Japan’s population will bounce back - sort of

From Wikipedia

Japan's TFR (Total Fertility Rate) is around 1.34. This is the average number of children a Japanese family will have in contemporary Japan. The TFR which maintains a steady population level is 2.1 (some fraction of children do not reproduce through death, ill-luck or disinclination).

People conclude that the Japanese as a country-community are doomed. Since European TFRs are similar, averaging around 1.6, this repugnant conclusion seems quite generalisable.

But people who write sensational stories in the media about this pay only lip service to evolutionary theory, they don't operationalise it. This bland, average TFR hides subpopulations, some of which don't reproduce at all, but others of which are quite prolific in family size.

Since there is parental genetic influence on the size of family [1] we can treat this fecundity-variance as setting up a process of genetic truncation selection. The structure and incentives of Japanese society (a proxy for almost all advanced countries) poses enormous Darwinian selection pressure against those individuals with genotypes which encourage them to fail to reproduce adequately.

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A simple Fermi estimate (a back of the envelope calculation) allows us to predict the result of this massive selection pressure on the Japanese population, in generation time steps.

Simplifying the numbers in [2] below, divide Japanese families into four categories with the following endogenous TFRs:

 - category zero is 25% of the population with TFR zero

 - category one is 33% of the population with TFR one

 - category two is 33% of the population with TFR two

 - category three is 9% of the population with TFR three.

So this is the population structure at generation 0. 

Assume for ease of calculation that the population of Japan is 123 million. We divide this into three generational age cohorts: 0-25, 25-50,50-75 and assume each cohort is equally numerous at 41 million people.

Over one generation the upper cohort dies (losing 41 million people) and the middle cohort reproduces to replace them (or not).

To make things more intuitive we will replace the percentages with 100 notional families representing those individuals who reproduce, namely the 41 million strong middle cohort. Call them 40 million to make the sums easier. So each 'family' represents 400,000 people. 

What happens to the population as the generations roll over?

Generation 1: 2025 => 2050

We started with 123 million. The elderly cohort dies leaving 82 million. And now the logic of extreme selection kicks in: 

 - category 0, 25 families, are culled from the gene pool and vanish 

 - the 33 families of category 1 are replaced by 16

 - the category two families simply replace themselves, remaining 33

 - the category three families increase their number by 50% to fourteen.

Total number of families is 16 + 33 + 14 = 63. The newborn population is 63 * 400,000 = 25 million. The new population is 82 million + 25 million =  107 million. This is consistent as it happens with the chart at the head of this post.

(Note: the resulting TFR here is 25/20.5 = 1.2 so our back of the envelope calculation is a slight under-estimate).

Quite a drop from 125 million.

What happens next? Those alleles which support a propensity to have children have increased in frequency, but we know the heritability of this trait is not high. So as generation 1 transitions to generation 2 in 2075, we will still see some families having zero offspring (or never forming a family unit at all) while the percentage of those families favouring more offspring will increase.

The modelling would be complex and noisy, but the direction of travel is clear. Darwinian selection is doing its work and a new population being selected for, composed of those families interested in having children despite all the many modern distractions. 

Inexorably, the population of individuals who genetically underpin category three will rise exponentially and will eventually dominate in the population, which will itself substantially rise in numbers if it can manage to sustain itself.

There is an interesting implication, which escapes no-one who thinks about this in an informed way, that any other genetically-informed traits which co-vary with fertility-promoting alleles will also be selected for. I admire many aspects of Japanese culture but my ignorance of the details of Japanese society is pretty much total. Still, someone much more informed than me should take a look.

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[1] Heritability of family size (from Bard)

Here are some examples of heritability estimates for family size in different countries:

Denmark: 15-20%

United States: 20-30%

Australia: 25-30%

Netherlands: 30-40%

Japan: 20%

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[2] From Bard - family sizes in Japan: 

Here are some specific percentages you might find helpful, based on data from 2020:

Percentage of women aged 45-49 with no children: 22.7%

Percentage of women aged 45-49 with one child: 32.5%

Percentage of women aged 45-49 with two children: 34.2%

Percentage of women aged 45-49 with three or more children: 10.6%