Get best of the week

Biodiversity may have evolved from the principle of playing rock-paper-scissors

Recent discoveries add weight to evidence that non-transitive species competition enriches nature diversity



It seems that some species compete in a game similar to “rock-paper-scissors”, in which no species achieves long-term dominance. Perhaps this is one of the reasons why nature is able to sustain such rich biodiversity.

Pioneer of Synthetic Biology at UCSD University of California, Jeff Haesty, has been developing strategies over his 20-year career to enable the collaboration of genetic patterns in artificially created bacteria. But a few years ago, Haesty had to admit that even he could not fool the modest bacterium Escherichia coli.

Haesty had no problem creating useful, well-regulated genetic properties, or making them work in cells. It was just that easy. More difficult, he soon discovered, was maintaining these properties. If a cell needs to redirect part of its resources to make the desired protein, it becomes noticeably less viable compared to other cells that do not synthesize it. And inevitably, the cells acquired mutations that turned off the genetic schemes introduced into them, after which the mutants quickly replaced the original cells. As a result, the desired characteristic disappeared, sometimes in just 36 hours.

“The question is not whether it will disappear, the question is only in time,” said Haesty.

Over the years, Haesty has watched the E. coli mutations override all his so elegantly designed systems. However, last September, Haesty, his graduate student Michael Liao, and their colleagues published in Strategy Science a strategy designed to prevent even bacteria susceptible to this from mutating with “pressure from other germs,” as explained in the commentary on the article . The UCSD team used three artificial E. coli strains working together. Each strain produced a toxin, its corresponding antitoxin for self-defense, and another toxin to protect against the toxins of one of the other two strains. The first strain could kill the second strain, but not the third; the second could kill the third, but not the first; the third could kill the first, but not the second.

This circular antagonism meant that by sequentially adding strains of bacteria, researchers could maintain a high concentration of E. coli, ensuring that new toxins would mow unnecessary mutants. The environmental interaction of cells stabilized the system.


Michael Liao, Postgraduate Student in Biodynamics and Synthetic Biology at UCSD

The project was drawing to a close when Liao discovered that other scientists were already paying attention to such a strategy. Researchers in ecology and evolution have been trying for decades to understand whether it is an answer to one of the main questions in their fields: how does such a huge biodiversity survive in nature? However, if we put aside the scientific history, we can recall that this strategy is better known under the guise of a game that children around the world use to resolve disputes on playgrounds.

It's a rock-paper-scissors game, “a classic game in game theory and evolutionary theory,” said mathematical biologist Barry Sinervo of the University of California at Santa Cruz, whose study of spotted-sided iguanas helped determine their importance for ecosystems.

The rules of the game are simple: scissors defeat the stone, paper defeats the scissors, the stone defeats the paper. None of the players have an advantage, and the chances of winning are equal, regardless of the player’s choice. When playing together, there is always a clear winner. But when you add more players, the game becomes more complicated, and the success of various strategies often grows and falls cyclically.

Biologists studying the rock-paper-scissors game modeled the course of this game for many, sometimes hundreds of species. They also investigated the question of how it changes with the interaction of species on different landscapes, species with different mobility and the desire for competition. They found that playing over time perhaps allows species to coexist in the same place, cyclically changing the dominant species.

Scientists still determine the true importance of this game for living systems, but their discoveries may already affect the theory of evolution or understanding of environmental dynamics, biotechnology, conservation policies. “This is a universal game, which is damn convenient,” said Cinervo. “Rock-paper-scissors cover the entire biological universe.”

Fertility equations


When Charles Darwin published his theory of natural selection in 1859, he and his contemporaries hypothesized that competition between individuals is the driving force behind evolution. More than 150 years of experiments following his work have confirmed that competition is indeed the main driving force behind evolution. There is only one problem.

If simple competition was the only driving force of evolution, then in billions of years only a small number of very competitive species would remain. Instead, the planet boasts an amazing array of different kinds. The number of species is almost impossible to estimate; in one of the last attempts, a number of 2 billion was called , but earlier this number was estimated in the range of 10 millionup to 1 trillion . More than 6,700 species of trees and 7300 species of other plants live in the lowlands of the Amazon jungle - and these numbers do not even come close to the number of species of insects, mammals, fungi and microbes living there.

“We study the situation and see that thousands, even millions of species of microbes live on one hectare of forest,” said Daniel Maynard, an ecologist at the Swiss Federal Institute of Technology. “And whatever you do, they all survive.” It doesn’t happen that one species scatters all the others. ”

One of the first breakthroughs in explaining biodiversity happened when studying not ecology, but mathematics. In 1910, American biophysicist and statistician Alfred Lotkadeveloped a set of equations describing certain chemical reactions. By 1925, he realized that the same equations could be used to describe the cyclical changes in predator populations and their prey. A year later, the Italian mathematician and physicist Vito Volterra independently developed a similar set of equations.

Their work showed how the number of predators depends on the amount of prey. A similar idea may seem obvious, says Margaret Mayfield , an ecologist at the University of Queensland in Australia, but Lotka and Volterra equations were a breakthrough at the time — they gave ecologists a way to measure and model nature.

