Thermodynamic-based ecological scaling theory in urban metabolic framework: a review

doi:10.1007/s11783-025-1924-8

Front. Environ. Sci. Eng.

2025, Vol. 19

Issue (1) : 4 https://doi.org/10.1007/s11783-025-1924-8

Thermodynamic-based ecological scaling theory in urban metabolic framework: a review

Gengyuan Liu^1,²(

), Mingwan Wu¹

¹. State Key Joint Laboratory of Environmental Simulation and Pollution Control, School of Environment, Beijing Normal University, Beijing 100875, China
². Beijing Engineering Research Center for Watershed Environmental Restoration & Integrated Ecological Regulation, Beijing 100875, China

Download: PDF(5334 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

● Under thermodynamic, urban ecosystem fits scaling law due to self-organization.

● Urban ecosystem has similar scaling to social economic system.

● The scaling law transitions are reflected in the multistable coexistence.

Prior research has consistently demonstrated that urban economic and social systems adhere to the empirical scaling law. Furthermore, a plethora of evidence, including the scale-free networks of energy metabolism, the allometric growth patterns of species and populations, and the scaling law relationship between exergy and transformity in biosphere systems across various levels, indicates that urban ecosystems exhibit multi-level scaling law characteristics in energy metabolism under self-organization, alongside significant human activity imprints. This study synthesizes these findings to hypothesize that urban ecological components are also aligned with system-level scaling theory within the urban metabolism framework. This encompasses: 1) the existence of multistable coexistence and mutual transformation phenomena, mirroring the dynamic nature of scaling laws; and 2) a nuanced balance between the ecosystem and the socio-economic system, particularly in the realms of spatial competition and output efficiency. The ecosystem scaling theory hypotheses of urban metabolic processes offer a theoretical foundation for identifying ecological security tipping points, which are pivotal in the strategic decision-making for ecological planning and management in the future.

Keywords Ecosystem scaling theory Urban metabolism Complexity Critical review

Corresponding Author(s): Gengyuan Liu

Issue Date: 18 October 2024

Cite this article:

Gengyuan Liu,Mingwan Wu. Thermodynamic-based ecological scaling theory in urban metabolic framework: a review[J]. Front. Environ. Sci. Eng., 2025, 19(1): 4.

URL:

https://academic.hep.com.cn/fese/EN/10.1007/s11783-025-1924-8
https://academic.hep.com.cn/fese/EN/Y2025/V19/I1/4

Elements	Indicator	Scaling coefficient lower limit	95%CI	Data source
Invention	New patents	1.27	± 0.02	Bettencourt et al. (2007)
Invention	Inventors	1.25–1.47	± 0.03/± 0.06	Bettencourt et al. (2007); Gomez-Lievano et al. (2017)
Invention	Supercreative employment	1.15	± 0.04	Bettencourt et al. (2007)
Productivity	GDP	1.13–1.26	± 0.10/± 0.017	Bettencourt et al. (2007)
Productivity	Wholesale brokers	1.29	± 0.03	Gomez-Lievano et al. (2017)
Productivity	Total wages	1.12	± 0.03	Bettencourt et al. (2007)
Productivity	Bank deposits	1.08	± 0.05	Bettencourt et al. (2007)
Productivity	Total employment	1.01	± 0.02	Bettencourt et al. (2007)
Consumption	Total housing	1.00	± 0.01	Bettencourt et al. (2007)
Consumption	Electrical consumption	1.00	± 0.17	Bettencourt et al. (2007)
Consumption	Household water consumption	1.01	± 0.10	Bettencourt et al. (2007)
Education	High school	1.00	± 0.00	Gomez-Lievano et al. (2017)
Education	Collage	1.11	± 0.02	Gomez-Lievano et al. (2017)
Health	New AIDS cases	1.23	± 0.05	Bettencourt et al. (2007)
Health	Chlamydia	1.06	± 0.02	Gomez-Lievano et al. (2017)
Health	Syphilis	1.46	± 0.05	Gomez-Lievano et al. (2017)
Health	All-cause of mortality	0.89–1.13	± 0.05	Bilal et al. (2021)
Social security	Serious crimes	1.16	± 0.05	Bettencourt et al. (2007)
Social security	Robbery	1.35	± 0.03	Gomez-Lievano et al. (2017)
Social security	Burglary	1.01	± 0.02	Gomez-Lievano et al. (2017)
Infrastructure	Gasoline stations	0.77	± 0.03	Bettencourt et al. (2007)
Infrastructure	Gasoline sales	0.79	± 0.06	Bettencourt et al. (2007)
Infrastructure	Length of electrical cables	0.87	± 0.06	Bettencourt et al. (2007)
Infrastructure	Road surface	0.83	± 0.08	Bettencourt et al. (2007)
Pollution	Waste water	1.15	± 0.04	Lu et al. (2024)
Pollution	Municipal solid waste	1.04	± 0.05	Lu et al. (2024)
Pollution	GHG emissions	0.85	± 0.10	Lu et al. (2024)

