Intransitive Competition

If simplistic competition were the only evolutionary force, then after four billion years we'd expect a handful of winners and a lot of losers. Instead the planet has somewhere between two million and a trillion species, depending on who's counting. One of the most elegant explanations for this embarrassment of riches is that competition in nature is often not a hierarchy at all — it's a game of rock-paper-scissors where no species gets to stay on top for long.

The Basic Idea

In transitive competition, if A beats B and B beats C, then A beats C. There's a clear winner and the rest trend toward extinction. Intransitive competition breaks this hierarchy: C can beat A, closing the loop. The result is cycling — each species dominates for a while, then gives way to its nemesis, which gives way to its nemesis, and so on. May and Leonard worked out the mathematics in 1975 by adapting the Lotka-Volterra equations, and later theorists showed these intransitive loops can involve hundreds or thousands of species.¹

The intuition is almost too simple. As Daniel Maynard puts it: in single combat against a skilled fighter you'll lose, but in a group of 100 fighters, you might form an alliance with someone stronger and outlast your competitors. "You can't be great at everything," Maynard says. "That genetically just can't exist." Every species has an Achilles' heel, and that vulnerability is precisely what prevents any one competitor from steamrolling the rest.¹

Side-Blotched Lizards

The most famous field study is Barry Sinervo's work on common side-blotched lizards in California's Inner Coast Range. Male lizards come in three throat colors, each with a different mating strategy. Orange-throated males are ultra-aggressive — they guard large harems and attack all rivals. Blue-throated males cooperate with each other to defend territory, which works against sneaky yellows but is only partly effective against the brute-force oranges. Yellow-throated males mimic females and sneak into orange males' territory to mate undetected.¹

Orange beats blue, blue beats yellow, yellow beats orange. In the field, each color dominated for a year or two before giving way to its rock-paper-scissors successor. Sinervo never observed just two colors coexisting — one always eliminated the other. But with three, the populations cycled. This is exactly what the math predicts: a pair of competing strategies allows a winner, but a triple of intransitive competitors creates a stable cycle.¹

Space Is Everything

The cleanest experimental demonstration comes from Benjamin Kerr and Brendan Bohannan's 2002 study of E. coli strains. They set up three strains in a natural rock-paper-scissors arrangement: colicin-producing (C) strains kill sensitive (S) strains, but resistant (R) strains outcompete C because they don't bear the cost of producing the toxin, while S strains outcompete R because resistance mutations impair nutrient transport.¹

In a well-mixed flask, where all strains interact freely, R wins every time. But on a static petri dish, where bacteria can only interact with neighbors, all three strains coexist in a beautiful cycling pattern. The spatial constraint is the key. When organisms can only compete locally, pockets of each strategy survive in different regions, and the cycling plays out as a spatial dance rather than a global takeover.¹

This result extends in surprising ways. Tristan Ursell's computational models showed that physical barriers in the landscape can flip outcomes completely: two species that would normally compete to extinction can coexist when there are obstacles, while three species locked in rock-paper-scissors can collapse to one when barriers disrupt their cycling.¹ The geometry of the environment isn't just a backdrop — it's a determinant of whether biodiversity survives at all.

The MEGA-plate experiments at Harvard reinforce this from a different angle. On a giant agar dish with increasing antibiotic concentrations, bacteria evolve resistance by advancing through lethal zones. But the winning mutations aren't always the fittest — they're the ones that happen to occur at the expanding wavefront, in the right place at the right time. Faster-growing mutants that arise behind the frontier get trapped because slower strains ahead of them have already consumed the nutrients. "You don't have to be better than everyone else around you; you just have to be the first in a new area."² Space doesn't just modulate competition; it determines who gets to compete at all.

Erwin Frey's group at Munich pushed this further for soil microbes. In the lab, the fastest-reproducing species always wins. In soil, with its complex pore structure and limited diffusion, thousands of species coexist per gram. The secret is the time it takes bacteria to adapt to changing local conditions, combined with the connectivity imposed by soil's physical architecture.¹

From Bacteria to Synthetic Biology

Jeff Hasty's group at UCSD turned intransitive competition from an ecological observation into an engineering tool. Their problem: engineered genetic circuits in E. coli inevitably break down as mutant cells that disable the costly circuit outcompete the engineered ones. Within 36 hours, the desired trait disappears.¹

Their solution was to engineer three strains, each producing a toxin, a self-protective antitoxin, and a second antitoxin protecting against one other strain — a deliberate rock-paper-scissors system. By sequentially adding strains, they maintained the engineered population while the newcomers' toxins eliminated unhelpful mutants. The ecological dynamics enforced genetic stability. It's a beautiful example of using emergence — the cycling behavior that naturally arises from intransitive competition — as a design tool rather than just a phenomenon to study.¹

The Conservation Lesson

The deeper implication, as Stefano Allesina's models show, is that biodiversity is self-reinforcing: more species means more intransitive loops, which means greater stability, which supports more species. Adding species to his computational models bolstered stability rather than undermining it.¹

This has a direct conservation consequence. You can't save individual species in isolation if they're embedded in intransitive networks. "Imagine that you only want to conserve the rock of the rock-paper-scissors trio," Allesina says. "You might not care about the paper or the scissors, but as soon as one goes extinct, that could reverberate through these networks of interactions to other species that you would never have guessed." This echoes the parasite story in food webs and trophic cascades — the network structure matters as much as the individual players.

I think this is one of those ideas that changes how you see the world once you absorb it. We're culturally primed to think of competition as hierarchical — there's a best and a worst and everything in between. But in biological reality, competition is often a tangled loop where the "best" strategy depends entirely on who else is in the game. It's closer to an ecosystem's immune system than a tournament bracket.