which is simpler than the exact Hamiltonianbut is still a good model.

The quantum energy–momentum latticeof the molecule consists of the eigenstates ofthis Hamiltonian, that is, the pure vibra-tional modes.For a fixed energy,these modescorrespond to two classical ‘constants ofmotion’ — angular momentum and a quan-tity related to the rotational symmetry. Theeigenstates can be characterized by twoquantum numbers, which are integers, sothese eigenstates form a regular planar latticelike a chessboard.

However, there is an extra quantum number, related to another classical variable,called the ‘action’. The new phenomenon

has been no well-controlled evidence thatanimals actually use transitive inference insocial situations. In the study reported onpage 778 of this issue, Paz-y-Miño and col-leagues2 provide this.

In effect, the authors staged the Andy-and-Bob scenario using pinyon jays (Gym-norhinus cyanocephalus; Fig. 1), a highlysocial member of the crow family. Thesebirds live in large, permanent flocks withclear pecking orders. Paz-y-Miño and col-leagues created groups of captive pinyon jaysthat were previously unknown to each other,and allowed stable dominance relationshipsto develop in each group. Then jays fromeach group were allowed to observe individ-uals from other groups interacting over apeanut, and later interacted with some ofthose same birds. In the experiment, theobserver saw a relatively dominant bird from

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732 NATURE | VOL 430 | 12 AUGUST 2004 | www.nature.com/nature

Cognitive science

Rank inferred by reasonSara J. Shettleworth

Pinyon jays seem to work out how to behave towards an unfamiliar jayby watching it in encounters with members of their own flock. Thefindings provide clues about how cognition evolved in social animals.

Susan is taller than Billy. Peter is tallerthan Susan. Who is taller, Billy orPeter? Knowledge about pairs of

objects linked by relationships such as ‘taller’or ‘stronger’ permits conclusions to bedrawn about novel pairs (here, Billy andPeter) — a process known as transitive infer-ence.Monkeys, rats and some birds can solvetransitive-inference tasks in the laboratory1,but why would this ability evolve? A plausibleanswer is that transitive inference is an evolutionary adaptation in certain kinds ofsocial group. For example, suppose I knowfrom bitter experience that Bob always beatsme in contests (that is, he dominates me).I now observe some new individual, Andy,dominating Bob. If I reason, “Andy domi-nates Bob, and Bob dominates me, thereforeAndy will dominate me”, I can avoid fights bydeferring to Andy when we meet. But there

Figure 2 The swing–spring. The swing–springcan stretch like a spring and swing like apendulum (a), and can be used as a simple modelfor the carbon dioxide molecule (b).

100 YEARS AGOThe result of this inquiry is to prove theexistence of a small number of more or less isolated hereditary centres, round which a large part of the total ability of thenation is clustered, with a closeness thatrapidly diminishes as the distance of kinshipfrom its centre increases. The materials arederived from the replies to a circular which I sent with a blank schedule, to all fellows of the Royal Society, asking for the namesand achievements of their “noteworthy”kinsfolk in each degree of near kinship as specified in the schedule. Noteworthinesswas defined as including any success thatwas, in the opinion of the sender, at leastequal in its way to that in which the honourof a fellowship of the Royal Society is heldby scientific men. Returns are still droppingin, and now exceed two hundred. Theycontinue to be very acceptable, but I judged it best to content myself with thenumber received up to a date when I couldconveniently work at them, and to publishthe preliminary results without delay… the experience gained through this inquiry has strongly confirmed an opinionexpressed in my lecture on Eugenics beforethe Sociological Society… that it would beboth feasible and advantageous to make aregister of gifted families. Francis Galton

From Nature 11 August 1904.