Tab.1 Scaling coefficients of urban system elements

Type	Scaling coefficient	Driving factor	Cases	References
Inverse scaling	$β < 0$	Optimize and improve efficiency	The ecological scale relationship between average population density (Y) and average species size (X) showed an inverse scale relationship (β < 0), such as primary consumers of mammals (β = −0.75) and Amazonian bird communities (β = −0.22). Changes in the equilibrium number or carrying capacity of an individual organism are inversely proportional to body size.	Damuth (1981); Brown et al. (2004)
Sub-linear scaling	$0 < β < 1$	Optimize and improve efficiency	There is a classical sub-linear scale relationship between an organism's metabolic rate (Y) and its body weight (X) (0 < β < 1), for instance, Kleber’s law (β = 3/4). The relationship between total biomass and body size was also sub-linear.	Kleiber (1947); West & Brown (2005); Brown et al. (2004)
Linear scaling	$β = 1$	Living and consumption	An individual-based human development indicator (Y) is usually linearly related to city size (X) (β = 1), such as total housing stock in the United States (β = 1.00), household electricity consumption in Germany (β = 1.00), and household water consumption in China (β = 1.01).	Bettencourt et al. (2007)
Super-linear scaling	$β > 1$	Information innovation, wealth generation, resource development	The total output benefit (Y) (e.g., wages, income, GDP growth, bank deposits, new patents) and city size (X) show a super-linear scale relationship (β > 1). The scaling coefficient of new patents in the United States is β = 1.27, R&D employment in China is β = 1.26, and GDP in the European Union is β = 1.26.	Bettencourt et al. (2007)

Tab.2 Summary of scaling types in urban complex systems

Fig.1 The diagram of energy hierarchy and multi-level transformation of urban ecosystem conform to the scaling law.

