Suppose a wildlife agency needs to know whether the moose in a northern Ontario management area are increasing or declining, so it can set hunting quotas. Nobody can count every moose in thousands of square kilometres of forest. The same problem faces anyone who studies a population, whether it is trilliums on a hillside, walleye in a lake or bacteria in a flask. Ecologists solve it by sampling: counting carefully in a part of the habitat and scaling up, or marking some animals and seeing how many turn up again. Once they have numbers, they also ask how the individuals are spread out, how many are born and die at each age, and whether the population is large enough to survive at all. Those measurements are the raw material for every model in this unit.
Size, density and dispersion
A population is a group of individuals of the same species living in the same area at the same time, able to interbreed. Its population size () is simply the number of individuals. Size alone can mislead: 500 white-tailed deer is a sparse population in a 1000 km² forest but a crowded one in a 5 km² park. Population density () corrects for this by dividing by the space occupied: individuals per unit area for land organisms (per m², per hectare, per km²) or per unit volume for aquatic and microscopic organisms (per litre, per mL). Crude density uses the total area; ecological density uses only the area of usable habitat, which is often more meaningful because a lake-dwelling loon cannot use the surrounding forest.
| Dispersion pattern | Usual cause | Examples |
|---|---|---|
| Clumped (most common) | Resources are patchy (water, food, shelter); social behaviour (herds, packs, schools); offspring stay near the parent (seeds that fall close, clonal roots). | Caribou herds, wolf packs, schooling fish, trembling aspen clones, mushrooms on a rotting log |
| Uniform (even spacing) | Individuals repel each other: territorial defence, competition for a scarce resource such as water, or chemicals that inhibit neighbours (allelopathy). | Nesting northern gannets on Bonaventure Island, Quebec; creosote bushes in a desert; plants near a black walnut, which releases the toxin juglone |
| Random | Resources are evenly spread and individuals neither attract nor repel each other. Rare in nature. | Dandelions grown from wind-blown seeds in a uniform lawn; some forest trees and invertebrates |
Estimating population size
For plants and slow-moving animals, ecologists use quadrats: square frames of known area (often 1 m² or 0.25 m²) placed at random points in the habitat. Every individual inside each quadrat is counted. Random placement matters, because choosing spots that look interesting biases the result. The sample density is the total count divided by the total area sampled (number of quadrats times the area of one quadrat), and the population estimate is that density multiplied by the total area of the habitat: . When conditions change across a habitat, such as from a pond edge up a slope or from a forest edge into a field, a transect is used instead: a line along which organisms are recorded at set intervals (a line transect) or within a strip of fixed width (a belt transect). Transects reveal how density changes along a gradient, which random quadrats would blur.
Animals that move, hide or live in water need a different method. In mark–recapture, researchers capture a sample, mark each animal harmlessly (ear tags, leg bands, a clipped fin, a dab of paint) and release them. After the marked animals have had time to mix back in, a second sample is captured. The key idea is that the fraction of marked animals in the second sample should equal the fraction of marked animals in the whole population: . Rearranging gives the Lincoln–Petersen index.
Births, deaths and survivorship
Natality is the birth rate: the number of offspring produced per unit time, often expressed per 1000 individuals. Fecundity is the potential reproductive capacity of an individual under ideal conditions (a female cod may release millions of eggs), which is usually far higher than fertility, the number of offspring actually produced. Mortality is the death rate: the number of individuals dying per unit time. To see how mortality changes with age, ecologists build a life table. They follow a cohort (a group born at the same time) and record how many are still alive at the start of each age interval. The mortality rate for an interval is the number that died during it divided by the number alive at its start. Plotting the number of survivors against age gives a survivorship curve. The survivor axis is usually logarithmic, so a straight line means a constant proportion dies in each interval.
| Curve | Pattern of mortality | Typical life history | Examples |
|---|---|---|---|
| Type I | Low mortality through youth and middle age; most deaths in old age. | Few offspring, much parental care | Humans in countries with good health care, Dall sheep, elephants |
| Type II | Roughly constant proportion dies at every age (a straight line on a log scale). | Moderate offspring numbers; risk from predators or accidents at every age | Many songbirds such as the American robin, grey squirrels, some lizards |
| Type III | Very high mortality among the young; the few that survive early life live relatively long. | Huge numbers of offspring, little or no parental care | Oysters, Atlantic cod, frogs, sugar maple seedlings |
Age structure is the proportion of a population in each age class, usually grouped as pre-reproductive, reproductive and post-reproductive. A population with many young individuals has built-in potential to grow as they reach breeding age; one dominated by older individuals will tend to decline. Small populations face a special danger. The minimum viable population (MVP) is the smallest population size that can persist for a set time (for example a 95% chance of surviving 100 years) despite chance events. Below it, a population becomes vulnerable to three kinds of randomness: demographic (by chance, one year's births are mostly male), environmental (one harsh winter or fire) and genetic (inbreeding and genetic drift erode variation). Individuals may also struggle to find mates. These effects feed on each other, a spiral sometimes called an extinction vortex. The Vancouver Island marmot, which fell to fewer than 30 animals in the wild in the early 2000s before captive breeding and releases, is a Canadian example of a population pushed below a safe size.