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A population changes only by births, deaths and migration; natural increase and net migration together give the whole change, and rates let places be compared.
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By the end of this lesson you will be able to write a place's population change as natural increase plus net migration, find crude rates, and estimate a doubling time.
You know that people live in places at every scale, from a town to a country, and that places grow and shrink. You can subtract, find a percent, and read a table. This lesson turns a population's growth into a short account with four entries, so the cause of a change can be read off rather than guessed.
| Term | What it means |
|---|---|
| Population | The number of people living in a stated place at a stated time. |
| Natural increase | Births minus deaths in a place over a stated period. |
| Net migration | People moving in minus people moving out over the same period. |
| Crude birth rate | Births in a year for every thousand people living in the place. |
| Crude death rate | Deaths in a year for every thousand people living in the place. |
| Growth rate | The total change in a year as a percent of the population. |
| Doubling time | The years a population takes to double at a steady growth rate, about seventy divided by the rate in percent. |
A population changes in only four ways:
$$\text{change} = (\text{births} - \text{deaths}) + (\text{in} - \text{out}).$$
Rates per thousand people let places of different sizes be compared, and a steady growth rate of $r$ percent a year doubles a population in about $70/r$ years.
Another way: picture
Picture a county as a bathtub. Births pour in from one tap and arrivals from another; deaths drain out of one plug and departures out of another. The water level rises only when the taps together beat the plugs together, and it can rise even when one plug runs faster than its tap.
Another way: steps
Density divides a population by a stated area. Distribution describes where people are located within it; concentration describes clustering in a small part of that area. Movement describes flows between places during a period. These answer different questions. An invented district with 800 residents over 40 square kilometers has a density of 20 people per square kilometer whether all residents occupy one riverside town or many scattered hamlets. A district average cannot locate a settlement.
To compare patterns, first hold the boundary and date constant. Imagine four equal map cells, west to east. A settlement count of 200, 200, 200, 200 is dispersed across the cells; 0, 0, 800, 0 is concentrated in the third cell. Both totals and district densities match. A relocation of 100 people from cell one to cell three changes the within-district distribution without changing district population. Arrivals across the district boundary, in contrast, enter its migration balance.
For a worked comparison, district Alder has 900 people over 30 square kilometers; Birch has 900 over 90. Divide to obtain 30 and 10 people per square kilometer. Alder is denser, but neither density tells us whether homes form clusters. Request a settlement map before explaining concentration. A flow arrow needs an origin, destination, period and magnitude; it cannot be read as the number currently resident at its destination.
Every change in a population can be written as a small account. Two entries add people: births and arrivals. Two take people away: deaths and departures. Nothing else can change the count, which is why geographers call this the demographic balancing equation.
Because the account must balance, a missing entry can be found from the others. If a census counts the people at the start and end of a decade, and birth and death records are complete, the difference that is left must be net migration.
Births minus deaths is called the natural increase, even when it is a decrease. A county with $620$ births and $410$ deaths in a year has a natural increase of $210$.
Natural increase depends heavily on the age of a population. A place full of young adults has many births and few deaths. A place with many retirees can have more deaths than births, so its natural increase is negative even when its families are healthy and its hospitals are good.
Arrivals minus departures is the net migration. A county that gains $350$ people and loses $280$ has a net migration of $70$. Arrivals can come from the next county, another state or another country, and the Census Bureau counts domestic and international migration separately for exactly that reason.
Net migration hides how many people actually moved. A college town may see thousands arrive and thousands leave every year, yet its net migration is small, because the students who graduate are replaced by new ones.
It is easy to assume a growing place must have more births than deaths. It need not. A retirement area in Florida or Arizona can record more deaths than births and still grow quickly, because many more people move in than move out.
The reverse also happens. A farming county on the Great Plains may have more births than deaths and still shrink, as young adults leave for jobs in cities. Reading only one side of the account gives the wrong explanation of the change.
A county with $2300$ births is not necessarily more fertile than one with $620$. It may simply be bigger. Dividing by the population and multiplying by a thousand turns a count into a crude rate, births or deaths for every thousand people.
The word crude is a warning, not an insult. The rate divides by everyone, young and old, so a place full of older people has a low crude birth rate partly because few of its residents are of an age to have children.
When the crude birth rate is $27$ per thousand and the crude death rate is $7$, the natural increase is $20$ per thousand. Per thousand divided by ten is per hundred, so the population is growing by $2$ percent a year from natural increase.
That small-looking number is large. A growth rate of $2$ percent a year adds a fifth to a population in about a decade, which means a fifth more classrooms, homes and jobs.
