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SC/NATS 1510, PopulationSC/NATS 1510, Population 11

The Population Explosion


The Accelerating Rate of Population Growth

The population of the world has been growing, not just at a rapid rate, but at a rapidly increasing rate.This is due to the tremendous advances in human health in the past two hundred years that have fought back infectious diseases.This has reduced infant mortality and brought a higher percentage of the population to childbearing years.And it has lengthened the life expectancy, leaving more people on the earth at a given time.


Counting Time in Billions

Consider the population in one billion increments and note the time taken for each increment.

Population in billions

Year when reached

Years required for each billion

1 1825 2,000,000

2 1925 100

3 1960 35

4 1975 15

5 1989 14

6 1999 10

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Different Growth Patterns

The overall increase varied widely from continent to continent and country to country at different periods.


Growth Pattern in Europe

Slow growth with fluctuations due to disease and famine, to about 140 million by mid-18th century.Then a rapid rise of 80% to 250 million in 1845.Then another 80% in 70 more years to a total of 450 million by 1914.


Causes of Growth Pattern in Europe

Slower growth through the 20th centuryThe period of rapid growth was due to a decline in mortality levels.The slower growth that followed was due to a fall in birth rates.

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Growth in Asia and Africa

Like Europe at the beginning, including the rapid rise in the 18th and 19th centuries.But then an increase in the rate during the 20th century.


Causes of Growth in Asia and Africa

The general pattern shows that in the 18th and 19th centuries, the growth of the population was due to the decline in mortality, as in Europe, due to better diet and hygiene.However, this has not been accompanied by a drop in the birth rate, so the population continues to soarThe exceptions are Asian industrialized countries (such as Japan) that have followed the European model.


Comparative population growth in Europe and China

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The Americas and OceaniaThe patterns in these parts of the world are much more complex because they are so heavily affected by colonization and immigration.North America, after a period of huge growth due to colonization, established patterns resembling Europe.South America’s patterns are more typical of the Third World.


World Models

Attempts to predict global trends by taking a few key statistics that describe critical indicators of the state of the world, and creating a model from them.The model is designed to change in approximately the same way that the world would respond to changes in these indicators.


World Models, 2

Key indicators, both for data and for prediction might be:

Population and birth/death ratesResources available & usage rateFood production & consumptionPollutionDisposable incomeCost of livingCapital investment

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The First World Model

Thomas Robert Malthus’Essay on Population, 1798Predicted

Misery = birth control or celibacyOr vice = war or murder

were inevitable


Malthus’ Axiomatic Argument

Two postulates:1. That food is necessary to the existence of

man.2. That the passion between the sexes is

necessary and will remain nearly in its present state.


Malthus’ Argument, 2

Two lemmas (preliminary theorems):1. Population, unchecked, will increase in a

geometric ratio. (2 parents, 4 offspring, 8 grandchildren, etc.)

2. Subsistence will increase in an arithmetic ratio. (1,2,3,4,5,6,…)

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Example of unfettered population growth (shown before)

The Northern Elephant seal population on the Channel Islands off the coasts of southern California and Mexico.

The seals were nearly hunted to extinction in the 19th century. There were only 12 left in 1890. Then, left alone, they rebounded at a rate of about 9% per year. By the mid-1970s had reached over 60,000.


Malthus’ example of unfettered population growth

Malthus looked for a comparable real-life example of unfettered human population growth.

I.e., an environment where humans had access to unlimited resources.He chose the newly formed United States, where according to rough estimates, population had been doubling every 25 years.A geometric ratio. (“Exponential”)


Malthus’ idea of unfettered food growth

Likewise, he needed a measure of a rate at which additional amounts of food may be produced from agriculture.For Malthus, food production was a direct function of the amount of land under cultivation.

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Unfettered food growth, 2

Here, Malthus just picked a formula out of the air:

He supposed one could put a steady amount of new land under cultivation year after year.For illustration, he supposed that Britain could double the land under cultivation in 1800 by 1825. Then have 3 times as much by 1850, 4 times by 1875, 5 times by 1900, etc.

An arithmetic ratio.


The Malthus Thesis illustrated

Let food production increase every 25 years by what Britain produced in 1798.

This is an arithmetic ratio.Meanwhile the population increases by a geometric ratio.

Doubling every 25 years.Thus, it is inevitable that the population’s food needs will outstrip the food supply.Therefore, misery or vice.


Why Malthus’ estimate was wrong (repeated)

Human population growth has been even greater than exponential.