1	M Alberti, E P Palkovacs, S D Roches, L D Meester, K I Brans, L Govaert, N B Grimm, N C Harris, A P Hendry, C J Schell. et al.. (2020). The complexity of urban eco-evolutionary dynamics. Bioscience, 70(9): 772–793 https://doi.org/10.1093/biosci/biaa079
2	D Alves, A P Barreira, M H Guimarães, T Panagopoulos. (2016). Historical trajectories of currently shrinking Portuguese cities: a typology of urban shrinkage. Cities (London, England), 52: 20–29 https://doi.org/10.1016/j.cities.2015.11.008
3	S Arshad, S Hu, B N Ashraf. (2018). Zipf’s law and city size distribution: a survey of the literature and future research agenda. Physica A: Statistical Mechanics and its Applications, 492: 75–92 https://doi.org/10.1016/j.physa.2017.10.005
4	F Auerbach. (1913). Das gesetz der bevölkerungskonzentration: the law of population concentration. Petermanns Geographische Mitteilungen, 59: 74–76
5	M Batty. (2008). The size, scale, and shape of cities. Science, 319(5864): 769–771 https://doi.org/10.1126/science.1151419
6	M A Benedict, E T McMahon (2012). Green Infrastructure: Linking Landscapes and Communities. Washington, DC: Island Press
7	L M Bettencourt. (2013). The origins of scaling in cities. Science, 340(6139): 1438–1441 https://doi.org/10.1126/science.1235823
8	L M Bettencourt, J Lobo, D Helbing, C Kühnert, G B West. (2007). Growth, innovation, scaling, and the pace of life in cities. Proceedings of the National Academy of Sciences of the United States of America, 104(17): 7301–7306 https://doi.org/10.1073/pnas.0610172104
9	U Bilal, Castro C P de, T Alfaro, T Barrientos-Gutierrez, M L Barreto, C M Leveau, K Martinez-Folgar, J J Miranda, F Montes, P Mullachery. et al.. (2021). Scaling of mortality in 742 metropolitan areas of the Americas. Science Advances, 7(50): eabl6325 https://doi.org/10.1126/sciadv.abl6325
10	D Bristow, C Kennedy. (2015). Why do cities grow? Insights from nonequilibrium thermodynamics at the urban and global scales. Journal of Industrial Ecology, 19(2): 211–221 https://doi.org/10.1111/jiec.12239
11	J H Brown, J F Gillooly, A P Allen, V M Savage, G B West. (2004). Toward a metabolic theory of ecology. Ecology, 85(7): 1771–1789 https://doi.org/10.1890/03-9000
12	M T Brown, D E Campbell, C de Vilbiss, S Ulgiati. (2016). The geobiosphere emergy baseline: a synthesis. Ecological Modelling, 339: 92–95 https://doi.org/10.1016/j.ecolmodel.2016.03.018
13	M T Brown, S Ulgiati. (2004). Energy quality, emergy, and transformity: H.T. Odum’s contributions to quantifying and understanding systems. Ecological Modelling, 178(1−2): 201–213 https://doi.org/10.1016/j.ecolmodel.2004.03.002
14	M T Brown, S Ulgiati. (2016). Assessing the global environmental sources driving the geobiosphere: a revised emergy baseline. Ecological Modelling, 339: 126–132 https://doi.org/10.1016/j.ecolmodel.2016.03.017
15	S Q Chen, B Chen. (2015). Urban energy consumption: different insights from energy flow analysis, input-output analysis and ecological network analysis. Applied Energy, 138: 99–107 https://doi.org/10.1016/j.apenergy.2014.10.055
16	Y Chen, G Liu, N Yan, Q Yang, H Gao, L Su, R Santagata. (2023). Comprehensive evaluation of urban greenspace ecological values marketability through the spatial relationship between housing price and ecosystem services. Ecological Modelling, 484: 110482 https://doi.org/10.1016/j.ecolmodel.2023.110482
17	M (2000) Conan. Environmentalism in Landscape Architecture. Washington, DC: Dumbarton Oaks
18	R Costanza, R de Groot, P Sutton, S van der Ploeg, S J Anderson, I Kubiszewski, S Farber, R K Turner. (2014). Changes in the global value of ecosystem services. Global Environmental Change, 26: 152–158 https://doi.org/10.1016/j.gloenvcha.2014.04.002
19	S Cristiano, A Zucaro, G Liu, S Ulgiati, F Gonella. (2020). On the systemic features of urban systems: a look at material flows and cultural dimensions to address post-growth resilience and sustainability. Frontiers in Sustainable Cities, 2: 12 https://doi.org/10.3389/frsc.2020.00012
20	J Cueva, I A Yakouchenkova, K Fröhlich, A F Dermann, F Dermann, M Köhler, J Grossmann, W Meier, J Bauhus, D Schroder. et al.. (2022). Synergies and trade-offs in ecosystem services from urban and peri-urban forests and their implication to sustainable city design and planning. Sustainable Cities and Society, 82: 103903 https://doi.org/10.1016/j.scs.2022.103903
21	D Cui, W H Zeng, B R Ma, Y Zhuo, Y X Xie. (2021). Ecological network analysis of an urban water metabolic system: integrated metabolic processes of physical and virtual water. Science of the Total Environment, 787: 147432 https://doi.org/10.1016/j.scitotenv.2021.147432
