Getting by in a Game without Winners

A time-honored tradition for choosing teams, riding shotgun, and settling other childish disputes, the game called rock-paper-scissors has been around far longer than humans have been playing it.

By | April 11, 2005


A time-honored tradition for choosing teams, riding shotgun, and settling other childish disputes, the game called rock-paper-scissors has been around far longer than humans have been playing it. Similar nontransitive games, in which no one strategy reigns over all others, are played out among certain lizards, microbes, and marine organisms. And some biologists are suggesting that, rather than being a mere biological oddity, the rock-paper-scissors dynamic is a widespread phenomenon that maintains genetic diversity within species and ecosystems.

"If the environment underlying the system is homogeneous, intuition would suggest there's going to be a good competitor that drives out all the others," says Ben Kerr, research associate at the University of Minnesota. "In rock-paper-scissors, the system itself has all the cogs and gears to generate diversity."


In California, rock-paper-scissors is played out between three male morphs of the side-blotched lizard, which are distinguished by their throat colors. Big, testosterone-pumped, orange-throated males beat up on their smaller, blue-throated rivals, who in turn dominate the smallest, yellow morph. So far, so transitive. But, by mimicking the female of the species, yellows escape the attention of oranges and get to poach the real females attracted to the oranges' spacious territories.

"Selection [tends] to push a species towards one nice little tidy optimum," says Barry Sinervo, professor of biology at the University of California, Santa Cruz, who described the lizard's nontransitive competitive dynamic in 1996.1 But the genetic, behavioral, and morphologic differences among the three morphs are on a par with those found between species, he says. Rock-paper-scissors "takes a species and stretches it out."

Kerr works on a similar game played out on the microscopic scale between strains of Escherichia coli living in rodent intestines. Certain strains produce toxins called colicins, which they release explosively, killing sensitive competing strains while sparing resistant clonal relatives. A third strain produces no colicins, but is resistant to those produced by others.

The respective costs associated with colicin resistance and production result in a linear growth hierarchy: In the absence of competitors, sensitive strains grow faster than resistant ones, and these outgrow producers. But in a mixed population, toxin producers loop the hierarchy by killing off those at the top.

Just as playing scissors would be the optimal strategy in the human version of the game if most of the competition played paper, the selective advantage to each bacterial strain or male lizard morph depends on the relative frequencies of the other two strategies. The result is a cycling in the densities of the three strategies.

<p>TURF WARS:</p>

© 2002 Nature Publishing Group

Plate environments were initiated by depositing small droplets from pure cultures in a randomly assigned hexagonal lattice pattern for colicin producers (C), resistant strains (R), and sensitive strains (S). The changing spatial configuration is shown at left. C cells being less dense are easily distinguished from S and R patches. So-called chasing between clumps is highlighted on the right hand panels. (From B. Kerr et al., Nature, 418:171–4, 2002.)

For E. coli, this dynamic has been demonstrated in silico2 and on agar plates,3 where patches of the three strains chase each other around in ecological time, snatching territory from one competitor while losing ground to the other. In the bacterium's natural habitat, the mouse gut, these chases occur between the dominant strains living in different mice. Strains are transmitted during social contact between mice, resulting in a cycle of colonization and displacement of different strains within individual animals.4

Kerr says these studies demonstrate the importance of a spatially structured population in maintaining the existence of all three players in the game. Colicins are persistent, potent compounds, produced in huge numbers by individual bacteria. "When you mix everything up, the sensitive guys just drop out of the system, and then you are just left with resistant and colicinogenic types," he says. "If you're left with just rock and paper, you have a fair idea of which is the best strategy." Spatial structure provides refuges where strains can persist out of reach of their respective nemeses.

It is the nontransitive interactions between the strains that allow all three to be maintained in an otherwise homogeneous environment, says Kerr. "Rocks do have a place; it's right next to scissors. And scissors have a place, wedged up against paper. They are each others' niches."

By itself, a single game of rock-paper-scissors has a modest impact on microbial diversity. Kerr says, however, that multiple strains of E. coli produce many different colicins, providing the potential – supported by computer simulations – for a network of interlacing rock-paper-scissors games, and therefore a significant, cumulative effect on diversity.



