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Population growth

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In biology, population growth is the increase in the number of individuals in a population.


Global human population growth amounts to around 75 million annually, or 1.1% per year. The global population has grown from 1 billion in 1800 to 7 billion in 2012. It is expected to keep growing, and estimates have put the total population at 8.4 billion by mid-2030, and 9.6 billion by mid-2050. Many nations with rapid population growth have low standards of living, whereas many nations with low rates of population growth have high standards of living.


The growth of the population started in the Western world during industrialization by the end of the 18th century. The reasons for the "Modern Rise of Population" were particularly investigated by the British health scientist Thomas McKeown (1912-1988). In his publications, McKeown challenged four theories about the population growth:

  1. McKeown stated that the growth in Western population, particularly surging in the 19th century, was not so much caused by an increase in fertility, but largely by a decline of mortality particularly of childhood mortality followed by infant mortality,
  2. The decline of mortality could largely be attributed to rising standards of living, whereby McKeown put most emphasis on improved nutritional status,
  3. His most controversial idea, at least his most disputed idea, was that he questioned the effectiveness of public health measurements, including sanitary reforms, vaccination and quarantine,
  4. The sometime very fierce disputes that his publication provoked around the "McKeown thesis", have overshadowed his more important and largely unchallenged argument that curative medical measures played little role in mortality decline, not only prior to the mid-20th century but also until well into the 20th century.

Although the McKeown thesis has been heavily disputed, recent studies have confirmed the value of his ideas. His work is pivotal for present day thinking about population growth, birth control, public health and medical care. McKeown had a major influence on many population researchers, such as health economists and Noble prize winners Robert W. Fogel (1993) and Angus Deaton (2015). The latter considered McKeown as 'the founder of social medicine'.

Population growth rate

The "population growth rate" is the rate at which the number of individuals in a population increases in a given time period, expressed as a fraction of the initial population. Specifically, population growth rate refers to the change in population over a unit time period, often expressed as a percentage of the number of individuals in the population at the beginning of that period. This can be written as the formula, valid for a sufficiently small time interval:

P o p u l a t i o n   g r o w t h   r a t e = P ( t 2 ) P ( t 1 ) P ( t 1 ) ( t 2 t 1 )

A positive growth rate indicates that the population is increasing, while a negative growth rate indicates that the population is decreasing. A growth ratio of zero indicates that there were the same number of individuals at the beginning and end of the period—a growth rate may be zero even when there are significant changes in the birth rates, death rates, immigration rates, and age distribution between the two times.

A related measure is the net reproduction rate. In the absence of migration, a net reproduction rate of more than 1 indicates that the population of females is increasing, while a net reproduction rate less than one (sub-replacement fertility) indicates that the population of females is decreasing.

Most populations do not grow exponentially, rather they follow a logistic model. Once the population has reached its carrying capacity, it will stabilize and the exponential curve will level off towards the carrying capacity, which is usually when a population has depleted most its natural resources.

The Logistic Equation

d P d t = k P ( 1 P K )


P ( t ) = the population after time t

t = time a population grows

k = relative growth rate coefficient

K = carrying capacity of the population; defined by ecologists as the maximum population size that a particular environment can sustain.

The Analytic Logistic Solution

This is a separable differential equation that can be derived through integration. The analytic solution is useful in analyzing the behavior of population models.

The equation is separable and to find the solution we integrate.

d P P ( 1 P K ) = k d t

Working on just the left side of the equation, the fraction in the denominator is eliminated by multiplying the variable K, and then the fraction is split in 2.

1 P ( 1 P K ) K K = K P ( K P )

K P ( K P ) = 1 P + 1 K P

The partial fraction is then integrated more easily.

( 1 P + 1 K P ) d P = k d t

After integrating and using U substitution, we get

ln | P | + ln | K P | = k t C

ln | K P P | = k t C

Exponentiate both sides to get rid of the natural log. This is the equation that remains:

| K P P | = e k t C

Get rid of the absolute value and split the e into 2 parts.

K P P = ± e C e k t

Let A = ± e C and get

K P P = A e k t

Solve for P to get the explicit solution to the logistic equation as

P ( t ) = K 1 + A e k t ; where A = K P 0 P 0 and P 0 = the initial population at time 0.

Human population growth rate

In 2009, the estimated annual growth rate was 1.1%. The CIA World Factbook gives the world annual birthrate, mortality rate, and growth rate as 1.86%, 0.78%, and 1.08% respectively. The last 100 years have seen a massive fourfold increase in the population, due to medical advances, lower mortality rates, and an increase in agricultural productivity made possible by the Green Revolution.

The annual increase in the number of living humans peaked at 88.0 million in 1989, then slowly declined to 73.9 million in 2003, after which it rose again to 75.2 million in 2006. In 2009, the human population increased by 74.6 million. Generally, developed nations have seen a decline in their growth rates in recent decades, though annual growth rates remain above 2% in poverty-stricken countries of the Middle East and Sub-Saharan Africa, and also in South Asia, Southeast Asia, and Latin America.

In some countries the population is declining, especially in Eastern Europe, mainly due to low fertility rates, high death rates and emigration. In Southern Africa, growth is slowing due to the high number of AIDS-related deaths. Some Western Europe countries might also experience population decline. Japan's population began decreasing in 2005; it now has the highest standard of living in the world.

The United Nations Population Division projects world population to peak at over 10 billion at the end of the 21st century, but Sanjeev Sanyal has argued that global fertility will fall below the replacement rate in the 2020s and that world population will peak below 9 billion by 2050, followed by a long decline. A 2014 study in Science concludes that the global population will reach 11 billion by 2100, with a 70% chance of continued growth into the 22nd century.

Growth by country

According to United Nations population statistics, the world population grew by 30%, or 1.6 billion humans, between 1990 and 2010. In number of people the increase was highest in India (350 million) and China (196 million). Population growth was among highest in the United Arab Emirates (315%) and Qatar (271%).

* Eritrea left Ethiopia in 1991. † Split into the nations of Sudan and South Sudan during 2011. ‡ Japan and the Ryukyu Islands merged in 1972. # India and Sikkim merged in 1975.

Into the future

According to the UN's 2010 revision to its population projections, world population is projected to peak at 10.1 billion in 2100 compared to 7 billion in 2011. A 2014 paper by demographers from several universities and the United Nations Population Division projected that the world's population would reach about 10.9 billion in 2100 and continue growing thereafter. One of its authors, Adrian Raftery, a University of Washington professor of statistics and of sociology, says "The consensus over the past 20 years or so was that world population, which is currently around 7 billion, would go up to 9 billion and level off or probably decline. We found there’s a 70 percent probability the world population will not stabilize this century. Population, which had sort of fallen off the world’s agenda, remains a very important issue." However, some experts dispute the UN's figures and have argued that birth rates will fall below replacement rate in the 2020s. According to their projections, population growth will be only sustained till the 2040s by rising longevity, but will peak below 9 bn by 2050.


Population growth Wikipedia