22	G S Cumming. (2013). Scale mismatches and reflexive law. Ecology and Society, 18(1): 15 https://doi.org/10.5751/ES-05407-180115
23	G S Cumming, D H Cumming, C L Redman. (2006). Scale mismatches in social-ecological systems: causes, consequences, and solutions. Ecology and Society, 11(1): 14 https://doi.org/10.5751/ES-01569-110114
24	G S Cumming, G D Peterson. (2017). Unifying research on social–ecological resilience and collapse. Trends in Ecology & Evolution, 32(9): 695–713
25	J Damuth. (1981). Population density and body size in mammals. Nature, 290(5808): 699–700 https://doi.org/10.1038/290699a0
26	R Dasgupta, M Basu, S Hashimoto, R C Estoque, P Kumar, B Johnson, B Mitra, P Mitra. (2022). Residents’ place attachment to urban green spaces in Greater Tokyo region: an empirical assessment of dimensionality and influencing socio-demographic factors. Urban Forestry & Urban Greening, 67: 127438 https://doi.org/10.1016/j.ufug.2021.127438
27	M Egerer, N Fouch, E C Anderson, M Clarke. (2020). Socio-ecological connectivity differs in magnitude and direction across urban landscapes. Scientific Reports, 10(1): 4252 https://doi.org/10.1038/s41598-020-61230-9
28	Z ElZein, A Abdou, I A ElGawad. (2016). Constructed wetlands as a sustainable wastewater treatment method in communities. Procedia Environmental Sciences, 34: 605–617 https://doi.org/10.1016/j.proenv.2016.04.053
29	B D Fath, H Asmus, R Asmus, D Baird, S R Borrett, Jonge V N de, A Ludovisi, N Niquil, U M Scharler, U Schückel. et al.. (2019). Ecological network analysis metrics: the need for an entire ecosystem approach in management and policy. Ocean and Coastal Management, 174: 1–14 https://doi.org/10.1016/j.ocecoaman.2019.03.007
30	M R Felipe-Lucia, S Soliveres, C Penone, M Fischer, C Ammer, S Boch, R S Boeddinghaus, M Bonkowski, F Buscot, A M Fiore-Donno. et al.. (2020). Land-use intensity alters networks between biodiversity, ecosystem functions, and services. Proceedings of the National Academy of Sciences of the United States of America, 117(45): 28140–28149 https://doi.org/10.1073/pnas.2016210117
31	F Feng, X Yang, B Jia, X Li, X Li, C Xu, K Wang. (2024). Variability of urban fractional vegetation cover and its driving factors in 328 cities in China. Science China. Earth Sciences, 67(2): 466–482 https://doi.org/10.1007/s11430-022-1219-2
32	N Galiana, M Lurgi, V A Bastazini, J Bosch, L Cagnolo, K Cazelles, B Claramunt-López, C Emer, M Fortin, I Grass. et al.. (2022). Ecological network complexity scales with area. Nature Ecology & Evolution, 6(3): 307–314 https://doi.org/10.1038/s41559-021-01644-4
33	J Gao, S Li. (2011). Detecting spatially non-stationary and scale-dependent relationships between urban landscape fragmentation and related factors using Geographically Weighted Regression. Applied Geography, 31(1): 292–302 https://doi.org/10.1016/j.apgeog.2010.06.003
34	A Gomez-Lievano, O Patterson-Lomba, R Hausmann. (2017). Explaining the prevalence, scaling and variance of urban phenomena. Nature Human Behaviour, 1(1): 0012 https://doi.org/10.1038/s41562-016-0012
35	P Gong, B Chen, X Li, H Liu, J Wang, Y Bai, J Chen, X Chen, L Fang, S Feng. et al.. (2020). Mapping essential urban land use categories in China (EULUC-China): preliminary results for 2018. Science Bulletin, 65(3): 182–187 https://doi.org/10.1016/j.scib.2019.12.007
36	L Govaert, E A Fronhofer, S Lion, C Eizaguirre, D Bonte, M Egas, A P Hendry, Brito Martins A de, C J Melián, J A Raeymaekers. et al.. (2019). Eco-evolutionary feedbacks: theoretical models and perspectives. Functional Ecology, 33(1): 13–30 https://doi.org/10.1111/1365-2435.13241
37	C Gu. (2019). Urbanization: processes and driving forces. Science China. Earth Sciences, 62(9): 1351–1360 https://doi.org/10.1007/s11430-018-9359-y
38	L He, Z Xie, H Wu, Z Liu, B Zheng, W Wan. (2024). Exploring the interrelations and driving factors among typical ecosystem services in the Yangtze River Economic Belt, China. Journal of Environmental Management, 351: 119794 https://doi.org/10.1016/j.jenvman.2023.119794
39	M T Johnson, J Munshi-South. (2017). Evolution of life in urban environments. Science, 358(6363): eaam8327 https://doi.org/10.1126/science.aam8327
40	M Keuschnigg, S Mutgan, P Hedström. (2019). Urban scaling and the regional divide. Science Advances, 5(1): eaav0042 https://doi.org/10.1126/sciadv.aav0042
41	M Kleiber. (1947). Body size and metabolic rate. Physiological Reviews, 27(4): 511–541 https://doi.org/10.1152/physrev.1947.27.4.511
