Population Dynamics & Growth

You’ll be able to

Identify the four factors that change population size and combine them into a growth rate
Distinguish exponential growth from logistic growth by their limiting conditions
Calculate a population’s growth rate as a percentage from birth, death, and migration data

What changes a population’s size

Only four processes change the number of individuals in a population. Two add individuals: births (natality) and immigration (moving in). Two remove them: deaths (mortality) and emigration (moving out). A population grows when additions exceed removals and shrinks when the reverse is true. Ecologists summarize births and deaths as rates — often the crude birth rate (CBR) and crude death rate (CDR), expressed per 1,000 individuals per year.

Biotic potential and exponential growth

Every population has a biotic potential — the maximum rate at which it could grow with unlimited resources and no limiting factors. Under those ideal conditions, growth is exponential: the population keeps multiplying by the same factor each period, producing a J-shaped curve that rises ever more steeply. Populations with high biotic potential (bacteria, insects, weeds) can explode in favorable conditions, but exponential growth cannot continue forever because resources are finite.

Logistic growth and the environmental ceiling

Real populations eventually run into limiting factors — food, water, space, disease — so growth slows as the population rises. This produces logistic growth, an S-shaped curve that climbs steeply, then levels off at the carrying capacity (K), the maximum population the environment can sustain over the long term. Early on, when the population is small relative to K, logistic growth looks nearly exponential; the difference appears as the population approaches its ceiling.

Population growth rate

growth rate (%) = [(births + immigration) − (deaths + emigration)] / N × 100

N is the starting population. A positive result means growth; a negative result means decline. If migration is negligible, growth rate ≈ (CBR − CDR) / 10 as a percent.

Worked example

A town of 10,000 people records, over one year: 400 births, 150 deaths, 50 people moving in, and 100 people moving out. What is the annual population growth rate as a percentage?

1.Add the inputs (individuals gained): births + immigration = 400 + 50 = 450.
2.Add the outputs (individuals lost): deaths + emigration = 150 + 100 = 250.
3.Net change = 450 − 250 = 200 individuals added over the year.
4.Divide by the starting population and convert to a percent: (200 / 10,000) × 100 = 2.0%.

Answer: The population grew by 2.0% that year. All four factors matter — leaving out immigration or emigration would give the wrong rate.

Checkpoint

A population of 5,000 deer has 600 births, 200 deaths, 0 immigrants, and 100 emigrants in one year. What is its annual growth rate?

Tip

Keep the sign conventions straight: births and immigration are the "plus" terms (individuals arriving), deaths and emigration are the "minus" terms (individuals leaving). A common slip is confusing immigration (in) with emigration (e = exit). Read the "e" in emigration as "exit."

Checkpoint

A bacterial population placed in a fresh, resource-rich flask doubles every 20 minutes for several hours. Which best describes this growth, and why can it not continue indefinitely?

On the exam

On the AP exam, "growth rate" almost always wants a percentage: compute the net change, divide by the starting population N, and multiply by 100. Show every step — even a wrong final number earns partial credit if the setup is right. Watch your units and don’t drop the ×100.

Answer the 2 checkpoints as you read.