On the relationship between mean and variance of world's human population density: A study using Taylor's power law

Animal ecology has devoted a great deal of effort to the study of the relations between the variance (V) and the average (M) of the density of a group of sub-populations (pi) belonging to the same territorial system, and thus, it has been possible to develop several ‘laws’. Among these laws, one of the best known is Taylor’s power law (TL), which provides that between V and M, there is a power law. Several studies have appeared on this topic only recently in the field of human demography, mainly those of Cohen and colleagues. This is quite surprising given the extreme importance of the population density indicator in population studies. This paper, for the first time, tests the relations between V and M at the world level by working on the sub-populations (pi) resident in each country belonging to five continents and following a long-term perspective (1950–2017). To estimate the unknown parameters of the relation we make use a simultaneous equation system (SUR). The results show that TL is verified in two out of five cases (Asia, and America), while in three cases (Africa, Europe and Oceania), a quadratic relationship shows better results.