It is not surprising that games as absorbingas bridge and chess have their world feder-ations and international unions. But not

everyone knows that even a game as lowly asrock–paper–scissors has its own society. Thisgame, which must surely be very old, can beexplained to any toddler. Two players signal,on a given cue, either rock (fist), paper (flathand) or scissors (two fingers). If I display aflat hand and you show me your fist, I win,as ‘paper wraps rock’. Similarly, scissors cutspaper, and rock smashes scissors. If bothplayers make the same signal, the game endsin a draw. And in case you think of it as arather simple-minded pastime, you shouldtake a look at the home page of the WorldRPS Society1, which is a treat. Among otherfeatures there are links to learned papers,although you are advised not to visit the linksin the probabilistic section, filled as it is with“pseudo-scholastics”. No such ban appearsagainst the link to a paper in Nature describ-ing three mating strategies of the male lizardUta stansburiana2. And now Nature should

hit the website again, with the report by Kerrand colleagues on page 171 of this issue3.

Kerr et al.3 set out to investigate themechanisms that maintain biodiversity inecosystems, by studying several diversestrains of Escherichia coli bacteria. Thesestrains can produce a toxin, or not; and theycan be resistant to the toxin, or not. We mayassume that the bacterial devices for pro-ducing both the toxin and the ‘antidote’ that confers resistance are costly in the sensethat they require resources that could other-wise have been used by the bacteria tomultiply faster.

There are four potential strains. The oneproducing the toxin but not the antidoteeffectively commits suicide. This strain is anon-starter, and we may ignore it (as didKerr et al.). The other three are engaged in arock–paper–scissors type of competition.The poison- and antidote-producing strainkills that which produces neither poison norantidote. The strain that produces the anti-dote but not the poison outgrows the one

that produces both, by economizing on thecost of an ineffective poison. And in theabsence of the toxin-producing strain, thestrain that produces no antidote outgrowsthe antidote-producing type, which is payingfor an unneeded device.

These two-way bacterial interactionshave been described previously. And similarrock–paper–scissors cycles of spiteful mea-sures and costly countermeasures occur inother evolutionary contexts, for instance inthe genetics of sexual species. Some chromo-somes acquire mutations that prevent theiropposite number (inherited from the otherparent) from making their way into eggs orsperm, and so to the next generation. Someof these mechanisms for subverting the fairsegregation of chromosomes act like thebacteria, by means of a poison-and-antidote-type principle4.

But what happens when the three E. colistrains are all in the same environment?The mere knowledge that the outcomes ofpair-wise competition form a rock–paper–scissors cycle is not enough to predict whathappens when all three types are present5,6.The three competitors might co-exist per-manently; this seems to apply, for instance,to the male lizards that have three differentmating strategies2. Or one type might beousted, and a second type outcompeted bythe third, leading to just one survivor. Kerret al. find that this latter outcome holds forour bacteria. If all three strains are equally

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Biodiversity

Bacterial game dynamicsMartin A. Nowak and Karl Sigmund

Studies of three bacterial strains engaged in an interaction that mimics thegame ‘rock–paper–scissors’ show the importance of localized interactionsin maintaining biodiversity.

Since its introduction more than 20years ago, the catalytic converterhas sharply reduced automotiveemissions. Using catalysts containingpalladium, platinum and rhodium,a converter breaks down harmfulcarbon monoxide, nitrogen oxidesand hydrocarbons before the exhaustleaves the car’s tailpipe. But theseprecious metals are expensive andare produced through the intensiveand polluting chemical processing ofsulphide ores extracted from oftentreacherous underground mines.

On page 164 of this issue, YasuoNishihata et al. (Nature 418,164–167; 2002) propose a newcatalyst for automotive-emissionscontrol that lasts longer andaccomplishes its task moreeffectively than conventionalcatalysts. The material, a perovskitecontaining small amounts ofpalladium (Pd), could reduce by70–90% the amount of preciousmetals needed to meet today’scar emission standards.

