in our social behaviour.
3. Per his earlier argument, the groups involved in selection became larger (culminating in the nation-state), and larger groups undergo less frequent selection events, so selection on them will proceed at a slower rate.

Stearns admits that the scenario he sketches is “not yet up to the standards used in evolutionary biology”. However, he thinks we should let it have “a good shot at attaining rigor, for if it does capture a significant piece of reality, it would tell us something very important about what we are, and it might help to explain major features of our history and politics.” I at least find his preliminary sketch quite plausible, but as Stearns himself admits, there are numerous difficulties in finding empirical evidence for it.

1. Stephen C. Stearns. Are we stalled part way through a major evolutionary transition from individual to group? Evolution, Vol. 61, No. 10. (2007), pp. 2275-2280.
2. Christine Taylor, Martin A. Nowak. Transforming the Dilemma. Evolution, Vol. 61, No. 10. (2007), pp. 2281-2292.
3. SA West, AS Griffin, A Gardner. Social semantics: altruism, cooperation, mutualism, strong reciprocity and group selection. Journal of Evolutionary Biology, Vol. 20, No. 2. (March 2007), pp. 415-432.

At first sight it might seem that pathogens have little to do with polygyny. But anyone who knows the ‘Red Queen’ theory can probably guess the link between the two. In brief, the Red Queen hypothesis suggests that sexual reproduction provides a major evolutionary advantage due to its incorporation of recombinations of two different genomes in order to form the offspring genomes. The diversity of genomes made available through the recombination process makes it difficult for pathogens to ever adapt optimally to the host organism, since with each new generation the host organisms generate offspring with genomes significantly different from its own. As this paper investigating a possible link between pathogen stress and polygyny says, “The greater the pathogen stress, the greater is the advantage to the production of variable offspring.”

Thus the authors of that paper hypothesize that populations under high pathogen stress (as measured by the extent of the pathogen’s presence in the population — e.g. absent, present but not common, widespread) would tend to have higher rates of polygyny than populations under lower pathogen stress. This is because polygynous reproduction leads to greater variability in offspring than monogamous reproduction — instead of the same two genomes recombining, one recombines one’s genome with a more genetically diverse set of partners. The implicit assumption is that polygyny is an adaptation towards high pathogen stress. A secondary hypothesis is that high pathogen stress has an inverse correlation with sororal polygyny — polygyny in which sisters share a husband. Because sisters share about half of their genes, sororal polygyny would give rise to less genetic variability in offspring than non-sororal polygyny, so for maximal adaptation to high pathogen stress, societies should move towards non-sororal polygyny.

Finally, the authors also test a hypothesis that has less to do with the Red Queen hypothesis and more to do with theories about sexual selection. W. D. Hamilton and Marlene Zuk proposed the following explanation for sexual dimorphism: Male secondary sexual characteristics are ’signalling tools’ that tell females how healthly a potential partner is. For example, a cock’s red crest could be an indicator of how resistant to parasites the cock is —- cocks with less vivid crests are more likely to be suffering from parasite infections. In this view, sexual dimorphism could well be ’caused’ by sexual selection under conditions of pathogen stress. It is plausible, therefore, that higher pathogen stress correlates with higher sexual dimorphism — the more effect pathogens have on an organism’s reproductive fitness, the more important it is to pick mates with high resistance to pathogens, and the more useful secondary sexual characteristics are as a signalling tool (and accentuated secondary sexual characteristics make for clearer signals). Biologically, humans have little sexual dimorphism. The author postulated that sexual dimorphism in humans comes in the form of socio-economic gaps — males tend to have higher incomes and hold higher ranks in society than women do. So sexual dimorphism in human societies was measured by the gender gap in socioeconomic status.

The author measured levels of polygyny in 186 societies in the Standard Cross-Cultural Sample, using four different measures of polygyny. The first two hypotheses were confirmed: Pathogen stress in a society correlated positively with polygyny and with non-sororal polygyny relative to sororal polygyny. It is well known, though, that populations in the tropics tend to be under higher pathogen stress. To rule out the possibility that polygyny simply correlates with tropical climates, the author considered marriage trends in tropical areas only, and still found a significant positive correlation between pathogen stress and polygyny.

The last hypothesis, however, was not confirmed. Little or no correlation was found between sexual dimorphism (gender gap in socioeconomic status) and pathogen stress. This could suggest that socioeconomic status, unlike bright feathers in birds, is a poor signal for resistance to parasites.