AP® Environmental Science review sheet from Aim for Five (aimforfive.com/enviro/units/3/3-8)
Unit 3 · Topic 3.8
3.8 Human Population Dynamics
A human population changes through births, deaths, immigration and emigration. You can calculate the growth rate from birth and death rates, estimate doubling time with the rule of 70, and explain limits on growth with density-dependent and density-independent factors.
Key terms
- crude birth rate
- crude death rate
- rate of natural increase
- rule of 70
- density-dependent factor
- density-independent factor
Four ways a population changes
Populations grow through births and immigration (people moving in) and shrink through deaths and emigration (people moving out). For a whole country:
Change in population = (births + immigrants) − (deaths + emigrants).
To get the growth rate as a percent, divide the change by the starting population and multiply by 100.
Crude rates and the rate of natural increase
The crude birth rate (CBR) is the number of births per 1,000 people per year. The crude death rate (CDR) is the number of deaths per 1,000 people per year. ‘Crude’ means they're based on the whole population, not adjusted for age.
The rate of natural increase leaves out migration: it's CBR − CDR, which gives the increase per 1,000 people. Since percent means per 100, divide by 10 to convert per 1,000 to a percent:
Growth rate (%) = (CBR − CDR) ÷ 10.
For example, a CBR of 25 and a CDR of 9 give (25 − 9) ÷ 10 = 1.6% per year.
The rule of 70
Doubling time is how long a population (or anything growing at a steady percentage) takes to double. The rule of 70 estimates it:
Doubling time (years) ≈ 70 ÷ growth rate (as a percent, not a decimal).
A population growing at 2% per year doubles in about 70 ÷ 2 = 35 years. At 1%, it takes about 70 years. The rule works because of how exponential growth compounds. It's an approximation, but it's very close for growth rates of a few percent.
Once you know the doubling time, you can project forward: after one doubling time the population is 2 times as large, after two it's 4 times, after three it's 8 times.
What limits population growth
Disease is density-dependent because it spreads faster when people or animals are close together. A hurricane is density-independent: it destroys a coastal area whether 100 or 10,000 animals live there.
For humans, technology has repeatedly raised carrying capacity. In 1798, Thomas Malthus argued that population would outgrow food supply and be checked by famine and disease. Advances like the Green Revolution have so far kept food production ahead of population on a global scale, though hunger persists in many places and the environmental costs are large. World population passed 8 billion in 2022.
| Factor type | Meaning | Examples |
|---|---|---|
| Density-dependent | Effect gets stronger as the population gets more crowded | Disease, competition for food and water, predation, parasites, stress |
| Density-independent | Effect is the same regardless of crowding | Droughts, floods, fires, hurricanes, extreme cold or heat |
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Growth rate and doubling time
A country has a crude birth rate of 32 per 1,000 and a crude death rate of 8 per 1,000. Ignoring migration, calculate its growth rate and doubling time.
Show the solutionHide the solution
- Step 1: Rate of natural increase = CBR − CDR = 32 − 8 = 24 per 1,000.
- Step 2: Convert to a percent: 24 ÷ 10 = 2.4% per year.
- Step 3: Rule of 70: doubling time ≈ 70 ÷ 2.4 = 29.2 years.
Answer: 2.4% per year; doubling time about 29 years.
- Example 2Calculator allowed
Including migration
A country of 5,000,000 people has 120,000 births, 40,000 deaths, 15,000 immigrants and 5,000 emigrants in one year. Calculate its growth rate and doubling time.
Show the solutionHide the solution
- Step 1: Change = (births + immigrants) − (deaths + emigrants) = (120,000 + 15,000) − (40,000 + 5,000) = 135,000 − 45,000 = 90,000.
- Step 2: Growth rate = 90,000 ÷ 5,000,000 × 100 = 1.8% per year.
- Step 3: Doubling time ≈ 70 ÷ 1.8 = 38.9 years.
Answer: 1.8% per year; doubling time about 39 years.
- Example 3
The per-1,000 trap
A country has a CBR of 20 and a CDR of 10. A student calculates a doubling time of 7 years. Find the error and the correct doubling time. If the population is 40 million now, about how large will it be in 140 years if the rate stays the same?
Show the solutionHide the solution
- Step 1: The student used 10 (per 1,000) as if it were 10%. Convert first: (20 − 10) ÷ 10 = 1.0% per year.
- Step 2: Doubling time ≈ 70 ÷ 1.0 = 70 years.
- Step 3: 140 years is 140 ÷ 70 = 2 doubling times.
- Step 4: After two doublings: 40 million × 2 × 2 = 160 million.
Answer: The correct doubling time is 70 years, not 7. In 140 years the population would be about 160 million.
Common mistakes
- Forgetting to divide (CBR − CDR) by 10 to get a percent. Rates per 1,000 aren't percents.
- Plugging a decimal into the rule of 70. Use 2 for 2%, not 0.02.
- Leaving out migration when the question gives immigration and emigration numbers.
- Calling disease density-independent. It spreads more easily in crowded populations, so it's density-dependent.
On the exam
- The calculation free-response question often includes growth rate or doubling time. Show each step with labels: the formula, the numbers substituted and the answer with units (percent or years).
- Be ready to classify factors as density-dependent or density-independent and explain why.
Connected topics
Videos
Check yourself
4 questions on 3.8 Human Population Dynamics. Pick an answer to see if you got it, and why.
A country has a crude birth rate of 30 per 1,000 and a crude death rate of 10 per 1,000. Ignoring migration, about how long will it take its population to double?
| Measure | Number |
|---|---|
| Population at the start of the year | 2,000,000 |
| Births | 50,000 |
| Deaths | 20,000 |
| Immigrants | 6,000 |
| Emigrants | 16,000 |
Hypothetical data
What was the city's population growth rate for the year, including migration?
If this growth rate stayed constant, about how many years would it take the city's population to double?
A town's population doubled from 15,000 to 30,000 in 28 years. Using the rule of 70, what was its approximate annual growth rate?
0 of 4 answered