Because of modern medicine, better hygiene and better nutrition, the human population has been increasing at a rate greater than exponential.

But also greater than linear growth of resources.Farming techniques improved enormously, getting far greater output from existing land due to fertilizers, irrigation, harvesting techniques and transportation to markets – and the Green Revolution with new crops.Also, we can now transport food vast distances before it rots, so we can grow food in one part of the world to feed other parts.

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The crisis is yet to come

Malthus’ use of a linear function for increase in food supply was just a guess, not based on data.But is was based on the notion that food production is constrained while population is not.Malthus’ main point: sooner or later, population is constrained by resources.


Feedback (repeated)

Malthus’ simple model pointed to the inevitability of the crisis to come but could not predict the timing of it.

It failed to account for interactions before the crisis hits.

Interactions take the form of feedback loops.

More sophisticated models incorporate feedback information.


Positive Feedback

Common examples:Population growth – More births mean more people. More people mean more births.Compound interest – More interest means greater bank balance. Greater bank balance means more interest.

These are exponential functions that runaway on the upside.

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Exponential FunctionsThe common form of growth phenomena.For example, compound interest

More interest means a greater bank balance.Greater bank balance means more interest.


Characteristic doubling periodof exponential functions

Rule of thumb:Divide annual % increase into 70 to get the approximate doubling period.E.g., a GIC at 5% interest doubles in 14 years, 3 months

The increase in the function at any point depends on its size at that point.


The Chessboard Illustration of an Exponential Function

Fable of a man who presented an ornate chessboard to the Shah of Persia and was offered any reward he chose:

He asked for one grain of rice on square one, two on square two, continuing doubling on each square after that.

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The Chessboard Illustration of an Exponential Function, 2

Therefore last square would have 264 grains of rice = 1.84 x 1019 or 1,840,000,000,000,000,000,000For the whole chessboard that is about 500 times the world harvest of rice.

26464

……

12481632641282565121024

1234567891011

Grains of riceSquare #


The Lily Pond IllustrationSuppose there is a pond in which lily pads are growing.Suppose the lily pads double their numbers every day.In 30 days, the pond is full of lily pads.When will it be half full?

Answer: On the 29th day.When will it be ¼ full?

Answer: On the 28th day.When is the last time it will less than 1% full?

Answer on the 23st day.


Exponential versus Linear

One of our difficulties imagining an exponential function is ourtendency to extrapolate from linear functions.

Given two amounts representing the quantity of something at two different times, we tend to think of a straight-line progression from one to the other.

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CyberneticsNorbert Weiner, 1948

From kubernetes – the steersman

Cognates, gubernator (Latin) and the English word, governor.

Feedback mechanismsNegative (e.g. steering, or the governor on a steam engine)Positive (e.g. population, or any exponential function)


World Population

Population is a quantity subject to positive feedback, basically an exponential function.

The more people there are in the world, the more births there will be. If the birth and death rates are constant, then population is an exponential function of time.

But birth and death rates do vary, so the rate of increase varies.Since the Industrial Revolution, steady increases in the standard of living, hygiene, and nutrition have brought about a very large increase in the birth rate and a decrease in the death rate.


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World Population (contd.)

The rate of increase of the population has been very high in the last 100 years.World population now exceeds 6 billion.

For an up to the minute estimate go to http://www.census.gov/cgi-bin/ipc/popclockw


The Declining Growth Rate

The pattern of increasing rates of growth in the 20th century would lead to infinite population in the 21st century!However, population growth rates have begun to decline, and are projected to continue to decline.


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The Population is still rising rapidly

The rate of increase is lower, but unless it turns negative, there will still be positive feedback and the population will rise.The birth rate (but also the death rate) has fallen recently in the developed world and is overall negative in some places.But in the undeveloped world it is still very high, though beginning to fall.


UN ProjectionThe UN projects that the world population will level out around 11 billion people by 2150.

What would be the effect on the world of the greater populations that are predicted?


The Club of Rome

Formed April 1968 at the Lincean Academy of Rome.Commissions reports on studies of the future of the world.

E.g. world models of population, natural resources, capital investment, pollution, quality of life.Published over 28 full-blown reports and many more documents assessing the state of the world or regions of the world.

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The First Two Reports to the Club of Rome

Limits to Growth, 1972Mankind at the Turning Point, 1974

These studies were World Models that used computer simulations based upon historical data on a number of significant variables, then projected forward using several scenarios to see what would be predicted.


Example from Limits to Growth

A Population-pollution interaction module.The number of births per year provides a positive feedback to the population level.The number of deaths provides negative feedback to population.The population level provides positive feedback to pollution.Pollution provides positive feedback to the mortality rate.


