F. Population Dynamics · Population DynamicsHuman Population Growth and the Demographic Transition
F1.1 F2.2 F3.2 F2.1 A1.9About 70 minutes
Learning goals- I can describe the history of human population growth and the factors that changed it.
- I can calculate rates of natural increase and doubling times from crude birth and death rates.
- I can explain the stages of the demographic transition model and interpret age pyramids.
- I can use current data (2026) to describe world and Canadian population trends, and explain why projections are uncertain.
Words to know
crude birth rate (CBR)
Births per 1000 people per year.
crude death rate (CDR)
Deaths per 1000 people per year.
rate of natural increase
(CBR − CDR) ÷ 10, as a percentage per year. It ignores migration.
total fertility rate (TFR)
The average number of children a woman would have over her lifetime at current age-specific birth rates.
replacement-level fertility
The TFR at which a population exactly replaces itself over generations without migration: about 2.1 children per woman in countries with low child mortality.
demographic transition
The shift from high birth and death rates to low birth and death rates as a society industrializes.
age pyramid (population pyramid)
A bar graph showing the numbers (or percentages) of males and females in each age group.
population momentum
The tendency of a population with many young people to keep growing for decades even after fertility falls to replacement level.
Eight billion and counting
For most of human history, our population grew very slowly. Hunting, gathering and early farming societies had high birth rates, but also high death rates, especially among babies and children. Then, in about two centuries, everything changed. The United Nations estimates that the world reached 1 billion people around 1804, 2 billion in 1927, and 8 billion on 15 November 2022. In 2026, the world population is about 8.3 billion.
In this lesson you will apply your population models to the most important species for our future: us.
Years in which the world reached each billion (United Nations estimates). Going from 1 to 2 billion took 123 years; going from 7 to 8 billion took only 11.Why did human growth speed up?
The population model is the same: ΔN = births − deaths (migration does not change the world total). What changed were the rates:
- Agriculture (beginning about 10 000 years ago) produced more food per hectare, supporting more people.
- The Industrial Revolution (from the late 1700s) and modern agriculture (machinery, fertilizers, improved crop varieties) increased the food supply further, a way of raising K.
- Sanitation, clean water, vaccines and antibiotics caused death rates to fall, especially for infants and children.
Birth rates fell much more slowly than death rates, so for a long time births greatly exceeded deaths. The world growth rate peaked at a little over 2% per year in the 1960s. It has roughly halved since and is now below 1% per year. The number of people added each year is still large, because the population is so big.
For much of the 20th century human growth was even faster than exponential: the per capita growth rate itself was rising. That is now reversing.
Measuring human population change
Demographers use rates per 1000 people:
- Rate of natural increase (%) = (CBR − CDR) ÷ 10.
For example, CBR = 30 and CDR = 8 give (30 − 8) ÷ 10 = 2.2% per year. By the rule of 70, that population doubles in about 70 ÷ 2.2 ≈ 32 years.
The total fertility rate (TFR) looks ahead: the average number of children per woman. Replacement level is about 2.1 where child mortality is low (slightly above 2, because not every child survives to have children, and slightly more boys than girls are born). Canada's TFR was 1.25 in 2024, a record low according to Statistics Canada. With fertility well below replacement, Canada's growth now comes mostly from immigration. Statistics Canada estimated Canada's population at about 41.8 million in July 2026, after revising its earlier estimates upward in September 2026: a reminder that even official population numbers are estimates that get corrected.
Worked exampleLet's compare two countries
Country A has CBR = 36 and CDR = 9. Country B has CBR = 9 and CDR = 11. (a) Find each rate of natural increase. (b) Find the doubling time for A (exact and by the rule of 70). (c) What must be true for B's population to grow?
- (a) A: (36 − 9) ÷ 10 = 2.7% per year. B: (9 − 11) ÷ 10 = −0.2% per year (natural decrease).
- (b) Exact: r = 0.027, so t_d = ln 2 ÷ 0.027 = 0.693 ÷ 0.027 = 25.7 years. Rule of 70: 70 ÷ 2.7 ≈ 26 years.
- (c) B has more deaths than births, so it can grow only if net immigration is greater than the natural decrease (more than 2 people per 1000 per year).
(a) A: +2.7% per year; B: −0.2% per year. (b) A doubles in about 26 years. (c) B needs net immigration above 2 per 1000 per year to grow.
The demographic transition model
As countries industrialize, their birth and death rates tend to change in a typical sequence:
- Stage 1, pre-industrial: high birth rates and high death rates; slow, unsteady growth. (No country is fully in Stage 1 today.)
- Stage 2, early transition: death rates fall (food, sanitation, medicine) while birth rates stay high: rapid growth.
- Stage 3, late transition: birth rates fall (urban living, education, especially for girls and women, access to family planning, lower child mortality so families no longer need many children); growth slows.
