Model, developed by Thomas R. Malthus (1766–1834), implying that, unchecked by environmental or social constraints, human populations would double every 25 years, regardless of the initial population size. Thus, if \(X_{i}\) denotes the population size during time period \(i\) and \(r\) the population growth rate, the Malthusian population model gives the relationship \[X(I + 1) = (1 + r)X_{i}\]