18.3 Population Growth and Regulation

18.3 Population Growth and Regulation

A population is a group of individuals of one species living in one place at one time. Two questions organize this section. How fast is the population changing, and what keeps it from growing without limit? The change comes from four counts. The brakes come from the environment, and they do not all work the same way. Regulation is the set of factors that slow growth or pull a population back down.

Four counts that change N

Natality is the birth rate, the addition of individuals by reproduction. Mortality is the death rate. Immigration is arrival from another population. Emigration is departure. Movement in and out is migration in this broad sense. If N is population size, the change in population equals births plus immigration minus deaths minus emigration. Individuals added are the ones born here and the ones that move in. Individuals removed are the ones that die and the ones that move out.

A population can grow while deaths are high, if births and immigration more than cover the losses. It can shrink while births are high, if emigration and mortality are higher still. These words are rates when they are measured per individual per time, and they are counts when a question gives a number of births or deaths. The signs do not change either way.

Population density is the number of individuals in a given area. Carrying capacity is not the birth rate, and it is not density itself. Carrying capacity, written K, is the population size that environment can sustain. It enters the story when resources start to run short.

Exponential growth, the J-shape

Exponential growth happens when resources are effectively unlimited and the per capita rate of increase stays constant and positive. The curve is a J-shape. It starts slowly and then rises more and more steeply. The introductory equation is dN/dt = rN. In words, the rate of change of population size equals r times N. The quantity r is the per capita rate of increase. Because the rate rises as N rises, the population does not add a fixed number of individuals each year. It adds a larger number as it gets bigger, because the new individuals themselves reproduce.

The J-shape describes unlimited conditions, not endless growth. Scarcity, or a density-independent disaster, eventually intervenes.

Logistic growth and carrying capacity

Logistic growth is the S-shaped correction. While N is small, the curve looks almost exponential. As N rises, growth slows. The population levels off at K. In words, the unused room is the fraction of carrying capacity still open, (K minus N) divided by K. When N is far below K, that fraction is near 1 and growth is close to the exponential rate. When N approaches K, the fraction approaches 0 and growth approaches 0. If N is briefly above K, the rate becomes negative and the population declines toward K. The result is an S-shape.

K is a property of the environment and of the way the species uses it. Add food, or remove a predator, and K can rise. Damage the habitat and K can fall. A population sitting at K can still have births. If deaths and emigration match births and immigration, net growth is zero. The signature of K is that net growth has leveled off. Carrying capacity is not the birth rate.

What slows growth

Density-dependent limits change their effect as density changes. They press harder when the population is crowded. Competition for food, water, nest sites, or light is the clearest case. Disease spreads more readily when hosts contact one another often. Predation can intensify when prey are common and easier to find. These factors are a major reason the logistic curve bends.

Density-independent limits, in the introductory model, do not depend on how many individuals are present. Many storms, fires, and sudden cold snaps kill a similar fraction in a sparse population and in a crowded one. A hard frost can cut insects in a thin field and in a packed one. These events can knock N down sharply. They do not, by themselves, draw the smooth leveling at K. Real populations feel both kinds of limits. A fire can reset N, and competition can set the ceiling that N approaches afterward.

r-selection and K-selection

r-selected species and K-selected species are two ends of a life-history contrast, named for r and K in the growth equations. They are tendencies, not sealed boxes. The classic contrast is the one to use.

r-selected organisms mature early. They produce many small offspring. They provide little parental care. They fit unpredictable or disturbed habitats, where the chance to reproduce may be brief. r-selected organisms cope with unpredictable, severe fluctuations. Weeds in a freshly cleared lot, many insects, and many small aquatic invertebrates are the usual pictures. The population can surge when conditions open and crash when they close.

K-selected organisms mature later. They produce fewer offspring, often larger ones. They provide more parental care. They fit stable habitats in which populations spend much of their time near carrying capacity, where competitive ability matters. Elephants, whales, and many large trees are the textbook pictures. Few offspring with long care is the K-selected pattern. It is not what r-selection means.