Competition

On the shore at Millport, Scotland, one barnacle lives high on the rock and another lives just below it. Take the lower species away, and the upper one survives well down in the zone it normally lacks. What was keeping it out?

The answer is its neighbour. This lesson is about that kind of interaction: what competition is, how you test for it in the field, how a simple model predicts whether two competitors can live together, and what it takes to show that competition has changed a species over generations.

The idea: competitors share a limit

Competition is an interaction in which individuals use a resource in short supply, so that each lowers the survival, growth or reproduction of the others. The resource can be food, water, light, nutrients or space.

Competition within a species, intraspecific competition, is already built into the logistic model in population growth: growth slows as numbers approach the carrying capacity K, the population size the environment can sustain. Interspecific competition is the same pressure between species that share a resource.

Competition also differs by route. In exploitation competition the effect is indirect: each competitor uses up a resource, leaving less for the other. In interference competition one individual acts directly on another, by fighting, overgrowing, or holding a territory. Think of two flatmates and one fridge. Exploitation is one of them eating the food first. Interference is a lock on the door.

In the 1930s Georgii Gause grew species of Paramecium alone and together in laboratory cultures. Each grew well alone, but in his mixed cultures Paramecium aurelia persisted and Paramecium caudatum declined toward disappearance. Results like this were later summed up as the competitive exclusion principle, a name popularized by Garrett Hardin in 1960: two species limited by exactly the same resource cannot coexist indefinitely.

Treat that as a model conclusion, not a law. It follows when there is a single limiting resource, a constant and well-mixed environment, and nothing else holding the winner down. Real places often break those conditions with several resources, changing seasons, patchy habitat, or predators that hit the commoner species. And exclusion means loss from one place. A species excluded from one pond or one band of rock may thrive elsewhere.

That last point connects to the niche ideas in niches and distributions. The fundamental niche is the set of conditions where a species could persist on its own; the realized niche is the narrower set it actually occupies with competitors and predators present.

Connell’s barnacles: removal as the test

Joseph Connell worked on the rocky shore at Millport, on the Isle of Cumbrae in the Firth of Clyde, and published the study in 1961. Adults of Chthamalus stellatus (the Cumbrae species is now identified as C. montagui) occupy a band high on the shore, and Balanus balanoides (now usually called Semibalanus balanoides) covers the rock below. A pattern like that has rival explanations. Chthamalus might tolerate too little immersion lower down, its predators might be worse there, or Balanus might be crowding it out.

Connell tested the competition explanation by changing it. He mapped patches of Chthamalus, divided each map, and chose one portion at random and removed the Balanus touching or surrounding each Chthamalus. The other portion was left untouched, with its Balanus in place. Separately, he fitted cages over some patches to exclude the predatory whelk Thais. He recounted the marked barnacles at intervals.

Chthamalus kept free of Balanus survived well at the shore levels he studied, and he saw Balanus kill Chthamalus by smothering, undercutting or crushing it. Much of this competition was direct, for space on the rock. So at Millport, Balanus set the lower limit of Chthamalus: its fundamental niche reached further down than its realized niche. Notice the direction. Removing Balanus helped Chthamalus, not the reverse.

That is one shore, one pair of species and one set of years. It does not tell you what sets barnacle limits on every coast, and its strength lies in the design rather than the generality.

Lotka-Volterra: when competitors coexist

The model named for Alfred Lotka and Vito Volterra extends the logistic to two species. Each species is slowed by its own numbers and by the other’s, converted into equivalent units:

dN1/dt = r1 N1 [1 - (N1 + alpha12 N2) / K1] dN2/dt = r2 N2 [1 - (N2 + alpha21 N1) / K2]

Here r is the maximum per-capita growth rate (per day), K the carrying capacity (individuals), and alpha12 the effect of one species 2 individual on species 1, measured in species 1 individuals. If alpha12 = 0.5, two individuals of species 2 crowd species 1 as much as one of its own. Keep the subscripts straight: alpha21 is species 1’s effect on species 2.

Worked problem. These values are invented for practice. Take r1 = 0.5 per day, r2 = 0.25 per day, K1 = 100 individuals, K2 = 80 individuals, alpha12 = alpha21 = 0.5, and start with N1 = N2 = 20. Assume constant parameters, no age structure and no migration.

1. Growth at the start. For species 1, dN1/dt = 0.5 x 20 x [1 - (20 + 0.5 x 20) / 100] = 10 x (1 - 30/100) = 7 individuals per day. For species 2, dN2/dt = 0.25 x 20 x [1 - (20 + 0.5 x 20) / 80] = 5 x (1 - 30/80) = 3.125 individuals per day. Both grow.
2. Isoclines. An isocline is the line where a species’ growth is zero. For species 1 it is N1 + 0.5 N2 = 100, running from N1 = 100 on its own axis to N2 = 200. For species 2 it is 0.5 N1 + N2 = 80, running from N2 = 80 to N1 = 160. Where they cross, both stop changing. Substitute N1 = 100 - 0.5 N2 into the second: 50 - 0.25 N2 + N2 = 80, so 0.75 N2 = 30, N2* = 40 and N1* = 80. Check: 80 + 0.5 x 40 = 100 and 0.5 x 80 + 40 = 80.
3. Stable or not? The coexistence conditions are K1 > alpha12 K2 and K2 > alpha21 K1. Here 100 > 0.5 x 80 = 40 and 80 > 0.5 x 100 = 50, so both hold. Check by invasion: species 1, rare among species 2 at its carrying capacity, grows at 0.5 x (1 - 0.5 x 80/100) = 0.3 per day. Species 2, rare among species 1 at N1 = 100, grows at 0.25 x (1 - 0.5 x 100/80) = 0.094 per day. Each can increase when rare, so the model predicts stable coexistence at 80 and 40.
4. Change one coefficient. Raise alpha21 to 1.0. Now 80 < 1.0 x 100, so the second condition fails. Species 2, rare among species 1 at N1 = 100, grows at 0.25 x (1 - 100/80) = -0.0625 per day: it cannot get started, while species 1 still can. The model predicts that species 1 excludes species 2.

