A majorizing forecast of the earth population in a reduced resource-limited model

Abstract

Three two-parameter phenomenological models of population growth dynamics of the Earth’s population N leading to a conclusion about the existence of its limiting number Nmax are briefly described. It is noted that the Ferhulst model, which assumes external resource constraints of exponential growth and leads to a logistic dependence N (t), has a maximum growth rate dN/dt at N = Nmax/2 and is adequate to asexual method of reproduction. Two other models are associated with sexual reproduction, however, in Kapitsa model, it is believed that N growth restriction is due only to internal causes (the “demographic imperative” of Kapitsa). The authors develop a model in which resource constraints are reflected by the square of Verhulst multiplier. It is significant that in such a model (as in Kapitsa model) there is not only a maximum growth rate, but also a maximum relative growth rate (1/N) dN/dt at N ≈ Nmax /2.7 for Kapitsa model and N = Nmax/3 in resource limited model. These features make it possible to estimate the value of Nmax using statistical data on N(t) dependence. The analysis of transition from “microscopic” to macroscopic description indicates the possibility of transition to a reduced model in which for (1/N) dN/dt the square of Verhulst multiplier is preserved, and data processing allows using the value Nmax = 14.7 billion. For this value Nmax after calibration of the model parameters according to the beginning of 2018 a population forecast was made. Comparison with two forecasts based on UN data showed that calculations of the reduced model majorize them, exceeding, for example, in 2050 by 1.4%. The effect of explicit concern of the rate of population decline due to mortality, leading to decrease in the Nmax estimates, is briefly discussed.