42	T Koellner, Baan L de, T Beck, M Brandão, B Civit, M Margni, L M Canals, R Saad, Souza D M de, R Müller-Wenk. (2013). UNEP-SETAC guideline on global land use impact assessment on biodiversity and ecosystem services in LCA. International Journal of Life Cycle Assessment, 18(6): 1188–1202 https://doi.org/10.1007/s11367-013-0579-z
43	I Kowarik. (2023). Urban biodiversity, ecosystems and the city. Insights from 50 years of the Berlin School of urban ecology. Landscape and Urban Planning, 240: 104877 https://doi.org/10.1016/j.landurbplan.2023.104877
44	D J Lee, M T Brown. (2021). Estimating the value of global ecosystem structure and productivity: a geographic information system and emergy based approach. Ecological Modelling, 439: 109307 https://doi.org/10.1016/j.ecolmodel.2020.109307
45	W Lei, L Jiao, G Xu. (2022). Understanding the urban scaling of urban land with an internal structure view to characterize China’s urbanization. Land Use Policy, 112: 105781 https://doi.org/10.1016/j.landusepol.2021.105781
46	T M Lenton, T A Kohler, P A Marquet, R A Boyle, M Crucifix, D M Wilkinson, M Scheffer. (2021). Survival of the systems. Trends in Ecology & Evolution, 36(4): 333–344 https://doi.org/10.1016/j.tree.2020.12.003
47	C Li, B Fu, S Wang, L C Stringer, W Zhou, Z Ren, M Hu, Y Zhang, E Rodriguez-Caballero, B Weber. et al.. (2023). Climate-driven ecological thresholds in China’s drylands modulated by grazing. Nature Sustainability, 6(11): 1363–1372 https://doi.org/10.1038/s41893-023-01187-5
48	R Li, L Dong, J Zhang, X Wang, W Wang, Z Di, H E Stanley. (2017). Simple spatial scaling rules behind complex cities. Nature Communications, 8(1): 1841 https://doi.org/10.1038/s41467-017-01882-w
49	T Li, Y Jin, Y Huang. (2022). Water quality improvement performance of two urban constructed water quality treatment wetland engineering landscaping in Hangzhou, China. Water Science and Technology, 85(5): 1454–1469 https://doi.org/10.2166/wst.2022.063
50	G Liu, Z Yang, B F Giannetti, M Casazza, F Agostinho, J Pan, N Yan, Y Hao, L Zhang, C M Almeida. (2021). Energy constrains to increasing complexity in the biosphere. The Innovation, 2(4): 100169 https://doi.org/10.1016/j.xinn.2021.100169
51	J Liu, T Dietz, S R Carpenter, M Alberti, C Folke, E Moran, A N Pell, P Deadman, T Kratz, J Lubchenco. et al.. (2007). Complexity of coupled human and natural systems. Science, 317(5844): 1513–1516 https://doi.org/10.1126/science.1144004
52	Z Liu, S Gao, W Cai, Z Li, C Wang, X Chen, Z Ma, Z Zhao. (2023a). Projections of heat-related excess mortality in china due to climate change, population and aging. Frontiers of Environmental Science & Engineering, 17(11): 132 https://doi.org/10.1007/s11783-023-1732-y
53	Z Liu, J Song, H Yu, G Hong (2022). Analysis of scaling law characteristics of Chinese urban parks. Chinese Landscape Architecture, 38(7): 50–55 (in Chinese)
54	Z Liu, S Wang, C Fang. (2023b). Spatiotemporal evolution and influencing mechanism of ecosystem service value in the Guangdong-Hong Kong-Macao Greater Bay Area. Journal of Geographical Sciences, 33(6): 1226–1244 https://doi.org/10.1007/s11442-023-2127-5
55	J Lobo, L M Bettencourt, M E Smith, S Ortman. (2020). Settlement scaling theory: Bridging the study of ancient and contemporary urban systems. Urban Studies, 57(4): 731–747 https://doi.org/10.1177/0042098019873796
56	J Loomis, P Kent, L Strange, K Fausch, A Covich. (2000). Measuring the total economic value of restoring ecosystem services in an impaired river basin: results from a contingent valuation survey. Ecological Economics, 33(1): 103–117 https://doi.org/10.1016/S0921-8009(99)00131-7
57	M Lu, C Zhou, C Wang, R B Jackson, C P Kempes. (2024). Worldwide scaling of waste generation in urban systems. Nature Cities, 1(2): 126–135 https://doi.org/10.1038/s44284-023-00021-5
58	A M Makarieva, V G Gorshkov, B Li. (2004). Body size, energy consumption and allometric scaling: a new dimension in the diversity–stability debate. Ecological Complexity, 1(2): 139–175 https://doi.org/10.1016/j.ecocom.2004.02.003
59	A M Makarieva, V G Gorshkov, B Li (2011). Have ecological human rights been globally lost? A conflict of ecological spatial requirements and cultural landscape opportunities in Modern Homo sapiens. In: Hong S K, Kim J E, Wu J, Nakagoshi N, eds. Landscape Ecology in Asian Cultures. Tokyo: Springer
60	P A Marquet, R A Quiñones, S Abades, F Labra, M Tognelli, M Arim, M Rivadeneira. (2005). Scaling and power-laws in ecological systems. Journal of Experimental Biology, 208(9): 1749–1769 https://doi.org/10.1242/jeb.01588
