Energy and Human Ambitions on a Finite Planet, 2021a

3 Population 38
halfway to the limiting value. A fit to the data (Figure 3.9) suggests
that r ≈ 0.028, corresponding to a timescale of 36 years (1/r). This
puts the overshoot-prone delay squarely into relevant timescales for
human lifetimes, generations, <strong>and</strong> societal change—thus leaving the
door open for an overshoot scenario.
3.2.2 Logistic Projection
As suggested by Figure 3.9, <strong>Human</strong> population is not following a strict
logistic curve. If it were, the early period would look exponential at the
∼2.8% rate corresponding to the best-fit logistic matching our recent
trajectory, but growth was substantially slower than 2.8% in the past.
Technology <strong>and</strong> fossil fuels have boosted our recent growth well beyond
the sub-percent rates typical before ∼1950. The point is that while
reference to mathematical models can be extremely helpful in framing
our thinking <strong>and</strong> exposing robust, generic modes of interest, we should
seldom take any mathematical model literally, as it likely does not capture
the full complexity of the system it is trying to model. In the present
case, it is enough to note that:
1. exponentials relentlessly drive toward infinity (ultimately unrealistic);
2. logistic curves add a sensible layer of reality, capping growth in
some steady-state outcome;
3. other dynamical factors such as delays can prevent a smooth
logistic function, possibly leading to overshoot; <strong>and</strong>
4. many other factors (medical <strong>and</strong> technological breakthroughs, war,
famine, climate change) can muddy the waters in ways that could
make the situation better or worse than simple projections.
3.3 Demographic Transition
Perhaps not surprisingly, the rate of a country’s population growth is
correlated to its wealth, as seen in Figure 3.10. An attractive path to
reducing population growth would be to have poor countries slide down
this curve to the right: becoming more affluent <strong>and</strong> transforming societal
values <strong>and</strong> pressures accordingly to produce a lower net population
growth rate.
Population growth happens when the birth rate exceeds the death rate.
Definition 3.3.1 Birth rate, typically expressed in births per 1,000 people
per year, minus death rate (also in deaths per 1,000 people per year) is the
net population rate. 17 If the difference is positive, the population grows, <strong>and</strong>
it shrinks if the difference is negative.
17: This ignores immigration, which just
shifts living persons around.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.