Competitive Exclusion Principle

What the principle actually says

Put two species in one container and give them a single food that runs short. Both eat it, both grow, both reproduce. Intuition says they should settle into a tense but stable truce — each holding some fraction of the resource. The competitive exclusion principle says no. If the two species are truly complete competitors — drawing on the exact same limiting resource with no other axis separating them — then one of them, the one that turns that resource into surviving offspring even slightly more efficiently, will inexorably grow at the other's expense until the loser's population falls to zero. There is no stable middle ground. The slogan version, due to Garrett Hardin's influential 1960 Science essay, is "complete competitors cannot coexist."

The key words are complete, limiting, and indefinitely. "Complete" means there is no dimension on which the species differ in how they use the resource. "Limiting" means the resource, not space or predators or weather, is what caps population growth. "Indefinitely" means the outcome is an asymptotic, equilibrium statement — exclusion can take many generations, and a fluctuating or frequently disturbed environment may never let it finish. Strip away any of those qualifiers and coexistence becomes possible again, which is exactly why the principle is so useful: it tells you precisely what must be true for two competitors to persist together.

The mechanism, step by step

The engine underneath is positive feedback acting on a shared, depletable pool. Consider two species, here labeled species 1 and species 2, both feeding on resource R (say bacterial cells in Gause's tubes, or dissolved silicate for diatoms).

1. Both species consume R, lowering its concentration. Each individual's birth rate depends on how much R it can capture. When R is abundant, both species grow exponentially and barely notice each other.
2. As populations rise, R falls. Consumption outpaces resource renewal, so the steady-state level of R drops toward the point where birth rate equals death rate for at least one species.
3. Each species has a break-even resource level, its R*. R* is the concentration of R at which that species exactly replaces itself — births balance deaths and growth is zero. Below R*, the species shrinks; above it, the species grows.
4. The species with the lower R* keeps eating below its rival's break-even point. Suppose species 1 can persist at R* = 1 unit but species 2 needs R* = 2 units. Species 1 will happily keep drawing R down to 1 unit. At that level species 2 is starving — R sits below the 2 units it needs — so species 2's death rate exceeds its birth rate.
5. The loser declines toward extinction; the winner settles at its own R*. Species 2 dwindles to zero while species 1 holds the resource at R* = 1. The outcome is set entirely by which species tolerates the scarcer resource, not by who got there first or who is bigger.

This is David Tilman's R* (resource-ratio) formulation, and its power is that R* is measurable: grow each species alone, let it deplete the resource, and read off the steady-state concentration it stabilizes at. The species with the lower R* is predicted to win in competition — a falsifiable, quantitative claim, not a hand-wave about "competitive superiority."

The math — Lotka-Volterra competition

The classical formal model predates R* theory: the Lotka-Volterra competition equations, derived independently by Alfred Lotka (1925) and Vito Volterra (1926). Two species with populations N₁ and N₂, intrinsic growth rates r, carrying capacities K, and competition coefficients α (effect of each species on the other) obey:

dN₁/dt = r₁·N₁·(K₁ − N₁ − α₁₂·N₂) / K₁
dN₂/dt = r₂·N₂·(K₂ − N₂ − α₂₁·N₁) / K₂

Here α₁₂ is how much one individual of species 2 suppresses species 1 (measured in species-1 equivalents), and α₂₁ the reverse. Analyzing the zero-growth isoclines (the lines where dN/dt = 0) gives four possible outcomes:

• Species 1 always wins — its isocline lies entirely outside species 2's; happens when interspecific competition on species 2 is stronger than the intraspecific competition holding it back.
• Species 2 always wins — the mirror image.
• Unstable coexistence — both isoclines cross but the equilibrium is a saddle point; whichever species starts more abundant wins (founder control).
• Stable coexistence — both isoclines cross with the equilibrium stable, which requires each species to limit itself more than it limits the other (α₁₂ < K₁/K₂ and α₂₁ < K₂/K₁). This is mathematically equivalent to the species occupying partly separate niches.

The competitive exclusion principle is the statement that, in the limit of complete competitors — where α₁₂ and α₂₁ approach the values implied by identical resource use — only the first three outcomes survive, and stable coexistence collapses. Self-limitation stronger than cross-limitation is the mathematical signature of niche difference, and it is the only thing that rescues coexistence.

Worked example — Gause's Paramecium

Gause's 1934 ciliate experiment is the textbook walkthrough. He used three species and a fixed renewing food supply (the bacterium Bacillus pyocyaneus or the yeast Saccharomyces):

• Monoculture controls. Grown alone, P. aurelia climbed to a carrying capacity of roughly 105 individuals per 0.5 mL sample; P. caudatum, the larger species, leveled off lower at about 64 per sample. Both followed clean logistic curves — proof that each is perfectly viable on the food provided.
• Mixed culture, same food. Started together, P. caudatum grew for the first few days, then turned over and declined as P. aurelia kept rising. By day 16-18 P. caudatum had fallen essentially to zero while P. aurelia persisted at a reduced density. The faster-reproducing species had monopolized the shared bacterial food and starved the other out — competitive exclusion in real numbers.
• The coexistence control. When Gause instead paired P. caudatum with P. bursaria (which harbors symbiotic Chlorella algae), the two persisted together indefinitely. P. bursaria fed mainly on bacteria settled at the tube's bottom and tolerated the low-oxygen conditions there (its symbiotic Chlorella supply oxygen by photosynthesis), while P. caudatum fed on bacteria suspended higher in the water column. Different microhabitats, different effective resource — niche differentiation rescued coexistence exactly as the theory demands.