61	K McGarigal (1995). FRAGSTATS: spatial pattern analysis program for quantifying landscape structure. Portland: US Department of Agriculture, Forest Service, Pacific Northwest Research Station
62	X Meng, Z Jiang, X Wang, Y Long. (2021). Shrinking cities on the globe: Evidence from LandScan 2000–2019. Environment and Planning A: Economy and Space, 53(6): 1244–1248 https://doi.org/10.1177/0308518X211006118
63	X Meng, Y Long. (2022). Shrinking cities in China: Evidence from the latest two population censuses 2010–2020. Environment and Planning A: Economy and Space, 54(3): 449–453 https://doi.org/10.1177/0308518X221076499
64	E Nelson, G Mendoza, J Regetz, S Polasky, H Tallis, D R Cameron, K Chan, G C Daily, J Goldstein, P M Kareiva. et al.. (2009). Modeling multiple ecosystem services, biodiversity conservation, commodity production, and tradeoffs at landscape scales. Frontiers in Ecology and the Environment, 7(1): 4–11 https://doi.org/10.1890/080023
65	M J Nieuwenhuijsen. (2016). Urban and transport planning, environmental exposures and health-new concepts, methods and tools to improve health in cities. Environmental Health, 15(S1): S38 https://doi.org/10.1186/s12940-016-0108-1
66	Y Niu, J Yang, Q Zhao, Y Gao, T Xue, Q Yin, P Yin, J Wang, M Zhou, Q Liu. (2023). The main and added effects of heat on mortality in 33 chinese cities from 2007 to 2013. Frontiers of Environmental Science & Engineering, 17(7): 81 https://doi.org/10.1007/s11783-023-1681-5
67	H T Odum (1971). Environment, Power, and Society. Hoboken: John Wiley & Sons Inc.
68	S G Ortman, J Lobo, M E Smith. (2020). Cities: complexity, theory and history. PLoS One, 15(12): e0243621 https://doi.org/10.1371/journal.pone.0243621
69	X Ouyang, L Tang, X Wei, Y Li. (2021). Spatial interaction between urbanization and ecosystem services in Chinese urban agglomerations. Land Use Policy, 109: 105587 https://doi.org/10.1016/j.landusepol.2021.105587
70	B C Patten, R J Mulholland, C M Gowdy (197197). Systems analysis and simulation in ecology. New York: Academic Press
71	B C Patten, E P Odum. (1981). The cybernetic nature of ecosystems. The American Naturalist, 118(6): 886–895 https://doi.org/10.1086/283881
72	J Peng, L Tian, Y X Liu, M Y Zhao, Y N Hu, J S Wu (2017). Ecosystem services response to urbanization in metropolitan areas: thresholds identification. Science of the Total Environment, 607–607: 706–714
73	G Perino, B Andrews, A Kontoleon, I Bateman. (2014). The value of urban green space in Britain: a methodological framework for spatially referenced benefit transfer. Environmental and Resource Economics, 57(2): 251–272 https://doi.org/10.1007/s10640-013-9665-8
74	S Piao, M Huang, Z Liu, X H Wang, P Ciais, J G Canadell, K Wang, A Bastos, P Friedlingstein, R A Houghton. et al.. (2018). Lower land-use emissions responsible for increased net land carbon sink during the slow warming period. Nature Geoscience, 11(10): 739–743 https://doi.org/10.1038/s41561-018-0204-7
75	S Piao, X Wang, T Park, C Chen, X U Lian, Y He, J W Bjerke, A Chen, P Ciais, H Tommervik. et al.. (2019). Characteristics, drivers and feedbacks of global greening. Nature Reviews. Earth & Environment, 1(1): 14–27 https://doi.org/10.1038/s43017-019-0001-x
76	S T Pickett, M L Cadenasso, J M Grove, C H Nilon, R V Pouyat, W C Zipperer, R Costanza. (2001). Urban ecological systems: linking terrestrial ecological, physical, and socioeconomic components of metropolitan areas. Annual Review of Ecology and Systematics, 32(1): 127–157 https://doi.org/10.1146/annurev.ecolsys.32.081501.114012
77	D Pinto-Ramos, M G Clerc, M Tlidi. (2023). Topological defects law for migrating banded vegetation patterns in arid climates. Science Advances, 9(31): eadf6620 https://doi.org/10.1126/sciadv.adf6620
78	Barrera P Pulido, Carreón J Rosales, Boer H J de. (2018). A multi-level framework for metabolism in urban energy systems from an ecological perspective. Resources, Conservation and Recycling, 132: 230–238 https://doi.org/10.1016/j.resconrec.2017.05.005
79	S Qu, K Yu, Y C Hu, C C Zhou, M Xu. (2023). Scaling of energy, water, and waste flows in China’s prefecture- level and provincial cities. Environmental Science & Technology, 57(2): 1186–1197 https://doi.org/10.1021/acs.est.1c04374
80	A Ramaswami, D Q Jiang, K K Tong, J Zhao. (2018). Impact of the economic structure of cities on urban scaling factors implications for urban material and energy flows in China. Journal of Industrial Ecology, 22(2): 392–405 https://doi.org/10.1111/jiec.12563
