Synopsis: There is a significant lag between changes to birthrates and the impact on population growth.

The concept of the population pipeline as explained below by Hans Rosling using blocks for simplified example for the world for a “peak child scenario” by a graphic animation for even a “below peak child” scenario of a hypothetical “Imaginania”, and then a third even simpler “filling the pipeline” model.

The population pipeline explains what happens in countries with low rates of immigration or to the entire planet in the absence of mass arriving or leaving the planet.

There are real world complications, particularly immigration, that can mean even a country with “births per woman” well below 2.0 as is common in many developed countries that should bring an end to population growth, completely outweighed by immigration.

Hans Rosling uses blocks to explain the lag.

Since making this page and model, I found another explanation of the same concept by Hans Rosling (see left for full video, this link to go direct to explanation).

Hans explains why, even if every couple was to have no more than two children from now into the future, the world’s population could continue to grow for a number of decades.

This is the real-world example of the population pipeline as it impacts the world today.

In the video Hans Rosling uses blocks of approximately 1 billion people each block, with the levels in the stack of blocks being the age groups of (from top to bottom):

• 60-and older
• 45-60
• 30-45
• 15-30
• 0-15

Graphic Animation for going beyond “peak child”.

This graphic animation illustrates how a switch from a birthrate that results in population growth to one that results in a decrease in population can take almost 60 years to result in a fall in population. The data uses a simplified model and while the end result does produce a pattern surprisingly closely matching the real experience of Japan, this is purely coincidence.

The graphic above is a graph in blue of the births during each 5-year period, as would be seen from census data for a country with a census every 5 years. This data is for a hypothetical ‘Imaginania’ where people all live 75 years from their birth, and births recorded per census keep increasing at a linear rate until “peak child” in 1965, and then number of births per 5-year period begin reducing at a linear rate.

Since in hypothetical “Imaginania” all people live for 75 years, at any point in time the total population will be all the people born prior 75 years. This is shown in the graphics as blue area within the population pipeline of the time. The graphic represents 5 snapshots of the historical population that are alive at each of 5 different points in time. In real countries, people to enter the pipeline in the year they are born, but while they could on average exit the pipeline 75 years later, it would be more complex as the age people exit the population varies.

The ‘snapshots’ are at:

• 1955: 8 Million people, and for every one of the past 75 years more children were born than the previous year.
• 1970: 9 million people, but since peak child in 1965, births have been falling at per 5 years census have been fallingbut ‘Birth population 8 million, since 1965 less babies born each year since 1965.
• 1985: 9.75 million people with 20 years after births beginning their decline population growth is only just starting to slow.
• 2000: 10 million people, and 45 years after “peak child” population numbers have finally peaked.
• 2015: 9.9 million people as now 60 years after peak population, numbers have finally began to fall.

The models is simplified, but I suggest still very useful. So, what happens to population numbers with this model?

1955: Population 8 million, since 1965 less babies born each year since 1965.

The right most end where newborn children enter the pipe shows 677,000 children born in the most recent 5-year block, and these will replace the 365,000 now 75-year-olds born 75 years earlier, the population is growing by just over 60,000 people per year.

1970: Population now 9 million, and still growing despite passing peak child.

So, 15 years of growth from 1955 at just over 60,000 per year as expected has added 1 million more people, and despite the number of children per 5 years having fallen by 30,000 from to the peak child of 1965 to just over 705,000, it is still far greater than the 413,000 75-year-olds they will replace, leaving population growth at still almost 60,000 per year.

1985: Population now 9.75 million, and with a small slowing of growth 20 years after peak child.

So, another 15 years and this time 3/4 of another million added. Now 20 years after peak-child over 100,000 less children per 5 years, but still at 624,000 it is more than the 467,000 born in 1910 these children will replace resulting population growth of 30,000 and half what it was at the peak.

2000: Population has risen to 10 million despite, previous 35 years falling birthrates.

Despite now 35 years since peak-child in 1965 and less and less babies being born every year, the population is still growing, but now at a far lower rate.

2015: Population now 9.9 million, with population finally falling 50 years after peak-child.

This model demonstrates that even with birth rates falling at a similar rate to the rate of growth prior to peak child, it can take almost 2/3 of a life span for the population to actually peak.

In 2015, the population increase has slowed, but there are now and 9.8 million in 2015 (being all those born between 1945 and 2015).  Even though the birth rate is modelled as below replacement level from 1970 through to 2000, the population has continued to climb until 2015. However, having now reached the same number of births as at the start of the block, population can now begin to decrease.

Filling the Pipeline with the simplest model.

Simplified Model.

Consider a simplistic country with 1 million people born in the first decade,  2 million in year the second decade, 3 million in the third up to 7 million in the seventh decade, but every decade following, 7 million are born, so population growth should stop.  But at decade 7, the population is

1+2+3+4+5+6+7 = 28 million. 

However, since each new group will be at that 7 million level, in another 6 decades it will be:

7+7+7+7+7+7+7 = 49 million!

So stopping the growth rate does not immediately stop population growth.  It means the number of people at the first stage of the pipeline will now be fixed, but until every stage of pipeline has been filled with this same number, growth keeps happening.  In this simplistic example, population growth was switched off at time 7 (seven decades), but growth still almost doubles over the next 6 decades.

Dotting the ‘i’s?

The simplified model above is simplified to make the calculations as simple as possible, but in the end, using realistic data presents a similar result, although the calculations become more complex.  The simplified simply adds 1 million each half generation or 10 year period during the growth period.   In the first period this represents doubling, yet by the 6th step, it is just adding another 1/6th, so linear growth automatically decreases relative growth while real growth should be relative.