Catalytic converters consist of ahighly porous ceramic structurecoated with finely divided catalyticmaterial. To ensure immediate actionwhen the car is started, convertersare placed close to the hottest part ofthe car, the engine. Over time, heatexposure causes the tiny particles ofprecious metal to agglomerate, thusreducing the catalyst’s overallsurface area and hence its activity.To counter this effect, conventionalcatalytic converters are loaded withan excess of precious metal,ensuring that performance targetsare met for vehicle use over theexpected range, usually 80,000 km.

Nishihata et al. demonstrate thatexcess-metal loading is not neededif the perovskite LaFe0.57Co0.38Pd0.05O3

is used as the catalyst. This material,first investigated for catalytic-converter applications in the 1970s,maintained its high metal dispersionand high catalytic activity during a100-hour test in engine exhaust.In the same test, the activity of aconventional catalyst (aluminaimpregnated with palladium)decreased by 10%.

The resilience against metal-particle agglomeration results fromthe perovskite’s ability to respondstructurally to the fluctuations in

exhaust-gas composition that occurin modern petrol engines. Thesefluctuations switch the exhaustenvironment continuously from anoxidizing to a reducing atmosphere.In separate tests, the authorsestablished that Pd is firmlyincorporated into the perovskitelattice of the oxidizedLaFe0.57Co0.38Pd0.05O3 catalyst (seefigure, left). But the Pd atom (red)moves out of the structure, beingreplaced by an iron atom (blue), inthe reduced material (see figure,right). It is this fully reversiblehopping of Pd into and out of theperovskite structure that seems tosuppress the agglomeration of themetal and thus the slow deactivationof the catalyst.

Although catalytic convertershave already made a significantcontribution to emissions control,Nishihata et al. show that more can still be done to address theenvironmental impact of car use.

Magdalena Helmer

Chemistry

Cleaning up catalysts

138 NATURE | VOL 418 | 11 JULY 2002 | www.nature.com/nature© 2002 Nature Publishing Group

frequent at first, the type producing antidotebut no poison eliminates the others.

Kerr et al. also show, however, that thisloss of diversity occurs only if the bacterialpopulations are well mixed. Otherwise, allthree strains survive. This conclusion hasbeen predicted on paper: a rush of theoreti-cal investigations during the past decadehas shown, in great generality, that if dis-persal of a population is limited and itsinteractions with other populations arelocalized, then diversity is protected to alarge degree7,8. This holds for an astonishingvariety of scenarios, for instance in epi-demiological models, community ecology,plant genetics, animal behaviour, molec-ular evolution9 and game theory10. Suchspatial models are usually much harder toanalyse than their homogenized ‘meanfield’ counterparts. But computer simula-tions warn us that, in many cases, ‘meanfield’ can lead to wrong conclusions.

And Kerr and colleagues are not the firstto show that localized interactions of therock–paper–scissors type can turn a ‘onewinner’ outcome into a dynamic coexistenceof all three types, endlessly chasing eachother across the board11. The beauty of theirpaper is that they show this not only on acomputer screen, but also in ‘real life’. To setup the well-mixed case, the authors put allthree strains in a flask, shake this cocktail,transfer a few drops to another flask, shake itagain, and so on. Soon the flasks contain onlythe resistant, non-toxic strain. To ensurelocalized interactions, on the other hand,Kerr et al. spread the strains on a plate to letthem grow, then press a cloth on the plate,transfer whatever clings to the cloth ontoanother plate, and so on. All three strainssurvive, with the boundaries between themshifting to and fro, reflecting the cyclic inva-sion and displacement of one strain by thenext. So the outcomes on the plate and in theflask are strikingly different.

This approach opens new vistas forunderstanding how biological communitiesare built up — one of the most intriguingaspects of the study of biodiversity. Theresults of sequential invasions and extinc-tions of species can create complex links andwebs in an ecosystem, not least because theoutcome of an invasion depends so muchon its timing and other contingencies.Large-scale experiments in communityconstruction are generally hard to come by— not often do volcanic rocks emerge, pro-viding barren ground for colonization. Soecologists have increasingly turned, sinceG. F. Gause’s work in the 1930s, to manipu-lating mini-worlds inhabited by microbialspecies12. The paper by Kerr et al. gives anew impetus to such investigations, bystressing the importance of the geometry ofneighbourhoods. Many habitats resemblethe surface of a pizza more than a well-stirredbowl of soup. ■