81	M Rietkerk, R Bastiaansen, S Banerjee, J van de Koppel, M Baudena, A Doelman. (2021). Evasion of tipping in complex systems through spatial pattern formation. Science, 374(6564): eabj0359 https://doi.org/10.1126/science.abj0359
82	J P Rodríguez, T D Jr Beard, E M Bennett, G S Cumming, S J Cork, J Agard, A P Dobson, G D Peterson. (2006). Trade-offs across space, time, and ecosystem services. Ecology and Society, 11(1): 28 https://doi.org/10.5751/ES-01667-110128
83	S Roy, J Byrne, C Pickering. (2012). A systematic quantitative review of urban tree benefits, costs, and assessment methods across cities in different climatic zones. Urban Forestry & Urban Greening, 11(4): 351–363 https://doi.org/10.1016/j.ufug.2012.06.006
84	E D Schneider, J J Kay. (1994). Complexity and thermodynamics: towards a new ecology. Futures, 26(6): 626–647 https://doi.org/10.1016/0016-3287(94)90034-5
85	F D Schneider, S Kéfi. (2016). Spatially heterogeneous pressure raises risk of catastrophic shifts. Theoretical Ecology, 9(2): 207–217 https://doi.org/10.1007/s12080-015-0289-1
86	A M Shah, G Liu, Y Chen, Q Yang, N Yan, F Agostinho, C M V B Almeida, B F Giannetti. (2023). Urban constructed wetlands: assessing ecosystem services and disservices for safe, resilient, and sustainable cities. Frontiers of Engineering Management, 10(4): 582–596 https://doi.org/10.1007/s42524-023-0268-y
87	Z Shao, Y Li, H Gong, H Chai. (2024). From risk control to resilience: developments and trends of urban roads designed as surface flood passages to cope with extreme storms. Frontiers of Environmental Science & Engineering, 18(2): 22 https://doi.org/10.1007/s11783-024-1782-9
88	A Sharifi, Y Yamagata. (2016). Principles and criteria for assessing urban energy resilience: a literature review. Renewable & Sustainable Energy Reviews, 60: 1654–1677 https://doi.org/10.1016/j.rser.2016.03.028
89	S T Shutters, R Muneepeerakul, J Lobo. (2015). Quantifying urban economic resilience through labour force interdependence. Palgrave Communications, 1: 15010 https://doi.org/10.1057/palcomms.2015.10
90	H W Singer. (1936). The “Courbe des Populations”: a parallel to Pareto’s law. Economic Journal, 46(182): 254–263 https://doi.org/10.2307/2225228
91	A L Soares, F C Rego, E G McPherson, J R Simpson, P J Peper, Q Xiao. (2011). Benefits and costs of street trees in Lisbon, Portugal. Urban Forestry & Urban Greening, 10(2): 69–78 https://doi.org/10.1016/j.ufug.2010.12.001
92	J Song, Y Lu, T Fischer, K Hu. (2024). Effects of the urban landscape on heatwave-mortality associations in Hong Kong: comparison of different heatwave definitions. Frontiers of Environmental Science & Engineering, 18(1): 11 https://doi.org/10.1007/s11783-024-1771-z
93	M Spyra, D La Rosa, I Zasada, M Sylla, A Shkaruba. (2020). Governance of ecosystem services trade-offs in Peri-urban landscapes. Land Use Policy, 95: 104617 https://doi.org/10.1016/j.landusepol.2020.104617
94	L Sugar, C Kennedy. (2021). Urban scaling and the benefits of living in cities. Sustainable Cities and Society, 66: 102617 https://doi.org/10.1016/j.scs.2020.102617
95	X Sun, Q Ma, G Fang. (2023). Spatial scaling of land use/land cover and ecosystem services across urban hierarchical levels: patterns and relationships. Landscape Ecology, 38(3): 753–777 https://doi.org/10.1007/s10980-021-01387-4
96	M Szulkin, C J Garroway, M Corsini, A Z Kotarba, D Dominoni. (2020). How to quantify urbanization when testing for urban evolution. Urban Evolutionary Biology, 13(1): 1861–1876 https://doi.org/10.1093/oso/9780198836841.003.0002
97	K Tzoulas, K Korpela, S Venn, V Yli-Pelkonen, A Kaźmierczak, J Niemela, P James. (2007). Promoting ecosystem and human health in urban areas using Green Infrastructure: A literature review. Landscape and Urban Planning, 81(3): 167–178 https://doi.org/10.1016/j.landurbplan.2007.02.001
98	R E Ulanowicz (2012). Growth and development: ecosystems phenomenology. Berlin: Springer Science & Business Media
99	den Elsen E van, L C Stringer, Ita C de, R Hessel, S Kéfi, F D Schneider, S Bautista, A G Mayor, M Baudena, M Rietkerk. et al.. (2020). Advances in understanding and managing catastrophic ecosystem shifts in mediterranean ecosystems. Frontiers in Ecology and Evolution, 8: 561101 https://doi.org/10.3389/fevo.2020.561101
100	M WackernagelW (1996) Rees. Our ecological footprint. Gabriola Island. British Columbia: New Society Publishers
