Population Dynamics: Density, Dispersion, and Demographics

Population dynamics describes how the size, density and distribution of a population change over time, and population size changes according to four processes: births, deaths, immigration and emigration. In brief: population density is the number of individuals per unit area or volume, and dispersion (distribution) describes how individuals are spread in space, in clumped, uniform or random patterns. The change in population size is given by N_t+1 = N_t + B − D + I − E. Demographics describe the structure of the population, such as age and survival.

Ecologists use these measures to decide how to protect endangered species, manage fisheries and control pests. This guide defines the key terms, explains the three patterns of dispersion, shows how growth is calculated from birth and death rates, introduces survivorship curves, works through a numerical population example and corrects common mistakes.

What determines population size?

A population is a group of individuals of the same species living in the same area. Its size (N) changes through four processes. Natality (births) and immigration (individuals moving in) increase it. Mortality (deaths) and emigration (individuals moving out) decrease it.

The equation is: change in N = (births + immigration) − (deaths + emigration). For many large populations, immigration and emigration are small, and the main change is determined by the difference between births and deaths, the natural increase. If births exceed deaths, the population grows. If deaths exceed births, it falls. If they are equal, the population is stable.

What is population density?

Population density is the number of individuals per unit of area (land) or volume (water): for example, 15 deer per square kilometer or 5 000 bacteria per milliliter. It is calculated by: density = number of individuals ÷ area.

Density is influenced by the resources available and the size of the organisms. Larger animals generally have lower densities, and tropical regions often have more species but not always higher densities of each. Density-dependent factors, such as disease or competition, have effects that vary with density, whereas density-independent factors, such as fire or storms, do not. These are explained in the article on limiting factors.

Counting every individual is possible only for large conspicuous organisms or small populations. Ecologists therefore use sampling: quadrats for plants and slow-moving animals, transects, and mark-recapture for mobile animals. Sampling methods are the subject of the next article.

What are the patterns of dispersion?

Dispersion (or distribution pattern) describes the spacing of individuals within the area they inhabit.

• Clumped: individuals are grouped in patches. This is the most common pattern. It occurs when resources are patchy (a few water holes in a savanna), when individuals live in groups (herds, schools, flocks) or when seeds fall near the parent plant.
• Uniform (regular): individuals are evenly spaced. It results from competition for resources or from territorial behavior, such as penguins nesting at a fixed distance from each other, or from plants that release chemicals that inhibit neighbors (allelopathy). Planted orchards are uniform because of human planning.
• Random: the position of one individual is independent of the others. This is rare and occurs where resources are even and individuals neither attract nor repel each other, as with some trees in a forest or spiders on a lawn.

How are birth rate and death rate used?

Crude birth rate and death rate are the numbers of births or deaths per 1 000 individuals per year. The rate of natural increase is (birth rate − death rate) ÷ 10 as a percentage. The per capita growth rate, r, is the average change per individual: r = (B − D) ÷ N, or birth rate per individual minus death rate per individual. The population growth is dN/dt = rN. In exponential growth models, N_t = N₀e^rt, which is discussed in the article on population growth models. Immigration and emigration are added when needed.

What are survivorship curves?

A survivorship curve plots the number of survivors in a group born at the same time (a cohort) against age. Three typical types are:

• Type I: low mortality in early and middle life, and high mortality in old age. Humans and large mammals, which produce few offspring and give them much care.
• Type II: a constant death rate at all ages, giving a straight diagonal line. Some birds, small mammals and lizards.
• Type III: very high mortality of the young, with survivors living longer. Oysters, many fish, insects and most plants, which produce huge numbers of offspring with little care.

Age structure, the proportions of individuals in different age groups, shows the future potential of the population. A population with many young individuals will grow, and one with a majority of older individuals will decline. For human populations, age structure is displayed in population pyramids.

Dispersion patterns compared

Worked example: calculating population change

A population of 2 000 voles lives in a meadow of 40 hectares. In one year, 1 200 are born, 900 die, 150 immigrate from a neighboring meadow and 100 emigrate.

1. Density at the start: 2 000 ÷ 40 = 50 voles per hectare.
2. Change in size: (1 200 + 150) − (900 + 100) = 1 350 − 1 000 = +350.
3. Population at the end: 2 000 + 350 = 2 350 voles.
4. Density at the end: 2 350 ÷ 40 = 58.75, about 59 voles per hectare.
5. Per capita growth rate: r = 350 ÷ 2 000 = 0.175, i.e. 17.5 percent per year.
6. Birth rate and death rate per 1 000: births 1 200 ÷ 2 000 × 1 000 = 600; deaths 900 ÷ 2 000 × 1 000 = 450. Natural increase = 150 per 1 000 = 15 percent, plus a net immigration of 50 ÷ 2 000 = 2.5 percent.

If the same r continued for 3 years, the population would reach about 2 000 × 1.175³ ≈ 3 245 voles, but real populations are limited by food, predators and disease, as the article on carrying capacity explains. The calculation shows how each component contributes: the natural increase of 15 percent plus a net immigration of 2.5 percent gives the total 17.5 percent.

How did population ecology develop?

Thomas Malthus wrote in 1798 on the tendency of populations to increase faster than food supplies. Raymond Pearl and Lowell Reed applied the logistic equation to human and fruit fly populations in the 1920s. Charles Elton studied the cycles of fur-bearing animals in Canada from the Hudson’s Bay Company records. Eugene Odum’s textbooks popularized ecosystem and population ideas from the 1950s. Today, remote sensing, GPS tracking and DNA techniques allow populations to be monitored in new ways.

Which mistakes are common?

Mistake 1: Confusing density with distribution

Density is how many individuals per area. Dispersion is how they are spaced.

Mistake 2: Ignoring migration in growth calculations

Population change includes immigration and emigration as well as births and deaths.

Mistake 3: Using the wrong denominator for rates

Per capita rates are divided by the population size, not by the area.

Mistake 4: Assuming that every population is clumped, uniform or random for the same reason

The pattern depends on the scale of observation as well. A species can be clumped at one scale and uniform at another.