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arxiv: 2509.16110 · v3 · submitted 2025-09-19 · ⚛️ physics.soc-ph

Scaling and Population Loss in Mexican Urban Centres

Gonzalo G. Peraza-Mues , Eugen Resendiz , Rodolfo Figueroa-Soriano , Rafael Prieto-Curiel , Roberto Ponce-Lopez This is my paper

Pith reviewed 2026-05-18 15:36 UTC · model grok-4.3

classification ⚛️ physics.soc-ph
keywords urban expansionpopulation densityMexican metropolitan areasradial distributionurban sprawlcensus data analysiscentral population loss
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The pith

Mexican metropolitan areas saw central populations drop by 2.5 million and average distances from city centers rise 28 percent from 1990 to 2020.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tracks urban growth across 69 Mexican metropolitan areas using census data from 1990 to 2020. Total urban population nearly doubled during this period, yet residents moved outward from central zones, producing a net loss of 2.5 million people in those cores. The authors apply a radial probability density function and an urban expansion factor to quantify how population distribution changed with distance from each city's center. This outward shift increased average distances by 28 percent on average. The findings illustrate a pattern of fragmented horizontal expansion that affects how cities use land and infrastructure over decades.

Core claim

Mexico's urban population nearly doubled from 1990 to 2020, but populations shifted outward, resulting in a decline of 2.5 million residents in central areas. Distances from the city centre increased by 28 percent on average, driven by population losses in central zones combined with growth in peripheral regions. The radial probability density function and urban expansion factor provide a framework for comparing these changes over time and across regions.

What carries the argument

The radial probability density function combined with the urban expansion factor, which models population distribution at varying distances from the center and measures the degree of outward spread.

If this is right

  • Central urban zones experience sustained population decline while outer zones absorb most new residents.
  • The spatial configuration of cities becomes more spread out, increasing the physical extent of built-up areas.
  • Urban form metrics based on distance from the center capture the combined effect of core losses and peripheral gains.
  • The same model allows direct numerical comparison of expansion rates among different Mexican regions over the three decades.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Longer average distances from centers may raise daily travel requirements for residents even if total population grows.
  • Similar radial-density analysis applied to other countries could test whether outward population shifts appear under comparable census conditions.
  • Policy responses focused only on central revitalization may miss the larger peripheral growth that drives overall urban expansion.

Load-bearing premise

The radial probability density function and urban expansion factor can compare urban expansion reliably across time and regions without needing to adjust for variations in city boundaries or data accuracy.

What would settle it

A re-calculation of the 69 areas using fixed historical city boundaries that eliminates the reported 28 percent distance increase or the 2.5 million central population loss.

Figures

Figures reproduced from arXiv: 2509.16110 by Eugen Resendiz, Gonzalo G. Peraza-Mues, Rafael Prieto-Curiel, Roberto Ponce-Lopez, Rodolfo Figueroa-Soriano.

Figure 1
Figure 1. Figure 1: a-e) Population difference by grid cell (2020-1990) in five Mexican metropolitan areas of different [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Population difference by grid cell (2020-1990) for the 69 Mexican metropolitan zones. Larger [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: a) Change in population density (∆σ) between 1990 and 2020 within concentric rings around each city’s centre at remoteness (r) measured at each ring’s mid-point in 2020. The inset shows population density σ(r) at remoteness r aggregated for all cities in each census year. b) Change in population density (∆¯σ) between 1990 and 2020 within disks of radius r around each city’s centre. The inset shows average … view at source ↗
Figure 4
Figure 4. Figure 4: Scaling of radial probability density func [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Growth factor P(tj )/P(ti) (horizontal axis) and empirical scaling factors Φij (vertical axis) for all cities and all three intercensal periods. Both axes are on a logarithmic scale. The right plot zooms into the cluster of cities to better distinguish individual points. Dotted lines divide regions with different population dynamics. Marginal distributions for Φij and P(tj )/P(ti) are shown as kernel densi… view at source ↗
Figure 6
Figure 6. Figure 6: a) Population aggregated over all metropolises at different remoteness brackets for all census years corresponding to the counterfactual scal￾ing at constant average density. b) Difference be￾tween the observed population and the counterfac￾tual population at each remoteness bracket for the same years. 2.3 Modelling the urban expansion factor The urban expansion factors Φij have similar distri￾butions for … view at source ↗
Figure 7
Figure 7. Figure 7: Empirical scaling factors Φij plotted against the growth factor P(tj )/P(ti) for all cities and all possible combinations of ti , tj for tj > ti and ti , ti in {1990, 2000, 2010, 2020}. Both axes are on a logarithmic scale. Coloured lines correspond to the fitted model (6) for observed values of ∆t. The line of constant density is shown (dashed line) for com￾parison. The fitted model lies in the region of … view at source ↗
Figure 8
Figure 8. Figure 8: Possible model behaviour for Φij (equa￾tion (5)) for different values of exponent β. Different cases enter and leave the density gain region at vari￾ous points. The boundary between regions of density loss and gain is given by Φij = p P(tj )/P(ti). Full coloured lines refer to models with α > 0. Dashed lines refer to models with α < 0 to the boundary between density gain and loss regions. If α > 0, it is i… view at source ↗
read the original abstract