50 YEARS AGOThe chromosomes of Mus musculus have a high chiasma frequency, and for thisreason very loose linkages are to beexpected. Many of the problems of linkageand independence in this species maytherefore have to be solved by cytogeneticmethods rather than the breeding techniquesof formal genetics. Among them is thequestion whether linkage group VII is carried in the pairing segment of the sexchromosome… With the object of obtainingevidence on questions such as this we haveinduced a number of translocations in themouse, using X-rays, and have identifiedlinkage groups in eleven of them…Translocation T 8 thus offers a means ofsettling the question whether linkage group VII is sex-linked. The translocationand the sex bivalent should be cytologicallyrecognizable in primary spermatocytes; itshould therefore be possible to establishtheir chromosomal independence orinterdependence. T. C. Carter, Mary F. Lyon

& Rita J. S. Phillips

From Nature 14 August 1954.

here is that, because of monodromy, theaction is defined only locally and cannot be consistently extended across the entirelattice. For fixed quantum numbers in thelattice, this additional quantum number cantake on infinitely many values, at equallyspaced points at right angles to the chess-board. The simplest structure of this kind is a three-dimensional cubic lattice — an infi-nite stack of chessboards, vertically aboveeach other. Monodromy implies that thetotality of all sets of quantum numbers doesnot form a cubic lattice. Instead, it has a sin-gle topological defect where the regularity ofthe lattice structure breaks down.

This analysis is important because it sug-gests, and supports, a general principle. Themost significant features of the quantum-mechanical description of a classical systemoccur at its singularities. The singularitiesintroduce defects into the ensemble of quan-tum eigenstates, but they also organize thestructure of those defects. Everywhere else,quantization works just as in previous, sim-pler examples. The authors suggest severaldirections for future progress, mostly to dev-elop the growing use of nonlinear dynamicsin the understanding of quantization. But the most tantalizing is the possibility ofdetecting quantum monodromy experimen-tally. Maybe we will soon be able to see howSchrödinger’s cat turns itself upside down. ■

Ian Stewart is at the Mathematics Institute,University of Warwick, Coventry CV4 7AL, UK.e-mail: ins@maths.warwick.ac.uk

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affect the health of an organism. Thisamount is determined in part by geneexpression — or how much messenger RNA(mRNA) is transcribed from the relevantDNA sequence — and the relative abun-dances of mRNA for many thousands ofgenes can now be routinely assessed for anyaccessible tissue. But gene expression is gen-erally regulated by DNA regions outside theparts of genes that actually encode proteins,and there is much that is not yet understoodabout this process. In particular, little isknown about how variation in DNAsequences might affect the variability inbaseline levels of gene expression amongindividuals — the topic of Morley and col-leagues’ investigations1.

Thus, their studies stand squarely at thecrossroads of some of the most challengingquestions in human genetics. Among themost pressing of these questions are:how can we identify regulatory elements?Does variation within regulatory elementshave the same frequency spectrum as the variation that occurs within genes and

On page 743 of this issue, Morley andcolleagues1 report how they success-fully determined the genomic loca-

tions of genetic determinants that influencethe variation in levels of gene expressionbetween people. How was this accom-plished, and why is it important?

In searching for the genetic basis of ameasurable trait, or phenotype — height oreye colour, for example — geneticists start by identifying people with variation in thattrait. In the simplest situations, the variationis traced to a single gene, and particular variations in the sequence of that gene areshown to determine the observed phenotypicvariation.

A less tangible, but no less significant,trait is the baseline level of gene expression.Much of our progress so far in understand-ing the basis of rare genetic diseases has come through identifying changes in genesequence that change the nature of theencoded protein, so that it is insufficiently orinappropriately functional. But changes inthe amount of protein produced might also

the experiences of captive animals can provide firm conclusions.

If transitive inference is used in social life,species with more complex societies shouldbe better at it. Laboratory studies using anabstract transitive-inference task providesome support for this idea. First, animals aretaught the relative reward value of five ormore pairs of colours7 — red is better thangreen, green is better than blue, and so on.Then they are tested with novel pairings.Monkeys behave in such tests as though theyare reasoning by transitive inference, where-as pigeons do not1. But this finding need notreflect a difference in sociality between mon-keys and pigeons because they differ in somany other ways. More relevant is a recentcomparison of pinyon jays with the closelyrelated, but less social, western scrub jay8.Pinyon jays perform more like monkeys inthe abstract task than do scrub jays.

