In September of 1802, Pierre Simon Laplace (1749–1827) used a capture– recapture type of approach to estimate the size of the human population of France (Cochran 1978; Stigler 1986). At that time, live births were recorded for all of France on an annual basis. In the year prior to September 1802, Laplace estimated the number of such births to be approximately X = 1,000,000. These newly born individuals constituted a marked population. Laplace then obtained census and live birth data from several communities “with zealous and intelligent mayors” across all of France. Recognizing some variation in annual birth rates, Laplace summed the number of births reported in these sample communities for the three years leading up to the time of his estimate, and divided by three to determine that there were x = 71,866 births per year (marked individuals) in those communities. The ratio of these marked individuals to the total number of individuals in the sampled communities, y = 2,037,615, was then the estimate
p = 71,866/2,037,615 = 0.0353
of the proportion of the total population in France that was newly born. On this basis, the one million marked individuals in the whole of France is related to the total population N as
Np ≈ 1,000,000
N ≈ 1,000,000/0.0353 =28,328,612
This estimation procedure is equivalent to the Lincoln-Peterson capture-recapture estimator described in chapter 2.