Population & community ecology

How populations change

A population is all the individuals of one species living in one area. Its size, written N, changes for four reasons: births and immigration add individuals, and deaths and emigration remove them. For a population with no migration, the change depends only on births (B) and deaths (D) over a period of time.

Ecologists usually work with per capita rates, meaning rates per individual. If b is the birth rate per individual and d is the death rate per individual, then the per capita growth rate is r = b − d. If r is positive the population grows; if it's negative the population shrinks.

Exponential growth

When resources are unlimited, each individual keeps reproducing at its maximum rate. The population's growth rate is then dN/dt = rN, which reads as: the change in population size per unit time equals r times the current size. Here r is at its maximum, sometimes written r_max, the intrinsic rate of increase.

Because the number added depends on the number already there, growth speeds up as the population gets bigger. This is exponential growth, and it makes a J-shaped curve. Start with 1,000 bacteria that double every hour, and you have 2,000 after one hour, 4,000 after two, and more than 16 billion after a day.

Exponential growth happens in real life, but only for a while: when a species arrives in a new habitat, or a population recovers after a crash. No population can keep it up for long.

Logistic growth and carrying capacity

Sooner or later, resources such as food, space or nesting sites run short. The largest population an environment can support over time is its carrying capacity, written K. The logistic model adds a brake to the exponential equation: dN/dt = rN(K − N)/K.

The fraction (K − N)/K is the share of the carrying capacity that's still unused. When N is small, it's close to 1, so growth is almost exponential. As N approaches K, it shrinks towards 0, and growth slows to a stop. The result is an S-shaped curve.

K isn't a fixed number for a species. It depends on the environment and changes with it: a wet year with more food raises K, a drought or a new predator lowers it. Real populations, like harbour seals, usually wobble around K rather than settling exactly on it.

What limits a population

Density-dependent factors have a stronger effect when the population is more crowded. Competition for food, the spread of disease, the build-up of waste and predation all hit harder at high density. They work like negative feedback: as N rises, they push the growth rate down, which keeps populations near K.

Density-independent factors kill the same fraction of the population whatever its density. A hard frost, a flood or a fire kills individuals whether there are ten or ten thousand of them.

Species also differ in their life history: how they share energy between growing, surviving and reproducing. Some produce huge numbers of small offspring with little care, suiting unpredictable environments (once called r-selected, like dandelions). Others produce a few large offspring and care for them, suiting crowded, stable environments (once called K-selected, like elephants). Many biologists now see this as a continuum, not two boxes, and the r/K theory has been largely reconsidered.

• A type I survivorship curve: most individuals survive to old age, then die (humans and most primates).
• A type II curve: individuals die at a roughly constant rate at every age (many birds).
• A type III curve: most die very young, but the few that survive live a long time (most fish, trees and marine invertebrates).

How species interact

A community is all the populations of different species living in one area. You can classify their interactions by the effect on each partner: + (helped), − (harmed) or 0 (unaffected).

• Competition (−/−): both species use the same limited resource, so each is worse off.
• Predation (+/−): one animal kills and eats another. Herbivory (+/−) is an animal eating a plant, often without killing it.
• Parasitism (+/−): a parasite lives on or in a host and feeds on it, usually without killing it quickly, like a tapeworm or the malaria parasite.
• Mutualism (+/+): both benefit. Termites and the microbes in their guts that digest wood; the fungus and alga that make up a lichen.
• Commensalism (+/0): one benefits and the other is unaffected, like a bird nesting in a tree.

In the early 1930s, the Russian biologist Georgy Gause grew two species of Paramecium together in the lab on the same food, under constant conditions, and described the results in his 1934 book The Struggle for Existence. One species eventually drove the other to extinction. This led to the competitive exclusion principle: two species can't share exactly the same niche (their role and use of resources) forever. In nature, competitors often coexist by resource partitioning, dividing up the resource by eating different foods, using different parts of the habitat or feeding at different times.

Predators and prey can drive each other's numbers in cycles. Snowshoe hare and lynx populations rise and fall in a cycle of about 10 years, with lynx peaks lagging 1–2 years behind hare peaks. More hares feed more lynx; more lynx eat down the hares; fewer hares starve the lynx; and the cycle restarts.

Keystone species and community change

A keystone species has a much bigger effect on its community than its numbers or mass would suggest. Paine's sea stars worked this way: by eating the mussels, the dominant competitor for space, they left room for many other species.

Sea otters are another example. When hunting for their fur cut sea otter numbers to an estimated 1,000–2,000 worldwide, the sea urchins they eat multiplied and grazed away the kelp forests. Where otters have returned, urchins have dropped and kelp has recovered.

Communities also change over time through succession. In primary succession, life colonises bare ground with no soil, such as new volcanic rock; hardy pioneer species like lichens arrive first and start building soil. In secondary succession, a community regrows after a disturbance such as a fire that leaves the soil in place, which is much faster.

Key terms

Per capita growth rate (r)

Births minus deaths per individual per unit time.

Exponential growth

Growth at a constant per capita rate, dN/dt = rN, giving a J-shaped curve.

Carrying capacity (K)

The largest population an environment can support over time; it changes as conditions change.

Logistic growth

Growth that slows as N approaches K, dN/dt = rN(K − N)/K, giving an S-shaped curve.

Density-dependent / density-independent factor

A limit that gets stronger as the population gets more crowded / one that acts regardless of density.

Competitive exclusion principle

Two species can't occupy exactly the same niche in the same place indefinitely.

Mutualism / commensalism / parasitism

Both partners benefit / one benefits, the other is unaffected / one benefits at the other's expense.

Keystone species

A species whose effect on its community is much larger than its abundance would suggest.

Succession

The gradual change in a community's species over time, on bare ground (primary) or after disturbance (secondary).

Check yourself

Try answering in your head before you open each answer.

• 1.In a kelp forest, sea otters eat sea urchins, and urchins eat kelp. Predict what happens to urchins, kelp and the fish that shelter in kelp if the otters disappear.Show answerHide

  Without otters, urchin numbers rise. The urchins overgraze the kelp, so the kelp forest shrinks. Fish and other animals that depend on the kelp for food or shelter decline. Removing one predator changes the whole community, which is what makes the otter a keystone species.

• 2.A fishery manager wants the largest catch every year that the fish population can keep replacing. Should she keep the population near K or near K/2? Why?Show answerHide

  Near K/2. In the logistic model the population adds new individuals fastest at K/2, so that's where the largest catch can be replaced each year. Near K, growth is close to zero, so almost nothing can be taken without the population falling.

• 3.Two bird species eat the same insects in the same forest, yet neither drives the other out. Suggest how this is possible, and name the idea it seems to contradict.Show answerHide

  They may be partitioning the resource: for example, one feeds high in the canopy and the other near the ground, or they take insects of different sizes, or feed at different times of day. This means their niches aren't identical, so the competitive exclusion principle isn't broken.