- Stage 4, post-industrial: low birth and death rates; slow or zero growth. Canada is here.
- Stage 5 (proposed): birth rate falls below death rate; the population shrinks without immigration (for example Japan and Italy).
Link to the unit: the transition is like a population moving from r-like reproduction (many children, high early mortality) toward K-like reproduction (few children, high investment in each), and survivorship shifting from Type II or III toward Type I.
The demographic transition model (a sketch). The gap between the birth-rate line and the death-rate line is the rate of natural increase; it is widest in Stage 2 and narrows in Stages 3 and 4.Age pyramids and population momentum
An age pyramid shows the population by age and sex.
- Expansive (wide base): many children, rapid growth; typical of countries in Stages 2 and 3, such as Niger.
- Stationary (straight sides): similar numbers in each age group until old age; slow growth.
- Constrictive (narrow base): fewer children than adults; an aging, possibly shrinking population, such as Japan. Canada's pyramid is becoming more constrictive: in recent years there have been more Canadians aged 65 and over than children under 15.
Population momentum: a country with a very young population keeps growing for decades even after its TFR drops to 2.1, because the large generation of children has not yet had its own children. This is one reason the UN projects that world population will keep growing until it peaks at about 10.3 billion in the mid-2080s (World Population Prospects 2024), even though global fertility is already falling.
Three shapes of age pyramid (sketches). The width of the youngest bars compared with the adult bars tells you whether a population is likely to grow or shrink.What is Earth's carrying capacity for humans?
No one knows a single number, and scientists' estimates vary enormously, because human K depends on how we live. A planet of people eating mostly plants, using renewable energy and living in efficient homes can support far more people than a planet where everyone consumes as much as the average Canadian. Technology can raise K (more food per hectare) but can also deplete resources that future generations need. The next lesson, Consumption, Technology and the Ecological Footprint, gives a way to measure this.
Evaluate your sources (A1.9)
Population figures change constantly and are revised. Use primary sources (Statistics Canada, the United Nations Population Division), check the date of every number, and look for a range or margin of error in projections. A projection is a scenario based on assumptions, not a prediction of certainty.
Just for funIt took our species hundreds of thousands of years to reach 1 billion people and only 11 years to go from 7 to 8 billion. If you ever feel the school hallway is crowded, blame the death rate for falling so successfully.
Hands-on activityBuild your family's or a country's age pyramid
You need: graph paper or a free spreadsheet, a pencil, and access to the Statistics Canada website (search "Statistics Canada age and sex population estimates") or a family tree.
Option A: a country. From Statistics Canada, record Canada's population in 5-year age groups (0-4, 5-9, ... 85+) for males and females. Draw an age pyramid with males on the left and females on the right. Repeat with an online pyramid for one other country (the UN World Population Prospects website has them). Classify each pyramid's shape and predict each country's growth over the next 30 years.
Option B: a family. Ask relatives (respectfully; some people prefer not to share) how many children were in each generation of your family: great-grandparents' generation, grandparents', parents', yours. Graph the average number of children per family in each generation. Discuss whether your family's pattern matches the demographic transition, and why it might not (immigration, culture, personal choice).
What to look for: Canada's pyramid is narrowest at the bottom and widest in the middle-aged groups, a constrictive shape; a country such as Niger has a very wide base (expansive). Many Canadian families show fewer children per family in recent generations, matching Stage 4, but individual families vary widely, which is why demographers study large populations.
Your turn
1Approximately when did the world population reach 1 billion and 8 billion?
About 1804 and 15 November 2022 (UN estimates).
2A country has CBR = 24 and CDR = 7. Find its rate of natural increase and approximate doubling time.
(24 − 7) ÷ 10 = 1.7% per year. Doubling time ≈ 70 ÷ 1.7 ≈ 41 years.
3Why did death rates fall before birth rates in the demographic transition?
Improvements in food, sanitation, clean water and medicine lower deaths quickly, while birth rates depend on social and economic changes (education, urban life, access to family planning, confidence that children will survive) that take longer.
4What is replacement-level fertility, and why is it about 2.1 rather than 2.0?
The TFR at which each generation exactly replaces the previous one. It is slightly above 2 because not all children survive to have children and slightly more boys than girls are born.
5Describe the shape of an age pyramid for a rapidly growing population.
Expansive: a wide base (many children) narrowing quickly toward the top.
6Canada's TFR is well below 2.1, yet its population usually grows. Explain.
Most of Canada's growth comes from immigration; natural increase (births minus deaths) is now very small.
7What is population momentum?
The continued growth of a population with many young people, even after fertility falls to replacement, because those young people are still entering their child-bearing years.
More practice: warm-up
1Which stage of the demographic transition has the fastest growth?