Courtesy Barry Sinervo

The three male morphs of the side-blotched lizard (Uta stansburiana). Morphs are determined by a gene complex that influences behavior and physiology as well as morphology. Aggressive orange males (top) dominate blues (middle), which cooperate to exclude the diminutive female-mimicking yellows (bottom). Yellows close the competitive circle by mating sneakily with females attracted to the oranges' spacious territories

Sinervo and Kerr both expect rock-paper-scissors to be more widespread than is currently recognized. Kerr points out that toxins analogous to colicins are produced by almost every major lineage of bacteria and that evidence exists for similar compounds in yeasts.

Sinervo has recently identified rock-paper-scissors in a second lizard species that has been separated from its side-blotched cousin for an estimated 135 million years. "Either the rock-paper-scissors game is that ancient, or it is a system that evolves quite easily," he says.

Indeed, he suspects that nontransitive systems are "all over the place." They're just harder to see. Unlike his lizards, with their conspicuous throat colors, "the vast majority of mammals are playing their games in an olfactory [dimension] that we, to all intents and purposes, have abandoned," he says.

Sinervo says a search of species that undergo population density cycles, for example, microtine rodents, might prove fruitful. "There should be these alternative male strategies that do well under different density conditions."

But both researchers are looking beyond individual species for rock-paper-scissors. "This need not play out within the same species," says Kerr. "It can play out between different species." He explains: "As long as you've got a toxin producer, as long as you've got resistant and sensitive types, and as long as there are ordered growth rates, then you have the potential at least for nontransitivity." The requirement for spatial structure points to systems of sessile organisms, or those with low dispersal rates, as the likeliest candidates.

Kerr cites a paper from 1979, which revealed nontransitive patterns of dominance within a community of encrusting marine organisms competing for space on coral reef substrates.5 It is intriguing, he says, that many of these organisms, which include corals, algae, sponges, ascidians, and ectoprocts, are known toxin producers.

In another scenario, allelopathic compounds manufactured by certain plants hamper the growth of competitors. Ragan Callaway of the University of Montana, who works on the role of allelopathy in biological invasions of introduced species, is impressed with the idea. "It really does set up a lot of potential for nontransitive effects being powerful in terms of really maintaining coexistence and diversity in systems."

But Alastair Fitter of the UK's University of York cautions that allelopathy itself is poorly understood. "There are one or two classic cases that seem to be well established," he says, but the general importance of allelopathy in plant ecosystems remains to be established.

Kerr also sees an analogy between the bacterial system and the ecology of fire-prone habitats such as California's chaparral and South Africa's fynbos, where certain plants have bizarre traits – the retention of dead branches, for example, or volatile leaf compounds – that enhance their flammability. "Plants might become more flammable in order to fend off more sensitive competitors," he says. He notes that many such plants have elaborate mechanisms for persisting through fire events (akin to colicinogenic E. coli being resistant to their own toxins), while other species (such as the third player in the colicin system) are not flammable but are fire-adapted. "This is very tentative," says Kerr. And empirical studies could prove problematic, he says: "People don't take too kindly to you lighting matches in the chaparral."


Considerable obstacles hamper the study of such ecological processes in long-lived organisms over multiple generations. "It's rather easier to construct a realistic microcosm experiment in a microbial system than to recreate a plant system, which is based on soil," says Fitter. "Controlling the biochemistry of that is extremely difficult."

Kerr maintains that the importance of nonhierarchical relationships is currently underappreciated. "I think there's probably a lot out there that is straight hierarchies," he says. "Whether [rock-paper-scissors] still make up a minority after the tallying is done, that's another issue."

And if nontransitive competition turns out to be common, then so might some counterintuitive evolutionary dynamics. Says Kerr: "In a nontransitive world, an organism is basically taking out the enemy of its enemy by being a better grower." This, he says, leads to a phenomenon that has been dubbed "survival of the weakest," in which selection can favor types that exercise some form of restraint in their competitive impact on others.6"If A slows down, that liberates B to take out C, which liberates A," he explains. "That makes this something that really is important rather than just being something that's kinda cute," says Callaway.

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