Demographer

A demographer studies human populations quantitatively: how many people are present, how their characteristics are distributed, and how births, deaths and human migration change those counts. The work connects population census definitions and statistical sampling to statistical estimation and mathematical models of population dynamics. A forecast must distinguish observed counts from assumptions about future rates.^[ref]

For example, in a closed demographic cohort with $n_a(t)$ people aged $a$ and common one-year survival probability $s_a(t)$ conditional on that count, a basic projection isA cohort of 1000 people with survival probability $0.998$ contributes an expected 998 survivors to the next age class. Births create a new youngest class, and human migration requires additional terms. This elementary calculation illustrates why a demographer works with age structure and explicit statistical parameters, rather than extrapolating a single total without assumptions.

Thomas Robert Malthus made the comparison between population growth and the growth of food supply explicit in his 1798 An Essay on the Principle of Population by Thomas Robert Malthus. In Chapters I–II, he assumed that unchecked numbers could follow a geometric progression, taking doubling every 25 years as his rule, while food supply gained a fixed amount in each such period, an arithmetic progression. These were different hypotheses about two quantities, rather than a calculation from a single universal growth law.^[ref]

With equal initial scales, his comparison can be written as $N_k=N_0{2}^k$ and $F_k=F_0(1+k)$ after $k$ periods of 25 years. Then $N_k/F_k=(N_0/F_0)2^k/(1+k)$ grows without bound. The corresponding continuous exponential growth rate for numbers would be $\log (2)/25$ per year. The mathematics describes the consequence of the assumed rates; it does not establish that actual birth, death, human migration and food-production rates stay fixed. Demography can test population assumptions against counts, age composition and measured rates.