The rule in words: two competitors coexist in this model when each limits itself more than it limits the other. If both conditions fail, the winner depends on the starting numbers. And r never appeared in the conditions. The fastest grower need not win. Abreu and colleagues (2019) showed this in soil-bacteria microcosms, where raising the dilution rate reversed which species of a pair won. They also found a pattern the basic model cannot produce, a reminder that these equations are a model with assumptions, not a description of every flask.

• species 1 isocline (dN1/dt = 0)
• species 2 isocline (dN2/dt = 0)
• start
• numbers at day 400 of the run
• isoclines cross

α₁₂, effect of one species 2 individual on species 1 0.50 α₂₁, effect of one species 1 individual on species 2 0.50 Start: species 1 numbers N₁ 20 Start: species 2 numbers N₂ 20

You can also click the plot to set the start point. Fixed: K₁ = 100, K₂ = 80 individuals; r₁ = 0.5, r₂ = 0.25 per day.

In this sketch: constant parameters, no age structure, no migration, and the two equations of the lesson are the only rules; the path steps the two equations forward 0.05 day at a time for 400 days, a choice of this sketch.

Growth at the start, species 1 (individuals per day)

Growth at the start, species 2 (individuals per day)

Species 1 rare, species 2 at K₂ (per day)

Species 2 rare, species 1 at K₁ (per day)

Expected from the conditions

Result of this run in the sketch, day 400

The outcome is set by two conditions, K₁ > α₁₂ K₂ and K₂ > α₂₁ K₁: both hold, coexistence; one holds, the other species is excluded; neither holds, the winner depends on the starting numbers. The growth rates r never appear in them. This picture is a sketch of the logic, not a prediction for real species.

Partitioning and character displacement

When competitors coexist, they often use resources differently. Resource partitioning is the division of resources among species by type, place or time. Robert MacArthur’s 1958 study of five warbler species in northeastern conifer forests found that they foraged in different parts of the same trees. The study was observational. It showed partitioning but did not test whether competition caused it, since no species was removed.

Partitioning has more than one possible cause. Past competition might have driven species apart. Each species might shift its behaviour when the other is present, which is plasticity. Or only species that already differed might have been able to settle together, called ecological sorting. Model work by D’Andrea and colleagues (2019) adds a twist: in their simulations, competition for resources sometimes produced clusters of similar species rather than evenly spaced ones.

Character displacement is evolutionary divergence in a trait caused by competition for limited resources. To claim it, you need a trait difference with a genetic basis, often tested in a common garden where populations are raised in the same environment, and a link between the trait and how the organism gets its resource. You must also rule out plasticity and sorting. Heritability of a trait like beak size is the subject of complex traits and GWAS.

On Daphne Major in the Galapagos, Peter and Rosemary Grant reported that the medium ground finch, Geospiza fortis, diverged in beak size from the large ground finch, G. magnirostris, 22 years after magnirostris arrived, when the two species together severely depleted the food supply. It is a natural experiment: one island, no random assignment, and a drought that coincided with the competition. Read it with testing evolutionary explanations in mind. It is strong evidence that competition and a food shortage acted together, and it is harder to separate the two.

Design problem

Chthamalus adults live high on the Millport shore and Balanus lower down. Connell mapped patches of Chthamalus, split each map, chose at random the portion where Balanus was removed, left the rest untouched, and put cages over some patches to exclude the whelk Thais. Chthamalus survived better where Balanus was removed. What does this design show, and what would you add?

One way to do it

Start with the comparison. The untouched portion of each map is the control: it shares the same rock height, immersion and weather, and differs only in whether Balanus is present, so a survival difference measures the effect of Balanus.

The random choice matters because a person choosing by eye might pick the patches that look healthiest for the removal. Random allocation removes that bias.

The cages separate a second cause. If Thais were killing Chthamalus, survival would differ between caged and open patches whatever Balanus did. Cages may not exclude every predator, so any conclusion should say how well the mesh worked.

Together with Connell’s observations of Balanus smothering, undercutting and crushing Chthamalus, this shows that at Millport competition from Balanus set the lower limit of Chthamalus, and that its fundamental niche extends below its realized one.

What to add: a handling control, in which you prod around Chthamalus with the needle without removing anything, would check that disturbance alone does not change survival. That is your improvement, not part of Connell’s design. Then repeat the removal on other shores, with other wave exposure and tidal ranges, before claiming the result holds beyond this one coast.