Growth compounds: each year's increase is added to a bigger base than the year before. A population growing steadily by $r$ percent a year doubles in about $70/r$ years. At $2$ percent that is $35$ years; at $3.5$ percent, only $20$.
The seventy comes from compound growth itself, and it gives a quick answer that is close enough for planning. It assumes the rate stays steady, which real rates rarely do for long, so a doubling time is a projection, not a prediction.
Checking an answer. A county rarely changes by more than a few percent in a year. A change of a quarter of the population, or a birth rate above fifty per thousand, usually means an entry was added that should have been subtracted.
People enter a population only by being born or moving in, and leave only by dying or moving out. So the change must equal the entries minus the exits, and grouping them into natural increase and net migration only rearranges the sum.
Dividing by the population is allowed because the rate describes the place, not its size. Two counties with the same crude birth rate have the same share of births, whatever their populations.
In the United States, births and deaths are registered by each state and collected by the National Center for Health Statistics. Migration has no such register. The Census Bureau estimates it from tax records, surveys and immigration data, and revises the estimates when better data arrive.
So the four entries are not equally certain. Births and deaths are counted almost exactly; migration is estimated. A careful geographer states which figures are counts, which are estimates, and which year and agency they come from.
At the scale of the whole world, net migration is zero, because every departure from one country is an arrival in another. World population changes only by births and deaths.
At the scale of a country, a state or a county, migration can matter as much as births and deaths, or more. The smaller the place, the more its population tends to depend on who moves in and out, which is why a place question must always name its scale.
The Census Bureau estimated that between July 2022 and July 2023 the United States grew by about $1.6$ million people, or half a percent, to about $335$ million. Births outnumbered deaths by about $0.5$ million.
Net international migration added about $1.1$ million, roughly twice the natural increase. So most of the nation's growth that year came from people arriving, not from births exceeding deaths, a pattern expected to strengthen as the population ages.
Natural increase follows age. Utah, with many young families, has one of the highest crude birth rates of any state. Maine and West Virginia, with older populations, have recorded more deaths than births in recent years.
This is why the same crude rates can mislead across places. A low birth rate in an older state does not show that its families are smaller; it may only show that a smaller share of its people are young adults.
A doubling time turns a percent into something a town can plan for. If a place growing at $3.5$ percent a year will double in about twenty years, then within that time it needs twice the water supply, twice the school seats and roads that carry twice the traffic.
Fast-growing suburbs of Phoenix, Austin and Boise have faced exactly this. Planners use the rule of seventy for a first estimate, then refine it with projections that let each flow change over time.
The most common slip is adding deaths or departures instead of subtracting them. Another is ignoring migration and reporting natural increase as the whole change.
A third is to multiply by one hundred instead of one thousand when finding a crude rate, which gives a number ten times too small. A fourth is to use the growth rate as a decimal in the rule of seventy: at $2$ percent, divide seventy by $2$, not by $0.02$.
The account says how a population changed, which is the start of an explanation rather than the end. The next question is why: why more people arrived, why births fell, why young adults left.
The later lessons of this course take up those causes. A good explanation of a place's growth always names which flow drove it, at what scale and over what period, and gives the figures with their year and source.
Every December the U.S. Census Bureau publishes estimates of the population of the nation, each state and each county as of the previous July. It builds them from the four flows. Birth and death certificates come from the states; domestic migration is estimated from tax returns and Medicare records that show where people filed from one year to the next; international migration is estimated from surveys and immigration data.
For the year to July 2023 the estimates showed the nation growing by about $1.6$ million, with net international migration of about $1.1$ million and a natural increase of about $0.5$ million. Among the states, Texas gained the most people, close to half a million, while several states in the Northeast and Midwest shrank because more residents moved to other states than arrived.
These numbers matter far beyond curiosity. Federal funding for roads, schools and health programs is shared out partly by population, and businesses use the estimates to decide where to open stores. Each year's estimates are revised as better migration data arrive, which is why a careful report always gives the vintage of the estimate it quotes.
Japan offers a contrast to the United States. Its population peaked around 2008 at about $128$ million and has fallen since. In 2023 its Ministry of Health, Labour and Welfare recorded fewer than $760000$ births against almost $1.6$ million deaths, a natural decrease of more than $800000$ people in a single year.
Japan's net migration has been positive in recent years, as more foreign workers arrive, but it has been far too small to balance the natural decrease. So the account shows a population shrinking mainly because deaths outnumber births, the result of decades of low fertility and one of the longest life expectancies in the world.
The consequences are visible across the country. Rural towns lose schools and shops, and some villages have been left almost empty. Planners in Japan now use the same account as planners in growing American suburbs, but to decide what to close and how to care for a large older population, rather than what to build.