Example from Limits to Growth, 2

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The Limits to GrowthPublished in 1972.

Ran several scenarios looking for a sustainable future, to see what changes would be necessary to assure survival.The Normal Run

The first scenario assumed imposed changes in patterns of consumption, production, fertility, etc., only those predicted by the interaction of the model.It predicted catastrophic declines in the 21st century.


The Normal Run in Limits to Growth


Prognosis of the Normal RunNatural resources slowly running down, population rising, food production rising. Capital investment begins to fall because more is devoted to scarce resources. Industrial output begins to decline. Agriculture collapses because of lack of fertilizer and farming equipment. Mortality rises due to starvation. And the population falls catastrophically.

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Another Run:

Technology finds new resources as needed (e.g., nuclear power).Industrial output therefore is maintained.Population and pollution increase alarmingly.In year 2050, pollution becomes so high as to cause mass deaths.Then population falls catastrophically.In every run they made only those with zero population growth avoided a catastrophe.


Over simplicity in Limits to Growth

The model viewed the world as a single unified culture. Birth rates, death rates, fertility, etc. were world-wide figures.

Shortages and surpluses in one part of the world would not necessarily cause reactions in another part of the world.Case in point: population.

Birth and death rates have followed separate trends in the developed and undeveloped worlds. In the developed world, affluence brought a lower birth rate.In the undeveloped world, it increased the birth rate.


Population vs Age Profile

Developed vs Developing Countries:The rich get richer. The poor get children.

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Mankind at the Turning Point, 1974

The Second Report to the Club of RomeMore complex model:

Recognized that birth rate completely out of control in 3rd words while consumption of resources out of control in the 1st world.Recommended improvement in medical services – despite the resulting increase in population that would result.


Mankind at the Turning Point, 2World was modeled not as one monolithic whole, but as 10 regions1. North America2. Western Europe3. Japan4. Other Capitalist Economies (Australia, New Zealand, South

Africa, Israel)5. Eastern Europe & U.S.S.R.6. China7. North Africa and the Middle East8. Latin America9. Tropical Africa10.South & Southeast Asia

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The 10 Regions of the World System in Mankind at the Turning Point.



Rationale:Birth rates vary significantly from region to region.Use of natural resources varies significantly.Not sufficient to curb overall birth rate.Must be curbed in the least developed nations where resources are least available.Not just a matter of food.

There has to be the technology and infrastructure to get it to the people.(50% of food in India rots before it reaches the population.)Need jobs housing, etc.



Income per capita between the developed regions and Region 6 (Latin America), and Region 9 (South Asia) projected to the year 2025, if present trends continue.

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Four scenarios were projected, calculating interactions between per capita income, birth rate, and economic infrastructure.

The first scenario is the base line that assumes no interventions other than the foreign aid programs in place in 1975.In the remaining scenarios huge amounts of foreign aid from the developed nations plus birth control programs are projected.

With a target of reaching relative per capita income levels between the developed world and Latin America of 3 to 1, and the developed world and South America of 5 to 1.



The graph shows the amount of aid projected to be required per year to achieve the target per capita income levels and make the undeveloped world self-sufficient.


Scenarios:No population policy

Would mean 12 billion people by 2010Famine unimaginable would strike 3rd world long before 2010 unless birth rates reduced

Massive birth control program immediately (i.e. 1975)Birth rate reaches equilibrium in 2010.Equilibrium level in 2050 of 6.27 billion in the underdeveloped nations.

Same program, but not implemented until 1985.Population rises to 7.97 billion by 2050 in underdeveloped nations

Same program with 20 year delayPopulation of 10.17 billion in 2050 in underdeveloped nations.

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Suppose the developed world responds with continuous aid to the underdeveloped nations.

To help them reach equilibrium where per capita income in the developed world is only 5 times the income of that in the underdeveloped world.

(This would make the underdeveloped world self-sufficient.)

Scenarios show that aid given sooner rather than later is much cheaper for the developed nations.


Population versus Cultivated Land

The number of people per unit of arable land in the undeveloped nations is already very high and will continue to get rise to an unsupportable level unless birth rates are sharply curbed.


World Models in general

All these world models suffer from the necessary over simplicity built into them.

They work with a (small) finite number of variables.They must treat their data as reliable.They assume that interactions are known.They cannot anticipate technological breakthroughs, epidemics, natural disasters, wars, etc.But they try. And they are getting more sophisticated all the time.

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