3What was Canada's TFR in 2024?
1.25 (a record low, Statistics Canada).
4About what is the world population in 2026?
5What is the rate of natural increase if CBR = CDR?
More practice: on your own
1How many years did it take the world to go from 3 billion (1960) to 6 billion (1999)? What average per capita growth rate does this imply?
39 years for a doubling. r = ln 2 ÷ 39 = 0.0178, about 1.8% per year.
2A country's CBR falls from 40 to 20 while its CDR falls from 30 to 10. Has its rate of natural increase changed? Which stages did it move between?
Before: (40 − 30) ÷ 10 = 1.0%. After: (20 − 10) ÷ 10 = 1.0%. The rate is the same, but the country moved from early Stage 2 (high birth and death rates) toward Stage 3 or 4 (both rates lower). Same growth rate, very different society.
3Explain why the world population is projected to keep growing until the 2080s even though global fertility is falling.
Population momentum: many countries have young age structures, so the number of people in their child-bearing years will keep rising for decades. Life expectancy is also rising, so deaths stay relatively low for a while.
4Explain how the demographic transition relates to survivorship curves and to r- and K-selection.
Stage 1 and 2 societies have high child mortality and many births (more Type III/II-like, more r-like). Post-industrial societies have low child mortality, few births and high investment per child (Type I, more K-like).
5A news article says, "Canada's population fell in early 2026." Later, Statistics Canada revised its estimates and said the population had kept growing. What should a careful reader learn from this?
Population figures are estimates based on data (for example, records of temporary residents arriving and leaving) that can be incomplete at first. Readers should check the date and source, look for revisions, and avoid drawing strong conclusions from one preliminary number.
Challenge
1World population was about 8.0 billion in late 2022 and the UN projects a peak of about 10.3 billion in the mid-2080s. (a) What average growth rate would take 8.0 billion to 10.3 billion in 62 years? (b) Compare this with the 1960s peak rate of about 2% per year. (c) Is human growth currently exponential or logistic-like? Explain.
(a) e^(62r) = 10.3 ÷ 8.0 = 1.2875. 62r = ln 1.2875 = 0.2527. r = 0.0041, about 0.4% per year on average. (b) That is about one fifth of the 1960s rate. (c) It is logistic-like in shape: the per capita growth rate is falling as the population grows, so growth is slowing toward a peak. But the cause is mainly falling fertility by choice and social change, not resource limits pressing on the population as in the simple logistic model.
2Some people argue that a falling birth rate is a problem for Canada; others argue it is good for the environment. Present one biological or economic argument for each view.
Concern: an aging population means fewer working-age people to support pensions and health care for a growing number of seniors (a constrictive pyramid), and labour shortages. Benefit: fewer people means lower total resource use and ecological footprint (if consumption per person does not rise), easing pressure on habitats and the climate. A strong answer notes that consumption per person matters as much as population size.
3A Stage 2 country has CBR = 38 and CDR = 12, and its TFR is falling by 0.1 per year. Explain why its population will still be much larger in 40 years, even if the TFR reaches 2.1 within 20 years.
Its current natural increase is (38 − 12) ÷ 10 = 2.6% per year, a doubling time of about 27 years. Even when TFR reaches replacement, its expansive age pyramid means a huge cohort of children will enter their child-bearing years, producing many births (momentum), while death rates stay low because the population is young. So the population keeps growing for decades after fertility falls.
Check your understandingQuiz
1. According to UN estimates, the world population reached 8 billion in:
2. A country has CBR = 28 and CDR = 8. Its rate of natural increase is:
3. In Stage 2 of the demographic transition:
4. An age pyramid with a narrow base and wide middle shows a population that is:
5. Canada's total fertility rate in 2024 was about:
6. Population momentum means that a young population:
For parents and teachersBig idea (F1.1, F2.2, F3.2): human population grew slowly for millennia, then rapidly as death rates fell. The demographic transition model explains the shift to low birth and death rates; age pyramids and population momentum explain why growth continues for a while after fertility falls. In 2026 the world has about 8.3 billion people and Canada about 41.8 million, with Canada's growth mainly from immigration.
How to help: the family-generations option can lead to rich conversations about history and immigration; be sensitive, since family size can be a personal topic. Encourage your teen to check the date and source of any population number they use.
Common difficulties:
- Rate of natural increase: divide (CBR − CDR) by 10 to get a percentage.
- Thinking a falling growth rate means a falling population: a positive but smaller rate still adds people.
Sources: United Nations, World Population Prospects 2024 (milestones, 8 billion on 15 November 2022, projected peak of about 10.3 billion in the mid-2080s); Statistics Canada (TFR 1.25 in 2024, The Daily, September 2025; population estimates and September 2026 revisions). Figures checked October 2026.