One Finite Planet

One Finite Planet

Births Per Woman: Not quite what you would expect.

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TLDR; The magic number is around 2.3, not the 2.0 you might expect, results in a stable population.

This is an exploration of what ‘births per woman’ means, and how it is measured. Key to discussion about population is population growth, which is most commonly analysed from ‘births per woman’, which is also called ‘fertility rate’. But what is ‘births per woman’? Answer: not quite what you might expect, which means a small adjustment is required for interpreting births per woman when predicting population growth.

What Exactly is Births Per Woman?

Births per woman, is perhaps even more confusingly also labelled ‘fertility rate’, or ‘total fertility rate’, but all are the same number and not some variation. This is, as explained below, the best figure able to be calculated.

Total fertility rate represents the number of children that would be born to a woman if she were to live to the end
of her childbearing years and bear children in accordance with age-specific fertility rates of the specified year.

Our World In Data: Fertility Rate.

Since actually tracking women over their lifetime would produce out of date information and require huge samples over long periods of time, this number, is the number of children for an imaginary woman who passes through her reproductive life subject to all the age-specific fertility rates for ages (typically 15–49) that were recorded for a given population in a given year.

As explained in ‘not quite what you might expect’, the number can only be calculated on the assumption all would live to the end of their childbearing years, since to project the number who do not would add extra guesswork.

This is a calculated figure, that is practical to collect, and as useful as possible, but is skewed to be higher than ‘births for every woman who was born’ as the number is accurate only for women who live their entire reproductive life.  The figure can be calculated from simply recording all births for a given year, together with the age of the mother for each birth.

Between the labels, used in different texts, I feel ‘births per woman’ is more descriptive, feel the label ‘fertility rate’ could be confusing, because to me ‘fertile’ suggests ability to reproduce, which differs from number of children. A society where less 18yr old women are having children does not necessarily mean 18yr old women are becoming infertile.

Note ‘births per woman’, requires two adjustment for two factors before determining the level for population stability.

  • Firstly, some women will fail to complete their fertile years, and as this number changes over time for reasons not directly linked to ‘births per woman’.
  • Secondly not all children will grow up to have their full allocation of children, and some will not even reach an age to have any children.

At current mortality levels, this means between 2.1 and 2.5 depending on health environment, is the level of ‘births per woman’ or ‘total fertility rate’ required for an exactly stable and thus sustainable population.

Not Quite what you might expect.

But why not take a large sample of women, and measure the number of children they actually have, and this would eliminate the need to adjust for mortality during fertile years. How else can you calculate ‘births per woman’ other then really record the births over a lifetime?

This simple approach could work as a statistic for a large period time, but year to year, or even over 10 year intervals, it becomes impossible to measure. Consider over a long period, say, between the years 1700 and 2000. Woman who had the potential to have children prior to 1700, as well as those who may still have children after the year 2000 need to be excluded from the sample, as you don’t have full data on these people, and the data partly is what took place outside the time interval being studied. But data from the first years after 1700 would have to exclude a lot of women, as for many of those women, most of their data apply to before 1700. Similarly for the years close to 2000 many who could still have more children would need be excluded, as you don’t know how many children they will have, plus some of that information is again for another time period. Still in this case, there is a lot of data, as many women had all their child bearing years within the window.

But what if we take a shorter span of time? Clearly, if we assume a maximum possible number of childbearing years as, for example, being 35 years, then with a sample time of 35 years, only the women born in one exact year could be part of the sample. With women living over 60 years, this would be 1/60th of the population. And even then, it takes 35 years of collecting data to have an answer, and during that time birth rates may change. In fact, the goal is to produce a new statistic each year. How can you measure something with could take 35 years to play out, in a single year?

To be practical, another way of measuring data is required.

Towards the Perfect Statistic

It could seem the perfect statistic for population growth would be ‘current annual population growth rate’, a factor we could use to know the current rate the population is growing. But in fact this is only ‘observed population growth’ and can hide what is actually happening at this time.

If there is a complete yearly record of births and deaths, we can calculate change in total global population, but since the births are people born now this current year, and the deaths on average represent people born a whole lifetime ago, which is around 70 years ago. So the number observed gives a comparison feeds from two groups of people separated by almost 70 years, and born to very different population counts. This figure reflects a combination of the births happening now, combined with the number of births around 70 years ago. One half up to date statistic, and the other half historical data.

Even if birth rates were now well below replacement levels, we would still expect births from the current over 7.5 billion people to be greater than they were in 1950 when the global population was 2.5 billion. So while a useful statistic, ‘current annual population growth’ is a mix of what happened a long time ago, and what is happening now.

We wish to current trends from year to year, not just trends comparing people a lifetime apart. What is the birth rate of the current generation, not the difference in number of children in the current generation, to the number of children 2, 3 or even 4 generations before.

For each person born today, how many children will they have? If we knew, for each person born, how many people will replace that person in the next generation, and exactly how long each generation would represent, then we would have a generation factor, which divided by the number of years in each generation, would give our perfect per annum figure.