To use realistic numbers, peak population growth was just over 2% around 1968, and as 1.02 to the power 10 is just over 1.2, this results in 20% growth per decade. To end with a similar end population with 20% per decade growth, a starting population of 2.4 million is required.

1	2	3	4	5	6	7
2.4	2.9	3.5	4.2	5.1	6.1	7.3

Sum total: 31.6 million.

Those figures are rounded to 1 decimal place.  Since the 20-30 year block is a more realistic age group to be parents for the new generation than the previous 0-10 block, we need to apply a 1.2 cubed factor to the figure two columns back to have the correct underlying calculation. This simply gives the same figures as before, but more correctly records what is required for a this growth rate, which is 1.2^3 children per person or 1.2^3*2 = 3.3 children per woman with zero infant mortality.  Remember the 5 children per woman was not maintained over the decade preceding 1968, and the was higher global infant mortality at the time than today.  Capping the population at a peak as fast as possible requires dropping the growth rate to 1.44 (1.2^2) and then 1.2, then level at 1.0 over three generations.  This requires applying the brakes between periods 4 and 5 so the rate of 1.44*generation 5, and 1.2*generation 6 are used during the rate slowdown.  (Note: applying the brakes as a single step would produce an oscillation population level due the parents being those born two steps back, and be like the birth rate changing overnight – I will supply that data if anyone asks).

It came to my attention looking at the results of these calculations that multiply these figures by 200,000 to match a world with a population of just over 6 billion, as was the case with the real world around a decade ago, with the brakes first applied around 30 years earlier.  Move the figures forward a decade, and the total (36.5) would correspond with 7.3 million, close to the figures today.  These figures with the pipeline starting to fill, correspond with ‘peak children‘, which again some people feel reflects the world today.  Multiply the final population (7.3 million) by 7 to get 51.1 million, which multiplied by 2,000 would give 10.2 billion, remarkably similar to UN projections for humanity.

This suggests that the current situation on Earth is, using UN data, close to peak children but with no further change to the number of children born each year and a population pipeline that will simply fill at the current level. 

‘Real World’ Complications.

Migration.

This type of model can predict growth for a country with no net migration.  The results are for the population excluding immigration,  however most developed nations are significantly impacted by migration.  These countries fall into one of two categories: people exporters or people importers.  Basically this is the ‘old world’ (exporting people) compared to the ‘new world’ (importing people).  Old world countries of Europe (such as the UK, France, Germany etc), throughout the growth age exported significant numbers of people to the  new world countries in the continents of North and South America and Australia/New Zealand(Oceania).

So for most countries, we need to then apply adjustments to a model such as the model for ‘Imaginania’, however Japan comes to mind as a country with relatively low migration.  In fact figures for Japan track extremely closely to those Imaginania (only around 10x larger).  This was neither intended or planned.  The model started working on a target population of 10 million and working backwards this resulted in a population back at 1900 of 4 million. In fact Japan basically moves from 40 million in 1900 to 100 million in 2000.  However there is some coincidence to this as many factors of real world Japan are not modelled.  Also, Japan has had lower birth rates than typical for developed countries or those used in the model, which is one reason the model still has an almost flat but still growing population in 2015 whereas Japan has actually already entered population decline.  But Japan is certainly close enough to suggest the model works for a case such as Japan.

However, for most countries, the model predicts only what would happen without migration.  Such data is still extremely useful in prediction how migration must be adjusted to counter underlying changes or how overall population growth will change in the absence of changes to migration numbers.

Wars, Disasters and Disease.

Wars have reduced population levels in specific countries, but there is no record of any war reducing the global population.

Nor is there any record of any recent natural disaster reducing global population, although the 1815 Tambora eruption reduced the total global population of human domestic animals. The 1976 Tangshan Earthquake in China would have reduced global population for a short time, but as this was during the population explosion, prior levels would have quickly been surpassed. The 1556 Shaangi Earthquake, the deadliest in recorded history, would have set global population levels back a number of years and the Toba volcanic eruption significantly impacted population and by some estimates came close to making humanity extinct. Of there was a meteor some some 70 million years ago that within a short time made a significant number of species extinct. So natural disasters can be deadly, but those that impact global population are rare and have not occurred for hundreds of years.

Disease also can, and periodically does, impact population, with the plague and the 1918 flu having a noticeable impact. Edit: Covid-19, despite a significant death toll, has not reached the scale of noticeably impacting global population, with a death toll of far less than 10% of that from the 1918 flu, and in 2020 the world has far more people than in 1918.

2024 Update: Real Pipelines vs simple models.

Now 8 years after this was first written and the world has changed. Japan now has a population that is falling, more significantly “peak child” has been reached globally.

Back 8 years ago Japan was tracking amazingly close to the model used for the graphic explanation, but this is coincidence. The pattern of a very slow initial slowing of growth will likely be repeated in the real world, but this model assumes a homogenous population and a simple flip from growth to population correction.

Key to patterns in the real world will be correctly identifying just what is causing birthrates to fall. In any situation declining birthrates are in response to people feeling the environment is already overcrowded, there could be an acceleration in the decline of birthrates during the time birthrates have fallen but population growth continues, bringing population growth to a more rapid halt.

updates:

• 2024 March 3 : Update in progress for page format and clarity, but not a new edition.
• 2020 June 15 : Update to add explanation by Hans Rosling