But the equations were still not perfect. They relied on useful, but simplified assumptions, and could not model the interaction between species that are not predators and prey for each other, but at the same time competing for resources.

Everything began to change in 1975, when mathematicians Robert May and Warren Leonard adaptedthe Lotka-Volterra classic equations to what ecologists call intransitive competition. When competition is transitive, it has a hierarchy: if A wins B, and B wins B, then A wins B as well, which makes A a winner in any competition. Non-transitive competition does not have such a hierarchy, B can defeat A in it. And instead of remaining the clear winner, A dominates for some time, then gives way to B, which gives way to B, followed by the revival of A.

May and Leonard In fact, they created math that describes rock-paper-scissors in ecology. Later, mathematicians expanded their work to show that an almost infinite number of species can participate in such nontransitive interactions.

Maynard suggested imagining this as a gladiator match. In the battle against an experienced fighter, the gladiator may lose. But if you take a group of 100 fighters, other defense options appear - for example, an alliance with a stronger fighter. Such a strategy can help him outweigh his competitors and become a winner.

Courtship games


In the 70s and 80s, scientists began to document real-life examples where the interaction of organisms living on coral reefs, as well as among the yeast strains Saccharomyces cerevisiae, obeyed the rules of the game stone-scissors-paper. Among the most famous studies was Cinervo's work on spotted-sided iguanas, published in Nature in 1996.


Male spotted-sided iguanas with a blue throat, like the one in the photo, come together to cooperatively protect their females. Other competitive species of these iguanas, with orange and yellow necks, use different strategies.

At first glance, the spotty-sided iguana ordinary lives up to its name. This is a small brown lizard the length of a person’s finger, the main distinguishing feature of which is the patterns on the back and the colored throat. However, the pairing of these iguanas is rather unusual. In 1990, Sinervo traveled to the very center of the spotted-sided iguanas, on the slopes of the California coastal ridge near the city of Merced. Sinervo studied for five years how iguana males convince their females to " swipe right " - and how they dare their rivals.

Sinervo knew that the mating strategy in males is determined by a colored spot on the throat. Orange-throated lizards are very competitive. They independently guard large harems of females and attack any males encroaching on their territory. Males with blue spots cooperate to protect the territory and females - such a strategy is more or less effective against orange. But on the other hand, it helps well against treacherous yellows, imitating the appearance of sexually mature females, and penetrating into the territory of oranges to mate there, without fear of competition.


Barry Sinervo, a mathematical biologist from the University of California at Santa Cruz

Sinervo noted that in the territory studied by him, each color dominated for a year or two, after which one of his rivals took up: blue gave way to orange, which gave way to yellow, which again gave way to blue. In some places there was only one color, but Sinervo never saw that only two colors lived together - one of them always completely replaced the other. But with three colors, dominance in the population was fluctuating. When Cinervo and colleagues later began writing down equations describing his observations, they soon realized that they were describing a type of rock-paper-scissors game.

Other natural examples of how this game guides evolution have been discovered. In the February issue of The American Naturalist for 2020, Sinervo and colleagues describeas this game explains the predominance of certain mating strategies among 288 species of rodents, and why monogamy, polygamy, or promiscuous relationships will prevail in certain species.

Nevertheless, observations of nature will not give us all the information. To understand in what environments the game of stone-scissors-paper between species occurs, and whether new equations can help explain biodiversity, scientists had to return to the laboratory.

Local environments change the game


The bacteria E. coli have a poor reputation as an intestinal inhabitant. However, over many years, microbiologists have identified hundreds of E. coli strains with different properties. In one family there is a group of Col genes that produce colicin toxin, as well as a protein that protects the bacterium itself. Some strains are sensitive to colicin, while others have mutations that make them immune to it. Resistant strains (known as R) grow faster than colicin-producing strains (C) because they do not have to spend resources on its production. Sensitive (S) strains can outperform R because protective mutations also disrupt the ability of cells to transmit nutrients. The ideal stone-scissors-paper situation arises in the system, since R defeats C, C defeats S, and S defeats R.

About two decades ago, Stanford University microbiologists forced these bacteria to play rock-paper-scissors in three different situations: in a flask where they were mixed; in a static Petri dish, where they were grouped, preventing movement; in a "mixed" environment, where they had a little more mobility. In a 2002 article for Nature, Benjamin Kerr (now working at the University of Washington), Brendan Bohannan (now working at the University of Oregon) and their colleagues found that in the flask and in the mixed Petri dish strain R quickly won over groups S and C.

However, everything went differently in a static Petri dish. When Kerry Bohannan analyzed the photographs of the bacterial colonies growing in it, they saw a drawing of stone-scissors-paper in places where different strains were in contact. These results showed that the local environment plays a critical role not only in the emergence of the rock-paper-scissors situation, but also in the subsequent emergence and maintenance of biodiversity, explained Stefano Allesina , an ecological theorist at the University of Chicago.

Allesina said he was “shocked” while reading this work as a graduate student. He took this study, showed it to his classmates, and asked a rhetorical question: can a rock-paper-scissors game work if there are 70 strains of E. coli?