Martin A. Nowak is at the Institute for AdvancedStudy, Princeton, New Jersey 08540, USA.e-mail: nowak@ias.eduKarl Sigmund is at the Institut für Mathematik,Universität Wien, Strudlhofgasse 4, A-1090 Vienna,and the Institute for Applied Systems Analysis, A-2361 Laxenburg, Austria.e-mail: karl.sigmund@univie.ac.at1. http://www.worldrps.com/archive/index.html

2. Sinervo, B. & Lively, C. M. Nature 380, 240–243 (1996).

3. Kerr, B., Riley, M. A., Feldman, M. W. & Bohannan, B. J. M.

Nature 418, 171–174 (2002).

4. Hartl, D. L. The Principles of Population Genetics (Sinauer,

Sunderland, Massachusetts, 1980).

5. Hofbauer, J. & Sigmund, K. Evolutionary Games and Population

Dynamics (Cambridge Univ. Press, 1998).

6. Weissing, F. J. in Game Equilibrium Models I (ed. Selten, R.)

29–96 (Springer, Berlin, 1991).

7. Durett, R. & Levine, S. Theor. Pop. Biol. 46, 363–394 (1994).

8. Dieckmann, U., Law, R. & Metz, J. A. J. (eds) The Geometry of

Ecological Interactions: Simplifying Spatial Complexity

(Cambridge Univ. Press, 2000).

9. Boerlijst, M. C. & Hogeweg, P. Physica D 48, 17–28 (1991).

10.Nowak, M. A. & May, R. Nature 359, 826–829 (1993).

11.Nowak, M. A., Bonhoeffer, S. & May, R. M. Int. J. Bifurc. Chaos

4, 33–56 (1994).

12.Weatherby, A. J., Warren, P. H. & Law, R. J. Anim. Ecol. 67,

554–566 (1998).

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NATURE | VOL 418 | 11 JULY 2002 | www.nature.com/nature 139

Making decisions on the basis of socialcues is an everyday challenge forhuman beings — and for our cells.

On page 200 of this issue, for instance, Brownand colleagues1 describe how predatoryimmune cells decide whether or not to eatother cells on the basis of a molecular‘handshake’.

This decision is made in the context of theprogrammed deletion of cells, or ‘apoptosis’,that is an essential feature of embryonicdevelopment, tissue organization and cellturnover in multicellular organisms2,3. Theprogramme basically consists of two tightlycoupled events, the death of cells and theirburial — or rather, their consumption by the

body’s professional predators, immune cellsknown as phagocytes. Three keywordsgovern the burial rite4: swiftness, because nocellular corpses are allowed to linger around;efficiency, because the day-to-day burden ofdead cells is enormous; and discretion, toprotect the surrounding environment fromharm. But between death and burial liesdecision-making: how do phagocytes dis-criminate between dead or dying cells andtheir healthy neighbours?

It is generally accepted that the onset ofthe death programme makes cells appetizingbecause it exposes attractive ‘eat me’ signals5.These involve changes in the cell surface,which can be tracked experimentally by the

Apoptosis

Repulsive encountersGiovanna Chimini

In multicellular organisms, cells are often required to die. They are theneaten by ‘phagocytic’ cells. But how do the phagocytes distinguishbetween dead and living prey? New work provides an unexpected answer.

Figure 1 To eat or not to eat? In vertebrates, predatory macrophage cells continuously meet potential‘prey’ and make contact with them through their respective CD31 proteins. a, When the target cellsare healthy and viable, ‘outside-in’ signalling is triggered, probably involving the modification oftyrosine amino acids in the intracellular tail of CD31 with phosphate (P-Tyr), and interaction withthe proteins SHP-1 and SHP-2. This results in ‘inside-out’ signalling, repelling the macrophage.b, When the target cells are dead or dying, outside-in signalling through CD31 is disabled and theinteraction with the macrophage persists. This assists definitive recognition of the dying prey byspecialized engulfment receptors on the macrophage.

?

SHP-1 SHP-2

TyrP-Tyr

Signalling

CD31

RepulsionNo

signalling

Engagement ofengulfment receptors

'Eat me'signals

Macrophage

Dying cellLiving cella b

© 2002 Nature Publishing Group