Page 50 - IJPS-8-2

International Journal of
Population Studies Used versus Offered densities of human population

indicators of average density put forward by Craig (1984) (iii) mobility analysis (An et al., 2022), (iv) economics
and Stairs (1977a), but also they are more informative in (Albouy & Stewart, 2012; Faberman & Freedman, 2016;
the case of France as of 2019. Krugman, 2013), and (v) environmental impacts (Huang
The Gini index constitutes a heterogeneity indicator of & Brown, 2021) and potentials (Lu et al., 2022). However,
its own kind. It is a statistical summary of the full Lorenz as of end 2022, population-weighted density still had not
curve, which is a more comprehensive tool but also more an entry of its own in the English-speaking Wikipedia,
disaggregate to apprehend heterogeneity in both x and where “living density” is just mentioned as an alternative
O
x . Some hints of that appeared in previous studies such measure of human density (Wikipedia, 2022).
U
as Aliaga et al. (2015) who mentioned that 35% of French 4.5. Further developments
people are living in even 90% of French communes: Up to
the difference between spatial entities and land units, the The notion of population-weighted density was introduced
mention is analogous to one point on the Lorenz curve. in the mid-1970s by a demographer (Craig) and a
The full Lorenz curve contains much more information. In chemistry scientist (Stairs), perhaps because quantitative
the 2019 France case, it was found that 80% of people live socioeconomic analysis is a science of composition as is
in 20% of space and conversely that the remaining 80% of chemistry. Since then it has been adopted by geographers,
space accommodate the remaining 20% of people. Thus, it economists interested in regional science and urban
constitutes yet another instance of the Pareto principle that economics, and transport scientists.
arises in many distributions from incomes in populations Lived density may well be viewed as a simple form of
to the sizes of firms. It is consistent with the linear-log spatial accessibility, as theorized by Hansen (1959), Poulit
model of the used density CDF, since this model makes the (1974) and Koenig (1974; 1980): The Hansen accessibility
used density PDF a limit Pareto law and the offered density index, taken at a given zone as origin of trip-making,
a truly Pareto law. aggregates opportunities of a given kind over a larger
territory, with numbers weighted by a declining function
4.4. On the applications of used density
of origin-destination distance – or travel time or cost in the
The local density of a place is a specific attribute of Poulit-Koenig formulation. This indicator has taken a central
individual people living there. The notion of x and its position in agglomeration economics (Fujita & Thisse, 2002)
U
probabilistic features from f to x and γ constitute a and geography economics (Krugman, 1997; Fujita et al.,
U
U
U
simple statistical model to analyze human population 1999); it is also called the effective density in economic
according to human spatial density. geography (Graham & Gibbons, 2019). It still remains to be
Ottensmann (2018a) pointed out to the existing areas considered as a property of the people residing in the origin
of application of the used density: (i) Primarily as “a zone, for all origin zones and all people, and to be analyzed as
descriptive measure of distribution, often in comparison a random variable among the statistical population of people.
with conventional density,” (ii) urbanization patterns 5. Concluding Remarks
and their dynamic variations, including urban sprawl,
(iii) mobility analysis relating residential and job densities The gist of the article is to model human density in
to the modal share of transit modes of transportation geographical space using basic probability theory:
(Barnes, 2001), (iv) agglomeration economies, relating (i) Statistical populations of land units and of people,
used density to total urban factor productivity (Rappaport, respectively, (ii) putting human density as a random
2008a) and to urban consumption amenities (Rappaport, variable in both statistical populations, with specific PDFs
2008b), and (v) energy use and GHG emissions from and CDFs, (iii) relating the used density PDF to the offered
household residential and travel patterns (Lee & Lee, density PDF through the probabilistic consumption model,
2014). (iv) deriving the statistical moments of the used density
from those of the offered density, and (v) considering the
In recent years, the concept of population-weighted
density has disseminated, notably through web online Lorenz curve and the Gini index. The original contribution
contributions showing its descriptive power (Bradford, is 3-fold: The formal statement as random variables,
2008a-c; Florida, 2012; NENAD, 2021; Ottensmann, 2016) the identification of the consumption model, and the
and above all in the academic literature of its various fields consideration of heterogeneity indicators for human
of applications: (i) Geographical analysis (Hanberry, 2022) density in space (interquartile ratios and Gini index).
including studies on the COVID epidemiology (Pascoal All of the concepts are well established in their own field,
& Rocha, 2022), (ii) urbanization patterns (Townsend & geography, or probabilistic modeling: The article provides
Ellis-Young, 2018) and urban sprawl (Ottensmann, 2018b), a fresh perspective to relate the two fields – casting one

Volume 8 Issue 2 (2022) 44 https://doi.org/10.36922/ijps.v8i2.297