101	G Wan, D Zhu, C Wang, X Zhang. (2020). The size distribution of cities in China: Evolution of urban system and deviations from Zipf’s law. Ecological Indicators, 111: 106003 https://doi.org/10.1016/j.ecolind.2019.106003
102	J Wang, P Song, Z Bi, L Wei, Z Ju (2016). An ecological niche evaluation model of social,economic,and natural complex ecosystems: a case study in Sichuan Province. Acta Ecologica Sinica, 36(20): 6628–6635 (in Chinese)
103	X C Wang, X B Dong, H M Liu, H J Wei, W G Fan, N C Lu, Z H Xu, J H Ren, K X Xing. (2017). Linking land use change, ecosystem services and human well-being: a case study of the Manas River Basin of Xinjiang, China. Ecosystem Services, 27: 113–123 https://doi.org/10.1016/j.ecoser.2017.08.013
104	G West (2018). Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies. New York: Penguin Press
105	G B West, J H Brown. (2005). The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization. Journal of Experimental Biology, 208(9): 1575–1592 https://doi.org/10.1242/jeb.01589
106	C R White, L A Alton, C L Bywater, E J Lombardi, D J Marshall. (2022). Metabolic scaling is the product of life-history optimization. Science, 377(6608): 834–839 https://doi.org/10.1126/science.abm7649
107	J R Wolch, J Byrne, J P Newell. (2014). Urban green space, public health, and environmental justice: the challenge of making cities ‘just green enough’. Landscape and Urban Planning, 125: 234–244 https://doi.org/10.1016/j.landurbplan.2014.01.017
108	S Wu, B Chen, C Webster, B Xu, P Gong. (2023). Improved human greenspace exposure equality during 21st century urbanization. Nature Communications, 14(1): 6460 https://doi.org/10.1038/s41467-023-41620-z
109	G D Xie, C X Zhang, L Zhen, L M Zhang. (2017). Dynamic changes in the value of China’s ecosystem services. Ecosystem Services, 26: 146–154 https://doi.org/10.1016/j.ecoser.2017.06.010
110	Z Xu, L Jiao, T Lan, Z Zhou, H Cui, C Li, G Xu, Y Liu. (2021). Mapping hierarchical urban boundaries for global urban settlements. International Journal of Applied Earth Observation and Geoinformation, 103: 102480 https://doi.org/10.1016/j.jag.2021.102480
111	Z Xu, J Zhang, C Li, Z Li, Y Geng, C Tan (2018). Study on the spatial competitiveness of Beijing-Tianjin-Hebei urban agglomeration based on niche. Chinese Journal of Agricultural Resources and Regional Planning, 39(4): 167–175 (in Chinese)
112	Z Yang, M Zheng, Z Yan, H Liu, X Liu, J Jin, J Wu, C Ou. (2024). Magnitude and direction of temperature variability affect hospitalization for myocardial infarction and stroke: population-based evidence from Guangzhou, China. Frontiers of Environmental Science & Engineering, 18(3): 27 https://doi.org/10.1007/s11783-024-1787-4
113	G Yu, X Zhu, Y Fu, H He, Q Wang, X Wen, X Li, L Zhang, L Zhang, W Su. et al.. (2013). Spatial patterns and climate drivers of carbon fluxes in terrestrial ecosystems of China. Global Change Biology, 19(3): 798–810 https://doi.org/10.1111/gcb.12079
114	J Yuan, B Wu, X Liu, M Lu. (2023). Boundary green infrastructure: a green infrastructure connecting natural and artificial spaces. Frontiers in Environmental Science, 11: 1155036 https://doi.org/10.3389/fenvs.2023.1155036
115	P Zhang, D Ghosh, S Park. (2023). Spatial measures and methods in sustainable urban morphology: a systematic review. Landscape and Urban Planning, 237: 104776 https://doi.org/10.1016/j.landurbplan.2023.104776
116	H Zheng, J Cheng, H C Ho, B Zhu, Z Ding, W Du, X Wang, Y Yu, J Fei, Z Xu. et al.. (2023). Evaluating the short-term effect of ambient temperature on non-fatal outdoor falls and road traffic injuries among children and adolescents in china: a time-stratified case-crossover study. Frontiers of Environmental Science & Engineering, 17(9): 105 https://doi.org/10.1007/s11783-023-1705-1
117	C Zhou, M Gong, Z Xu, S Qu. (2022). Urban scaling patterns for sustainable development goals related to water, energy, infrastructure, and society in China. Resources, Conservation and Recycling, 185: 106443 https://doi.org/10.1016/j.resconrec.2022.106443
118	A L Zhu, N Weins, J Lu, T Harlan, J Qian, F Barbi Seleguim. (2024). China’s nature-based solutions in the Global South: Evidence from Asia, Africa, and Latin America. Global Environmental Change, 86: 102842 https://doi.org/10.1016/j.gloenvcha.2024.102842
119	G K Zipf (1949). Human Behaviour and the Principle of Least-Effort. Cambridge: Addison-Wesley Press
120	D Zünd, L M A Bettencourt. (2019). Growth and development in prefecture-level cities in China. PLoS One, 14(9): e0221017 https://doi.org/10.1371/journal.pone.0221017

Viewed

Full text

Abstract

Cited

Shared

Discussed