Factors that regulate population size

1Why do armyworm outbreaks end?

Some years, caterpillars of the fall armyworm multiply so fast in maize fields that farmers fear for the whole harvest. Yet an outbreak never grows forever. As the caterpillars become crowded, food runs short, diseases spread from one to the next, and predators and parasitic wasps gather where prey is plentiful. Then a dry spell or heavy rain may kill many more, whatever their numbers.

These are the two kinds of factor that regulate every population: those whose effect depends on how crowded the population is, and those whose effect does not. This lesson separates them, with data, and looks at predators and their prey, competition and the life strategies of different species.

2Two kinds of factor

Figure 1: Mortality from a density-dependent factor (a virus) and a density-independent factor (frost), illustrative data.

Figure 1 shows how to tell the two apart from data. Plot the percentage killed against density:

• If the percentage rises with density, the factor is density-dependent. A virus spreads more easily between crowded caterpillars, so it kills a larger fraction of a dense population. This acts as negative feedback: the more the population grows above its carrying capacity, the harder the factor pushes it back, so these factors keep a population near $KK$.
• If the percentage stays the same at every density, the factor is density-independent. A night of frost kills about 30 % of the caterpillars whether there are 10 or 80 per square metre. Such factors cause sudden crashes, but they cannot regulate a population around a set level.

3Competition

Intraspecific competition is the strongest density-dependent factor, because members of one species need exactly the same resources. In plants it shows as smaller individuals: crowded seedlings share the same light, water and minerals.

Interspecific competition occurs when two species share a limiting resource. The competitive exclusion principle states that two species cannot occupy the same niche in the same place indefinitely: one will be eliminated, unless the two divide the resource between them (resource partitioning), for example by feeding at different heights or times.

4Predators and prey

A predator population depends on its prey, and the prey population is reduced by its predators. The result can be linked cycles. The Lotka–Volterra model describes them:

$$\frac{dH}{dt}=aH-bHP\frac{dP}{dt}=eHP-dP\backslash frac\{dH\}\{dt\}\; =\; aH\; -\; bHP\; \backslash qquad\; \backslash frac\{dP\}\{dt\}\; =\; eHP\; -\; dP$$

where $HH$ is the prey (herbivore) population, $PP$ the predators, $aa$ the prey's birth rate, $bb$ the rate at which predators catch prey, $ee$ how efficiently caught prey become new predators, and $dd$ the predators' death rate. Figure 2 shows the model run for 30 years.

Figure 2: Predator–prey cycles computed from the Lotka–Volterra model (a = 1.0, b = 0.02, e = 0.01, d = 0.6 per year). The predator peak lags the prey peak by about 1.6 years.

The cycle has four stages: (1) prey are plentiful, so predators breed well and increase; (2) more predators eat more prey, so the prey decline; (3) with less food, predators starve and decline; (4) with fewer predators, the prey recover, and the cycle repeats. The predator peak always lags behind the prey peak, because it takes time for extra food to become extra predators. Real cycles, such as the famous records of snowshoe hares and lynx in Canada, are less regular, because food supply, disease and weather also act on both species.

5Life strategies: r-selected and K-selected species

Most species lie somewhere between the two extremes. The distinction matters for conservation: a K-selected species such as the mountain gorilla, whose females raise one infant at a time over several years, can take decades to recover from losses, which is why protecting every individual in Volcanoes National Park matters so much.