Despite its pervasive implications, many cities worldwide continue to expand in a fragmented, horizontal manner. We analyse urban growth dynamics in 69 Mexican metropolitan areas from 1990 to 2020 using census data, developing a model of urban form change based on population size, density, and spatial configuration. We employ a radial probability density function and the urban expansion factor to create a framework for comparing urban expansion over time and across different regions. Over the past three decades, Mexico's urban population has nearly doubled. However, populations have shifted outward, resulting in a decline of 2.5 million residents in central areas. Our analysis shows that distances from the city centre have increased by 28% on average, driven by population losses in central zones combined with growth in peripheral regions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes urban growth dynamics in 69 Mexican metropolitan areas from 1990 to 2020 using census data. It develops a framework based on population size, density, and spatial configuration, employing a radial probability density function together with an urban expansion factor to compare expansion over time and regions. The central empirical claims are that urban population nearly doubled while central areas lost 2.5 million residents, producing a 28% average increase in distances from the city centre driven by central losses and peripheral gains.

Significance. If the boundary and robustness issues are resolved, the work would supply a multi-decade, multi-city empirical record of outward population shifts in Mexican urban centres, contributing to debates on horizontal urban expansion and its planning implications. The scale of the dataset (69 areas) offers potential for comparative insights, though the absence of error bars and validation currently limits the strength of the quantitative claims.

major comments (2)
  1. [Methods] Methods section (radial PDF and urban expansion factor): the framework does not describe any harmonization of time-varying metropolitan boundaries or fixed-boundary counterfactuals. Because Mexican census tracts and administrative definitions change between 1990 and 2020, the reported 28% distance increase and 2.5 M central loss could be driven by reclassification of peripheral tracts rather than genuine relocation; this directly affects the load-bearing claim that the model isolates outward shifts.
  2. [Results] Results (28% distance increase and central population loss): no error bars, confidence intervals, or sensitivity tests to radial binning choices or centre definitions are reported. Without these, it is impossible to evaluate whether the 28% figure is robust or sensitive to the PDF model assumptions.
minor comments (2)
  1. [Abstract] Abstract: the title refers to 'scaling' yet the abstract provides no explicit scaling relation or exponent; a brief statement of any scaling result would improve clarity.
  2. [Methods] Clarify the operational definition of 'city centre' and how it is held constant across the 69 areas and three decades.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which identify key areas where additional methodological detail and robustness checks will strengthen the manuscript. We respond to each major comment below and outline the revisions we will implement.

read point-by-point responses

  1. Referee: [Methods] Methods section (radial PDF and urban expansion factor): the framework does not describe any harmonization of time-varying metropolitan boundaries or fixed-boundary counterfactuals. Because Mexican census tracts and administrative definitions change between 1990 and 2020, the reported 28% distance increase and 2.5 M central loss could be driven by reclassification of peripheral tracts rather than genuine relocation; this directly affects the load-bearing claim that the model isolates outward shifts.

    Authors: We agree that explicit treatment of boundary changes is necessary. Our analysis employed the official INEGI metropolitan area definitions for each census year, but we did not previously detail potential reclassification effects. In the revised Methods section we will add a description of how we aligned tract-level data across years and include a fixed-boundary counterfactual restricted to metropolitan areas with stable delineations. This will allow us to quantify the contribution of administrative changes versus genuine population relocation to the reported 28% distance increase and central losses. revision: yes

  2. Referee: [Results] Results (28% distance increase and central population loss): no error bars, confidence intervals, or sensitivity tests to radial binning choices or centre definitions are reported. Without these, it is impossible to evaluate whether the 28% figure is robust or sensitive to the PDF model assumptions.

    Authors: We acknowledge that the current presentation lacks quantitative uncertainty measures and sensitivity tests. In the revised Results section we will add bootstrap-derived confidence intervals to the reported average distance increase and central population loss figures. We will also include sensitivity analyses that vary radial bin widths and test alternative centre definitions (geometric centroid versus population-weighted). These additions will demonstrate the robustness of the 28% figure to the modelling choices. revision: yes

Circularity Check

0 steps flagged

No circularity detected; results rest on direct census tabulations

full rationale

The paper analyzes 1990–2020 census data for 69 Mexican metropolitan areas, tabulating population shifts, central losses of 2.5 million, and a 28% average increase in distances from the city centre. It introduces a radial probability density function and urban expansion factor as a comparative framework, but no equations are shown that reduce these outputs to fitted parameters, self-citations, or ansatzes by construction. The central claims derive from external data processing rather than internal redefinition or prediction of inputs, making the derivation self-contained against the census benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; all modeling details are omitted.

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