Peak Population

Explore the timing of peak births and peak population in an age-structured population with falling fertility

This app shows the dynamics of populations undergoing declining fertility rates. It is useful for investigating the case of exponentially declining fertility with constant mortality, what we call the 'Coale Scenario'. It can also be used to see the impact of increasing longevity and of fertility that levels-out below replacement

Advance time with 'play' button or with slider to project the population

Options:

Exercises:

1. Where will births peak -- before or after NRR reaches replacement? Extra-credit: does this change with 'k'?

2. To undertand why, check 'plot generational slope' box and notice that when the slope is zero, the peak is about half-way between t = -30 and t = 0.

3. When does population peak? More extra-credit: does this change with 'k'

4. How much does longevity increase delay peak population?

5. How much does leveling of NRR below replacement delay poplation?

6. How accurate are the analytical approximations?

t_B = t_0 - mu_0/2 (Coale)

t_N = t_B + A_0 (Coale)

t_N^+ = t_N + (-rho/k1)*mu_0 (Goldstein and Cassidy)

t_N2 = t_N + (1/2)*(-k2/k1)*sigma_0^2 (Goldstein and Cassidy)