It is natural to think a growing place must be one where more people are born than die. But a population is changed by four flows, not two. A retirement county can have more deaths than births and still grow fast, because arrivals outnumber departures; a rural county can have more births than deaths and still shrink.
In 2023, most of the growth of the United States came from net international migration rather than natural increase. Reading one pair of flows without the other gives the wrong explanation of the change.
A county starts with $60000$ people, records $700$ births and $520$ deaths. Find the natural increase.
$700 - 520 = 180$
Births minus deaths.
During the year $900$ people move in and $650$ move out. Find the net migration.
$900 - 650 = 250$
In minus out.
Find the total change.
$180 + 250 = 430$
Both flows together.
Find the year-end population.
$60000 + 430 = 60430$
Start plus change.
A retirement county of $90000$ records $610$ births and $1150$ deaths. Find the natural increase.
$610 - 1150 = -540$
More deaths than births.
It gains $4200$ arrivals and loses $2100$ departures. Find the net migration.
$4200 - 2100 = 2100$
Many more arrivals.
Find the total change.
$-540 + 2100 = 1560$
Migration outweighs the natural decrease.
Find the growth rate.
$\dfrac{1560}{90000} \times 100 \approx 1.7\%$
Change over population, as a percent.
Name the flow that drove the change.
$\text{net migration}$
It is the larger entry, and it is positive.
A country of $20$ million records $760000$ births in a year. Find the crude birth rate.
$\dfrac{760000}{20000000} \times 1000 = 38$
Births per thousand.
It records $160000$ deaths. Find the crude death rate.
$\dfrac{160000}{20000000} \times 1000 = 8$
Deaths per thousand.
Find the natural increase per thousand.
$38 - 8 = 30$
Birth rate minus death rate.
Convert it to a percent.
$30 \div 10 = 3\%$
Per hundred.
Find the doubling time.
$70 \div 3 \approx 23\ \text{years}$
Rule of seventy.
Say what the doubling time assumes.
$\text{steady rate, no net migration}$
A projection, not a forecast.
Find the natural increase.
$480 - 350 = 130$
Births minus deaths.
Find the net migration.
$300 - 410 = -110$
More people left than arrived.
Add the two for the total.
A county had $36000$ people at the start of a year. During the year there were $410$ births and $480$ deaths, $520$ people moved in and $300$ people moved out. How many people lived there at the end of the year?
Complete the worked solution: a country has a crude birth rate of $27$ and a crude death rate of $7$, both per thousand people, and no net migration. Find its natural increase per thousand, its growth rate in percent, and the years it takes to double at that rate.
Subtract the death rate from the birth rate.
$27 - 7 =$ n
Natural increase per thousand.
Turn it into a percent.
$\dfrac{\text{per thousand}}{10} =$ r
Per hundred is a tenth of per thousand.
Apply the rule of seventy.
$\dfrac{70}{\text{rate in } \%} =$ t
Years to double.
Check that faster growth doubles sooner.
$\text{a higher rate gives fewer years}$
The rate is in the denominator.
Match each term to its meaning.
| births minus deaths | people moving in minus people moving out | births per thousand people in a year | the years a steady growth rate takes to double a population | |
|---|---|---|---|---|
| natural increase | ||||
| net migration | ||||
| crude birth rate | ||||
| doubling time |
In one year a county recorded $950$ births and $720$ deaths; $640$ people moved in and $410$ moved out. Fill in its natural increase, its net migration and its total change. Write a loss as a negative number.
| value | |
|---|---|
| natural increase (people) | |
| net migration (people) | |
| total change (people) |
A county starts a year with $48000$ people and records $620$ births and $410$ deaths. Its net migration for the year, $m$, is not yet known. Write the county's population at the end of the year as a function of $m$.
Answer:
A county of $45000$ people recorded $540$ births in a year. What is its crude birth rate, in births per thousand people?
Answer: per 1,000
A planning office supposes that a small city in Utah keeps growing by $1.4$ percent a year. About how many years will its population take to double?
Answer: years
East and West each have 6 hundred residents in 20 square kilometers. East's homes cluster at one station; West's are evenly spread. An arrow records 40 moves from East to West last year. Mark every sentence that belongs in an evidence-supported interpretation, including its limits.
This task has no paper form; do it on a device.
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A county starts a year with $36000$ people and records $410$ births and $480$ deaths. Its net migration for the year, $m$, is not yet known. Write the county's population at the end of the year as a function of $m$.
Answer:
You can account for a population change. Explain how a county can grow even though more people die there than are born.
28. Your turn: a county records $480$ births, $350$ deaths, $300$ arrivals and $410$ departures. What is its total change?, step 3
$130 + (-110) = 20$
A small gain.