This question did not leave his thoughts, and Allesina decided to concentrate on developing computational models capable of simulating rock-paper-scissors for a large number of players. He found that adding additional species to his model strengthened the stability of the system , reducing the likelihood of extinction of any population. Maynard came to the same conclusion in his study: biodiversity generates even greater biodiversity due to the stability of the system, since then more organisms can coexist.

This interdependence is one of the reasons for the prevalence of non-transitivity, says Maynard. “You can't be the best at everything,” he said. “Such a genome cannot exist.” Each species has its own Achilles heel, which allows the stone-scissors-paper effect to manifest itself, and makes each species vulnerable, but does not allow predators to breed too much. More diverse systems have higher levels of stability and non-transitivity.

“It is difficult to consider what we observe in nature as unstable,” Allesina said. And with an increase in the diversity of the system, more possibilities of interspecific interaction appear in it, which can give rise to even greater biodiversity and coexistence.

Tristan Urselfrom Oregon University, inspired by the work of Kerr and Bohannan, wanted to take the next step. Although their study demonstrated that the key to the stone-scissors-paper pattern is the distribution of organisms, there were no physical barriers to the movement of bacteria in the environments used in their experiments. In nature, this is not so - the environment of a microbe living on the roots of a plant or hidden in our guts is full of obstacles. Ursel, being a biophysicist and not a microbiologist, decided to create several computer models to see how physical obstacles can affect stone-scissor-paper cycles.

Starting the project, Ursel assumed that the obstacles would have minimal impact on the simulation. “I did not expect that in some cases they will dramatically affect stability,” he said.


The collision of two species with each other in an open area usually ended with one of them completely replacing the other. However, if there were barriers in the landscape of Ursel’s computer model, it often turned out that two species could coexist. The three species involved in the game stone-scissors-paper in open space could coexist, cyclically changing the dominant form. However, the introduction of barriers into their world often led to the fact that one species eliminated the other. Ursel's

final work with Nick Vallespire Lowry, published in the online journal Proceedings of the National Academies of Science in December 2018, was another of the works demonstrating the hidden difficulties that exist in real-life stone-scissor-paper games. For example, a team of scientists led byErwin Frey and Marianne Bauer from the University of Munich. Ludwig Maximilian created mathematical models of soil microbes that receive nutrients and water through small pores of the soil - these same pores allow them to interact with their neighbors. If you try to grow microbes living in the soil in the laboratory, then the fastest-reproducing species will win. However, in nature, a gram of soil can contain more than 10,000 types of microbes.


Red, blue and yellow “germs” in the simulation participate in a non-transitive competition. With right-handed mobility, their ever-changing patterns of dominance lead to the appearance of tangled rotating spirals covering the landscape. By changing their mobility or introducing obstacles, you can completely change the final picture.

Frey and Bauer found that the secret is how long it takes for the bacteria to adapt to changing environmental conditions. Due to these limitations and the interconnectedness of the complex physical structure of the soil, thousands of microbes continue to coexist.

The feedback between ecology and evolution is critical, said Swati Patel , an applied mathematician at Tulane University, because these interactions can lead to stability or extinction - this follows from her mathematical work , published in The American Naturalist. She explained that if, for example, species A begins to die out, then B can evolve in such a way that A will restore the population. And vice versa.

“Our human influence on various ecosystems can lead to unpredictable evolution of species,” Patel said.

Long-term environmental stability and coexistence do not guarantee the preservation of a certain number of population members. Patel said oscillations are built into these models. However, the whole point is how strongly and quickly they fluctuate.

Daniel Staufer, an ecologist at the University of Canterbury in New Zealand who often works with Mayfield, says that weaker interactions help keep these fluctuations at an average level. Environmentalists call this the conservation effect. “Species do not always need to be better. There should only be enough moments in which he will be good enough to survive the bad years, ”Staufer said.

If the number of individuals of one species falls too low, then a random event like an epidemic or drought can lead to its disappearance. This creates a vacuum in the ecosystem, which can cause a cascade of extinction or open a place for the restoration of other organisms. This domino effect also gives clues to conservation biologists working to conserve endangered species. Allesina says that theoretical work on rock-paper-scissors shows that ecologists may have to concentrate on preserving whole ecosystems, rather than individual species.

“Imagine that you want to save only stone from a trinity of rock-paper-scissors,” he said. Scissors or paper may not bother you, but as soon as one of them dies out, "the waves will go through the entire network of interactions to other species that you did not know about."

Despite all the breakthroughs in theoretical work describing how rock-paper-scissors can work in large ecosystems, Staufer says that biologists have described a relatively small number of examples of such non-transitive dynamics in nature. Models show that they must exist, but the task of determining their dominance remains difficult for specialists in the evolutionary theory of games.

Maynard says it will be best to look for clues in nature itself. He began to develop a new statistical approach that could enable him to understand how species interact and how to identify persistent patterns in these interactions. However, he says that it’s important to remember that rock-paper-scissors are just one piece of a big puzzle of biodiversity, and that the main rule of nature - whether it is gene mutation and evolution or natural climate change - is a constant change.

More articles:


All Articles