The pair of results together is what makes the experiment so persuasive: the same two-species logic predicts exclusion when the niche is shared and coexistence when it is split.

The conditions that decide the outcome

Condition	Required for exclusion	Why it matters
Single limiting resource	Yes — exactly one	Multiple independent resources allow each species its own R*
Constant environment	Yes	Fluctuation lets each species "win" at different times (storage effect)
Equilibrium reached	Yes — enough time	Disturbance can reset the system before exclusion completes
Density-dependent growth	Yes	Both species must be regulated by the shared resource, not by predators
No niche difference	Yes (complete competitors)	Any axis of separation (food size, time, space) breaks the principle
Closed system	Effectively	Immigration can rescue a losing species (mass effect / source-sink)

Exclusion vs niche-differentiated coexistence

Property	Competitive exclusion	Stable coexistence
Resource use overlap	Complete (identical niche)	Partial — niches differ on ≥1 axis
Self vs cross limitation	Cross ≈ self limitation	Each limits itself more (α < K ratio)
Number of limiting factors	1 for 2 species	≥ n factors for n species
Long-term outcome	One species → 0	Both persist at stable equilibrium
R* relationship	Lower-R* species wins outright	Each species best at a different resource
Canonical example	P. aurelia vs P. caudatum	MacArthur's warblers; Darwin's finches
How invasives exploit it	Grey squirrel ousting red squirrel	Native + introduced partition habitat

Where it shows up — real organisms and field cases

• MacArthur's warblers (1958). Five species of Setophaga (Dendroica) warbler feed in the same New England spruce trees on the same insects, an apparent violation. Robert MacArthur's painstaking timed observations showed each species concentrates its foraging in a distinct vertical band and behaves differently — the Cape May warbler near the top and outer buds, the bay-breasted warbler in the dense middle. They had partitioned a single tree into five niches. This study essentially launched modern niche theory.
• Tilman's diatoms. David Tilman grew the freshwater diatoms Asterionella formosa and Cyclotella meneghiniana competing for silicate and phosphate in chemostats. Whichever species had the lower R* for the limiting nutrient always won, and when silicate-to-phosphate ratios were tuned so each species was limited by a different nutrient, both coexisted — a clean confirmation of R* theory and the n-resources rule.
• Grey vs red squirrel. The North American grey squirrel (Sciurus carolinensis), introduced to Britain around 1876, has displaced the native red squirrel (Sciurus vulgaris) across most of England and Wales. The grey is larger, can digest unripe acorns the red cannot, and carries squirrelpox virus to which it is immune but the red is not — competitive exclusion sharpened by apparent competition via a shared pathogen.
• Barnacles on a Scottish shore (Connell 1961). Joseph Connell's rocky-intertidal study showed the barnacle Balanus physically outcompetes and crowds out Chthamalus in the lower shore by undercutting and overgrowing it; Chthamalus survives only higher up where Balanus cannot tolerate desiccation. Competition sets the lower limit of Chthamalus; physical stress sets its upper limit.
• The paradox of the plankton (Hutchinson 1961). Open-water phytoplankton communities sustain dozens of species on a handful of limiting nutrients (nitrogen, phosphorus, silicon, light) — far more species than the principle allows. G. Evelyn Hutchinson's resolution was that the environment never reaches equilibrium: turbulence, seasonal turnover, and patchiness keep resetting the competition so no single best competitor ever finishes the job. This drove the discovery of fluctuation-dependent coexistence (the storage effect, relative nonlinearity).

Common misconceptions and pitfalls

• "It means species never compete and coexist." No — it forbids only stable coexistence of complete competitors on a single limiting resource. Species coexist all the time precisely because they differ on some axis. The principle is a tool for finding that axis, not a prohibition on coexistence.
• "Exclusion is fast." It can be slow. The outcome is an equilibrium prediction; with similar competitors it may take hundreds of generations, and a fluctuating or disturbed environment can postpone it indefinitely. The plankton paradox is the canonical case of exclusion never reaching its conclusion.
• "The bigger or stronger species wins." The winner is whichever species can persist at the lowest resource level (lowest R*), which has nothing to do with body size or aggression. In Gause's tubes the smaller P. aurelia beat the larger P. caudatum.
• "Predators always make competition worse." Often the opposite: a predator that preferentially eats the dominant competitor (keystone predation, as in Robert Paine's Pisaster starfish removing mussels) can prevent exclusion and raise diversity. Removing the predator collapses the community to a single dominant.
• "One limiting resource means one food item." A "resource" in the principle is any independent regulating factor — a nutrient, a nesting site, even a shared predator or pathogen (apparent competition). Two species can be excluded by sharing an enemy just as by sharing a food.
• "It's been disproven because real communities are diverse." Diversity is not a counterexample; it is the principle's prediction in reverse. High diversity tells you there are many limiting factors and many niches. The principle is "wrong" only if you misapply it to species that aren't actually complete competitors.