Members of the crow family, such as NewCaledonian crows9, western scrub jays10 andravens,feature in recent reports of remarkablecognitive abilities including making andusing tools, episodic-like memory and formsof social learning. Each of these abilities isthought to reflect a species-specific adapta-tion, for example to extract prey or retrievestored food.Comparisons of different species

its own group (‘Bob’ in our scenario) losingencounters with a stranger from anothergroup (‘Andy’). To ensure that the strangerwould not be seen only to dominate others, the observer also watched the samestranger losing contests with anotherstranger. As a control, other observer birdswatched a stranger both winning and losingto members of the stranger’s own group, anexperience that should give observers noinformation on whether the stranger will beable to dominate them.

If pinyon jays infer social status transi-tively, observers should behave more sub-missively in their first encounter with thestranger in the experimental condition thanin the control — and this is what Paz-y-Miñoand colleagues2 observed. To act in this way,the observers must first have identified boththe individuals they watched and their rolesin the observed encounter, and then retainedthis information for later use. Thus, theirbehaviour implies a more complex set ofcognitive skills than that implied by anotherrecent report of birds’ sensitivity to a genericsocial relation (whether mated or not)between unfamiliar individuals present3.

It is noteworthy that the animals in thisstudy are birds. The idea that the demands of a complex social life might drive the evolution of cognition was originally pro-posed to explain the apparently high intelli-gence of monkeys and apes4. However, other mammals, such as hyenas and elephants,andsome birds also form long-lasting groups ofidentifiable individuals with differentiatedsocial roles. Long-term field studies indicatethat social complexity has shaped cognitionin a similar way across species5,6, but in fieldwork it can be difficult to know all the ani-mals’ relevant experiences. The experimen-tal approach of Paz-y-Miño and colleagues2

will serve as a model of how manipulating

Human genetics

An expression of interestNancy J. Cox

The baseline level of gene expression varies from person to person, buthow is this determined genetically? The answer may improve ourunderstanding of complex traits, including some genetic diseases.

Figure 1 Pinyon jays — watching and learning.

in similar tasks are necessary to test whethersuch abilities are in fact associated with theecological factors supposed to select for them.Nevertheless, such findings underline theimportance of viewing animal intelligence asconsisting partly of species-specific adapta-tions, rather than being an entirely undiffer-entiated ‘general intelligence’.So,comparativepsychology can provide experimental sup-port for the idea that cognitive modules haveevolved for solving different kinds of task —an idea so popular, but often untestable, inhuman evolutionary psychology5. ■

Sara J. Shettleworth is in the Departments ofPsychology and Zoology, University of Toronto,Toronto, Ontario M5S 3G3, Canada.e-mail: shettle@psych.utoronto.ca1. Shettleworth, S. J. Cognition, Evolution, and Behavior (Oxford

Univ. Press, 1998).

2. Paz-y-Miño C, G., Bond, A. B., Kamil, A. C. & Balda, R. P.

Nature 430, 778–781 (2004).

3. Vignal, C., Mathevon, N. & Mottin, S. Nature 430, 448–451

(2004).

4. Jolly, A. Science 153, 501–506 (1966).

5. Kamil, A. C. Trends Cogn. Sci. 8, 195–197 (2004).

6. de Waal, F. B. M. & Tyack, P. L. (eds) Animal Social Complexity

(Harvard Univ. Press, Cambridge, 2003).

7. McGonigle, B. O. & Chalmers, M. Nature 267, 694–696 (1977).

8. Bond, A. B., Kamil, A. C. & Balda, R. P. Anim. Behav. 65,

479–487 (2003).

9. Weir, A. A. S., Chappell, J. & Kacelnik, A. Science 297, 981

(2002).

10.Clayton, N. S. & Dickinson, A. Nature 395, 272–274 (1998).

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