There is a life-time length lag or delay between any change in birth-rates, and those birth-rates being fully reflected in the population growth (or reduction) rate.

This can create the paradox where a country with low birth rates, may still grow in population for decades. It is also why the world population will continue to grow for decades, after birth rates a low enough to end population growth. Population growth is the difference between the number of people who are born, and the number of people who die. People enter the population pipeline at birth, and remain in the pipe-line their entire life. On the world average, people die at 73, which means death rates are determined by population of people who became parents 73 years, while births are determined by the population of who be become parents this year. This takes a full lifetime of 73 years, between a change in birth-rates, and population growth reflecting the new birth rate.

- The Lag Explained In Detail And Graphs.
- Hans Rosling uses blocks to explain the lag.
- Filling the Pipeline Explanation.
- ‘Real World’ Population level Complications
- Immigration/Emigration
- Wars and Natural Disasters.
- Conclusion.

## Hans Rosling uses blocks to explain the lag.

Since making this page and model, I have 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 with every couple having only two children in the future, the worlds population with continue to grow for a number of decades.

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

Hans uses 1 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

## The Lag Explained In Detail And Graphs.

- Introducing the hypothetical ‘Imaginania’.
- 1970: Birth population 8 million, since 1965 less babies born each year since 1965.
- 2000: Population has risen to 9.6 million despite, previous 35 years of less babies born every year.
- 2015: Population now 9.8 million, but about to start to fall, 50 years after the decline in births began.

#### Introducing the hypothetical ‘Imaginania’.

To demonstrate I have made a simple model, based on the imaginary country ‘Imaginania’ (population approximately 10million in the year 2000). In this imaginary country, birth rates in the year 1900 are at a level consistent with developed countries at that time, and in the model this, rate continues until 1965. Then, from 1965, the model then uses a new birth-rate typical of developed countries in the late 20th century and up until the present, where less babies are now born every year.

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

As expected, the number of people born each block of five years from 1900 until 1965 becomes a larger number. Then from 1970 until now a progressively smaller number are born each year.

The three ‘yellow blocks’ represent the population pipeline for three years: 1970, 2000 and 2015. People enter the pipeline at birth, and exit when they die. So the pipeline for any given year stretches back from that year to the average life expectancy number of years ago. Starting from the right side of the pipeline, the people born in the previous 5 years, the next age group to the left is those the next oldest, and so on to the very oldest at the left of the pipeline being those born longest ago.

#### 1970: Birth population 8 million, since 1965 less babies born each year since 1965.

So for the 1970 yellow block, the 70 year-olds were born back in 1900 when the population was smaller, and there were 400,000 born in that first five year block. The pipelines for any year assume that everyone dies in the oldest age group 5 year block. Although in reality some die earlier, a similar number live longer, so total number in each yellow block should be about correct, although with some alive at any given time being born earlier and some dying younger, the shape would need to be more complex to be more accurate. So you can form a pipeline for any year by including all the people born in the previous 70-75 years with this simple model. The longer ago the people were born, the earlier they entered the pipeline and thus the older they are at the time being considered.

For each of the three years being considered, the yellow area is the previous 70-75 years, as it is assumed they are all of the age groups alive in that year. So for 1970, all the people born between 1900 and 1970 are alive so the ‘pipeline’ is the box from 1900 to 1970, with those entering the pipeline first at the very left and now being the oldest. So the 400,000 people entering the 1970 pipeline in 1900 would in 1970 be now 70, and those 600,00 entering in 1920 would in 1970 be 50.

Totalling each sector (each age group) within the ‘yellow area’ or ‘pipeline’ reveals that ‘Imaginania’ has a total of just under 4 million people in 1900 (not illustrated), and as shown, 8 million in 1970 (with all those born between 1900 and 1970 being alive at that time).

#### 2000: Population has risen to 9.6 million despite, previous 35 years of less babies born every year.

Despite every year since 1965 there being less babies being born every year, the population would reach 9.6 million in 2000, with that population being all those born between 1930 and 2000. This is because even though the number of children being born keeps decreasing, that number has not yet fallen back to the number of children being born at the start of the block in 1925. Until the number children being born drops to the number at the start of the relevant ‘yellow block’, population continues to increase.

#### 2015: Population now 9.8 million, but about to start to fall, 50 years after the decline in births began.

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.

This is the principle of the ‘lag’. The peak population group is those born in the block ‘1965’, and aged 0-5 in the year 1965. The total population in 1970 is the 1970 group (0-5 year olds), the 1965 group (now 5-10 year olds), the 1960 group (10-15 year olds) through to the 1900 group (70+ year olds). To move from 1970 to 1975, we add the new 1975 group as the new 0-5 year olds, and each other group moves through the pipeline and becomes 5 years older, with a group of the size of the 1900s group leaving the pipeline and the statistics. Even though the group for 1975 is smaller than the previous 1970 group, the population is still increasing in total the group dropping out is the 1900 group. This pattern continues as the pipeline slides through to 2000. Ever smaller groups are added to the pipeline on the right, but as these new groups remain larger than the groups dropping out of the pipeline on the left, the number of people in the population pipeline continues to grow. In the second transition, from 2000 to 2015, the population is still growing, but has almost levelled off. Continue this model through to 2050, and the model shows the population of the ‘Imaginania’ would fall back to around 9 million.

# Filling the Pipeline.

**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.

# Pipeline Examples.

To be updated.

Consider this, a sudden ‘boom’ such as the ‘baby boom’, should cause another ‘boom’ in the birth rate 18-35 years later as that large number of people born in the boom have children, then cause a drop in the population 70 to 80 years later when that same large group will most likely have health problems and many will pass away. This is one group passing though the pipeline, and the pipeline is simply all the groups passing through the pipeline at one time added together.

# ‘Real World’ Complications.

### Immigration and Emigration.

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 occured 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.

## Conclusion.

The pipeline perfectly explains world population levels, but the greater the effect of immigration or emigration, the smaller role the pipeline plays in the overall picture of population growth in any given country.