The challenges include:

  • there are two parents for each child, so number of children relates to two parents, not ‘each person’
  • there not just children per ‘two parents’, as adults can have children with different partners
  • children do not directly replace their parents as there is an overlap
  • people have children at a wide variety of ages, meaning collecting data could take many years
  • accidents and illness can shorten lives and preventing people becoming parents

The first step in solving these problems it to consider children of one gender only, then divide by two since there are almost equal numbers of men and women. Women are the logical gender to choose, as women are unlikely to have children without realising it, and are present at birth allowing easier collection of statistics.

However, tracking women over their entire lifetime is not only impractical, it would also yield confusing data. To calculate data for birth rates applicable for the year 1950, should we include all women of child bearing age during 1950? Obviously many of those women have not necessarily had all their children yet. Some had their children over a decade earlier, so their statistics could be no longer relevant.

The end result is the best statistic we have is ‘births per woman’. This is a practical figure which can be calculated from the data collected in a single year, but there are some limitations to the accuracy of calculation possible in just one year.

Interpreting Births Per Woman: Calculating Population Growth Rate.

To get the population growth per annum figure, first subtract from the ‘births per woman’ the appropriate figure to allow for deaths prior to reaching full children potential, then divide by two correcting for men and women to get the ‘per generation’ population growth. Then, that figure should then be divided by the ‘average age when giving birth’ to provide the average ‘generation’ duration, and this will give ‘underlying population growth rate’. This is the growth rate within the parent-child cycle. If all parents died immediately at the end of their fertility, this would be rate of population growth, however the rate observed at any one time is distorted by the fact that the people actually dying due to old age are a group born earlier than the parents. Currently, as the people dying are from an earlier, and often smaller generation, the ‘observed population growth’ is higher than the underlying population growth.

So there is :

  • underlying population growth
    • calculated from births per woman alone
    • is an accurate reflection of the current growth trend, can take decades dictate observed growth
    • does reveal future observed population growth if rate remains in place.
  • observed population growth
    • also requires also number of deaths, which is related to births from a lifetime ago
    • is an inaccurate reflection of the current growth trend, and a poor predictor of future.

However, the calculated population growth rate, could take half a lifetime to become the observed population growth rate.

The Magic ‘Peak Child’ Number: 2.2 through 2.4.

At what number of births per woman would a population with zero immigration/emigration be stable?

The divide by 2 above is clear, as this is required because very close to 50% of people are women. There are two reasons the number is not an exact 2.0.

  1. There needs to be an allowance for child mortality.
  2. There needs to be and adjustment for women who do not survive their entire number of fertile years.

Firstly, not all children will become adults and have their own children. The ‘magic’ number would need to be adjusted so that at least 2 of those children get to become adults, and get to have their expected number of children. When

Secondly, and more complex, the calculation of divide births by the ‘average age when giving birth’ only matters works for calculating births in a given year, and in the long term you would think would project the number of children a women would have, but to have that number of children, the woman must continue as a fertile woman for the entire period, and not every one does.

The women that do go through all their fertile years capable of having children need to have a few extra children to compensate for those who die or become infertile, slightly increasing the number over than needed to allow for infant mortality.

How much the number must be increased beyond 2.0 is not exact, as death and illness rates vary over time, making the statistic a little fuzzy. Some optimistic people believe we could enable reduce infant mortality and enable enough women to exist trouble free through their fertile years for the number to eventually become 2.1 or even lower, but estimates for the current rate range between 2.2 and 2.4 as the correct answers for zero population growth.

A very good source of data is The link provide is interactive and shows data as at 2018 at a level of 2.415. This is 0.215 the level of lower estimates for ‘births per woman for stable population’, but back the data also shows that in 2002 the figure was 2.644. From 2002 to 2018, the rate dropped by 0.229. If the rate continues on the current trend, then births per woman would be below 2.2 by 2034. So depending on which level is chosen between 2.2 and 2.4, that level should be reached between 2020 and 2034.

What Drives The Fall in Births Per Woman?

In the 1950 and 1960, there were some dire predictions about global population. Unless population growth slowed dramatically – there would be dire consequences!

Strangely, humanity effectively heeded these warnings. Countries such as Singapore, Bangladesh and China have all taken government action to reduce population growth, but similar countries without government action achieved similar outcomes.

I have recently seen articles where authors claim alarms of overpopulation have always been false alarms, but we do not know they were false because humanity, for whatever reason, did take evasive action. Like telling the driver you must not have needed to put on the brakes because when you did put on the brakes we did not crash. Humanity put on the population growth brakes, and may well have avoided a crash, as if birthrates had remained at 5 per woman, we would have over twice the current world population today, with over 14 billion people.

But why did birth rates fall?

There are lots of theories, and many of these accurately provide some of the factors. But I have seen no one theory that seems to explain it all. We just do not know with certainty what all of the factors are.

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