Total fertility, measured in births per woman, differs from the annual birth rate per thousand people. Here we explore fertility and generational replacement: what happens to younger cohorts when a rate persists for decades.

One initial pyramid, different rates

Presets for South Korea, Japan, the European Union, and Latin America and the Caribbean use World Bank fertility observations for 2023. Only fertility changes: all start with the same synthetic population. This isolates its effect without presenting the diagram as an actual national population pyramid.

Fertility and generational replacementSynthetic age-cohort model
Below replacement
Replacement 2.1South Korea0.72Japan1.2Europe (EU)1.38Latin America & Caribbean1.8
Men (50%)Women (50%)0–40–4: 10.885–95–9: 11.5210–1410–14: 11.6815–1915–19: 12.7820–2420–24: 17.1925–2925–29: 23.8130–3430–34: 30.3935–3935–39: 33.5740–4440–44: 33.3445–4945–49: 3350–5450–54: 32.5155–5955–59: 31.760–6460–64: 88.7565–6965–69: 82.9870–7470–74: 73.8575–7975–79: 59.8280–8480–84: 40.6885–8985–89: 19.53Age groups · synthetic cohort indices
Population index (start=100)
42.11
Share aged 65–89 (%)
42.73
Age 0–4 cohort (start=100)
10.88

Presets use World Bank 2023 total fertility rates, rounded to two decimals. Europe means the EU; Latin America includes the Caribbean. Every preset starts from the same synthetic pyramid: these are not national population forecasts. Mortality is fixed, migration is zero, sexes are split 50/50, and the model ends at age 89. Horizontal scale adjusts; dashed outlines retain the initial cohort sizes.

Cohort values (both sexes)
AgeCohort index
0–410.88
5–911.52
10–1411.68
15–1912.78
20–2417.19
25–2923.81
30–3430.39
35–3933.57
40–4433.34
45–4933
50–5432.51
55–5931.7
60–6488.75
65–6982.98
70–7473.85
75–7959.82
80–8440.68
85–8919.53

World Bank · Total fertility rate · Reference API snapshot · Retrieved 2026-10-28.

The replacement threshold

In low-mortality populations, approximately 2.12.1 births per woman is a common replacement reference without migration. It is not universal: survival and sex ratios matter. Persistently lower fertility narrows new cohorts, but does not imply an immediate collapse of total population.

This experiment calibrates replacement exactly at f∗=2.1f_*=2.1. Ages advance in five-year steps with fixed survival. For cohort size nin_i and survival sis_i:

ni+1(t+5)=sini(t).n_{i+1}(t+5)=s_i n_i(t).

New births depend on ages 20–44, using synthetic reproductive weights wiw_i:

n0(t+5)=100 f2.1 ∑iwini(t)∑iwini(0).n_0(t+5)=100\,\frac{f}{2.1}\,\frac{\sum_i w_i n_i(t)}{\sum_i w_i n_i(0)}.

The initial distribution is stationary at f=2.1f=2.1. There is no migration, survival is identical across presets, sexes are split 50/50, and the model ends at ages 85–89. The reference line, initial outlines, and indices help distinguish relative ageing from absolute shrinkage. Horizontal scale adjusts to the scenario; use the indices and table to compare magnitudes.

Preset source: World Bank, total fertility rate, indicator SP.DYN.TFRT.IN, 2023 observations rounded to two decimals. “Europe” means the EU here, and “Latin America” includes the Caribbean. The horizon is simulated time from an invented population, not a dated forecast.