Page 41 - IJPS-8-2

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

Yet, the basic indicator of human density pertains, density is also the “used density,” since people are the users
essentially to space. As geographical space is likely to of the settlement services. The relation between the PDFs
exhibit heterogeneity of human occupation, the average enables one to build average indicators in a straightforward
plain density (rather than “crude density” as worded by way. It also allows for considering classical indicators of
Craig, 1984) does not indicate much about the effective heterogeneity in a simple way: we introduce interquartile
intensity of human occupation that people experience in ratios and above all the Lorenz curve and the Gini index of
their everyday life, in the places that they frequent – home, human density in a given geographical space.
workplace, etc. This is why alternative, population-
weighted indicators of density have been developed by The rest of the article is organized in four parts: After
pioneering researchers in the mid-1970s. Stairs (1977a; stating the methodology, we will apply it to a case study of
1977b) introduced the person-average density as “the communal density in France as of 2019, before providing
local density experienced by people, that is, spatial density a discussion and a short conclusion. Four appendices
of human population weighted by the number of people provide more details on (A) the notation table, (B) the
experiencing it.” This indicator was called population- consumption model, (C) the lognormal distribution and
weighted (arithmetic mean) density by Craig (1984). The its use for consumption models, and (D) the linear-log
name of “population-weighted density” has popularized model of used density CDF.
among geographers and economists that have used the
indicator to understand “density as lived by people” and 2. Theoretical background
its effects on urbanization (Eidlin, 2010, Florida, 2012), We shall first define land units to deal with a geographical
mobility practices (Barnes, 2001), as well as greenhouse space as a statistical population of such elementary places
gas (GHG) emissions of travel (Lee & Lee, 2014). As (§2.1). Then, human density is put as a random variable
stated by Barnes (2001: p.16), “we are interested in human with its own probabilistic distribution, mean and other
behavior; what we want to know is what people perceive statistical moments, and heterogeneity measures (§2.2).
density to be: This would be more closely captured by The next step is to shift the statistical perspective from
giving equal weight to each person, rather than to each the statistical population of land units to that of people:
square mile of land…. thus (we shall) use a new measure The random variable of used human density inherits
called ‘perceived density,’ which is defined as a weighted its probabilistic features – probability distribution and
average of traffic zone densities, where each zone is statistical moments including the average value – from its
weighted by the number of residents.” Ottensmann (2018a) offered counterpart on the basis of a consumption model
provided a comprehensive literature review of the concept, (§2.3). We then recall the Lorenz curve and the Gini index
its applications and the related issues, together with a as classical tools for inequality measurement and adapt
diachronic application to major US cities. them to the inequality of human population among land
So far, the concept of “lived density” and “population- units (§2.4). Finally, we recall some previously proposed
weighted density” has been expressed using mathematical indicators of heterogeneity for human density and we
formulas of weighted averages involving the numbers of restate them using our notation (§2.5).
people living in pre-defined zones (Barnes, 2001; Craig,
1984; Ottensmann, 2018a; Stairs, 1977). The relationship 2.1. Geographical space as a statistical distribution
between lived and plain density averages has been of land units
established by Lewontin & Levins (1989) and Ottensmann 2.1.1. Territory, zoning system, and population
(2018a) using lengthy proofs. This article is aimed to
state plain density and lived density in the standard To analyze human density in a geographical space, it is
probabilistic framework, involving statistical populations, convenient to model that space using a set Z of zones z.
respectively, of land units and people, local human density Each zone has its own ground area, A z, and human
as a random variable in either statistical population, their population, P z. Its spatial density of human population is
respective probability density functions (PDFs), and the simply:
general relation between them. This relation consists in a x = PA/ (1)
specific instance of a well-known probabilistic model: The z z z
Z
“consumption model” that arises in various fields from The territory has total ground area of A A and
z
Z

z
economics to traffic theory. To emphasize the consumption total population of P P . Its human density averaged
model that relates plain density to lived density, we consider Z z
Z

z
land units as servers of spatial settlement for people. Then, over space is therefore
plain density is also the offered density, whereas lived x = P / A Z (2)
Z
Z
Volume 8 Issue 2 (2022) 35 https://doi.org/10.36922/ijps.v8i2.297