What Is a Population? Size, Density, Distribution and Minimum Viable Size

Welcome to Population Dynamics

How many moose can Algonquin Park feed? Why do snowshoe hares boom and crash about every ten years? How many people can Earth support, and how big is your share of the planet? This unit answers questions like these with the tools that ecologists, wildlife managers and demographers use every day.

Remember from Grade 11: in Diversity of Living Things you sampled a local ecosystem with quadrats, transects and mark-recapture and calculated Simpson's diversity index. In Evolution you met Malthus and saw that populations can grow faster than their food supply. This unit turns those ideas into models you can calculate with.

We start with the most basic question: what exactly is a population, and how do we describe one?

What counts as a population?

A population is all the individuals of one species living in the same area at the same time, so they can interbreed. The white-tailed deer of Pelee Island form a population. All the white-tailed deer in North America do not form one population, because a deer in Ontario will never meet a deer in Texas.

Where you draw the boundary depends on the question. A fisheries biologist might treat the lake trout of one lake as a population. A geneticist might group several connected lakes.

Ecologists describe a population with a few key characteristics:

• Size (N): how many individuals.
• Density (D): how crowded they are.
• Dispersion: how they are spaced out.
• Age structure and sex ratio: how many young, adults and old individuals; how many males and females.
• Rates of change: births (natality), deaths (mortality), immigration and emigration. You will calculate these in Measuring Population Change.

Density: crude and ecological

Population density is the number of individuals per unit of space:

D = N ÷ A (for land) or D = N ÷ V (for water or soil, per litre or per m³).

Always give units: deer/km², dandelions/m², water fleas/L.

But not all of an area is good habitat. Moose need young forest and wetlands, not open lake or bare rock. So ecologists sometimes use two densities:

• Crude density: N divided by the total area.
• Ecological density: N divided by the area of suitable habitat only.

Ecological density is always the same as or higher than crude density, and it tells you how crowded the animals really feel.

Dispersion: how individuals are spaced

There are three basic patterns.

• Clumped: individuals gather in groups. This is the most common pattern in nature. Causes: resources are patchy (cattails grow only where the soil is wet), animals live in social groups (wolf packs, schools of yellow perch), or seeds fall near the parent plant.
• Uniform: individuals are evenly spaced. Causes: territorial behaviour (nesting northern gannets on Bonaventure Island, Quebec, space their nests about a neck-stretch apart) or competition for water and nutrients (some desert shrubs). Some plants release chemicals that stop others from growing nearby (allelopathy).
• Random: the position of one individual does not affect the others. This is uncommon. It happens when resources are evenly spread and individuals neither attract nor repel each other, for example dandelions whose wind-blown seeds land by chance on a uniform lawn.

The pattern can change with scale. Trees may be clumped across a whole valley (where the soil is good) but uniform within one patch (where each tree shades its neighbours).

Testing dispersion with numbers: the variance-to-mean ratio

Your eyes can be fooled, so ecologists test dispersion with quadrat counts. Put down many equal-sized quadrats, count the individuals in each, then compare the variance (s²) of the counts with their mean (x̄).

s² = Σ(x − x̄)² ÷ (n − 1), where n is the number of quadrats.

• s² ÷ x̄ ≈ 1: random (counts vary about as much as chance predicts).
• s² ÷ x̄ < 1: uniform (every quadrat gets about the same number).
• s² ÷ x̄ > 1: clumped (some quadrats are crowded, many are empty).

This connects to your math courses: for counts scattered purely at random (a Poisson distribution), the variance equals the mean. A ratio far from 1 means something non-random is going on.

Age structure and sex ratio

Two populations of 1000 can have very different futures. If most individuals are young and not yet breeding, the population is likely to grow when they mature. If most are old, it is likely to shrink. Ecologists show this with an age pyramid (you will use them for human populations in Human Population Growth and the Demographic Transition).

The sex ratio matters too. In many species, the number of females limits how many young can be born. That is one reason some hunting regulations in Ontario limit the harvest of antlerless (mostly female) deer more strictly than antlered bucks.

Minimum viable population

Some populations are so small that bad luck alone can wipe them out. A minimum viable population (MVP) is the smallest population that has a high probability (often set at 95%) of surviving for a chosen time (often 100 years). There is no single magic number; MVP depends on the species and its threats. Why are small populations so fragile?

• Demographic chance: in a population of 10, a few unlucky years with mostly male births or a few early deaths can end it.
• Environmental chance: one ice storm, drought or disease outbreak can kill a large fraction.
• Genetic problems: small populations lose genetic variation through genetic drift and suffer inbreeding (Grade 11 Evolution), which can reduce survival and fertility.
• The Allee effect: when individuals are scattered, they may fail to find mates, or groups become too small to defend themselves or hunt together.

These effects feed on each other in a downward spiral that conservation biologists call the extinction vortex. An old rule of thumb, the "50/500 rule", suggested at least 50 breeding individuals to avoid inbreeding in the short term and 500 to keep long-term variation; many biologists now think real MVPs are often higher.

A Canadian example: the migratory whooping crane flock that nests in Wood Buffalo National Park (Alberta and the Northwest Territories) fell to about 15 birds in 1941. With strict protection it has grown to several hundred birds, but it still has low genetic diversity, which is one reason recovery teams watch it so closely.