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Article

An Analysis of the Urban Green Space Index in Ecuadorian Cities Through Mathematical Modeling: A Territorial Analysis

by
Andrea Damaris Hernández-Allauca
1,*,
Jorge Gualberto Paredes Gavilánez
2,
Sandra Patricia Miranda Salazar
1,
Carla Sofía Arguello Guadalupe
1,
Juan Federico Villacis Uvidia
3,
Eduardo Patricio Salazar Castañeda
3,
Vilma Fernanda Noboa Silva
3 and
Roberto Fabián Sánchez Chávez
3
1
Faculty of Natural Resources, Escuela Superior Politécnica de Chimborazo, Panamericana Sur, km 1 ½, Riobamba EC-060155, Ecuador
2
Facultad de Ciencias Empresariales, Universidad Técnica Estatal de Quevedo, Av. Carlos J. Arosemena 38, Quevedo EC-120550, Ecuador
3
Independent Researcher, Riobamba EC-060155, Ecuador
*
Author to whom correspondence should be addressed.
Urban Sci. 2025, 9(6), 232; https://doi.org/10.3390/urbansci9060232
Submission received: 28 January 2025 / Revised: 14 May 2025 / Accepted: 9 June 2025 / Published: 19 June 2025

Abstract

:
The Urban Green Space Index (UGSI) is an indicator that measures the quantity, quality, accessibility, and distribution of green spaces in urban environments. This study focused on analyzing the UGSI in Ecuadorian cities through a multiple linear regression model, analyzing the UGSI from both territorial and public management perspectives. Ecuador was selected as a case study due to the limited availability of research on urban green spaces in the country, despite its high ecological diversity and increasing urbanization. The model was used to explore relationships among various factors influencing urban green spaces. Government variables and key factors, such as budget allocations, were analyzed. The model revealed an inverse relationship between urban population size and per capita green space availability. In cities with 50,000 inhabitants, the average is 60 m2 per person, which decreases significantly to just 5 m2 per person in cities with 300,000 residents. This trend highlights the pressure of urbanization on green spaces and emphasizes the need for evidence-based urban planning to ensure equitable access and to improve quality of life. However, challenges such as the lack of updated data and opportunities for improvement in territorial planning were also identified.

1. Introduction

Green spaces are one of the most important components of urban infrastructure [1]. They play a significant social, economic, and environmental role in cities [2], contributing to human well-being [3]. In the social context, green spaces provide communities with areas for interaction [4], fostering social cohesion and a sense of belonging among citizens [5]. Furthermore, they help improve mental health by providing places where people can exercise, socialize, and reduce stress [6]. Economically, they increase the real estate value of nearby properties [7], generate employment related to their maintenance and management [8], and may reduce healthcare costs by promoting a healthier lifestyle [9]. Environmentally, they improve air quality, contribute to climate regulation, and provide habitats for various species [10,11]. Thus, green spaces become a fundamental pillar for sustainability and quality of life in cities [12,13], promoting a balance between human needs and environmental protection.
However, despite the multiple benefits they offer, the distribution of these spaces in many cities remains unequal [14], leading to disparities in access to them, particularly in areas of high population density or peripheral neighborhoods [15]. In recent years, the trend of increasing urban population and, consequently, the physical expansion of cities has led to numerous problems in urban centers [16,17]. Thus, the consequences of urban development and the complexity of current environmental issues have affected many urban communities [18], resulting in a significant reduction in the proportion of green spaces [19].
In this context, the Urban Green Space Index (UGSI) serves as a crucial tool for evaluating the status of green spaces in urban areas [20], enabling the measurement of their quantity, accessibility, and quality [21]. Additionally, it helps identify areas with deficiencies and propose solutions to enhance the distribution and coverage of these spaces [22]. It also facilitates monitoring the progress of public policies aimed at promoting environmental and social sustainability [23]. Therefore, the use of mathematical models, such as those based on geospatial analysis [24], multivariate statistics, or simulations, can significantly contribute to these assessments [25,26]. These models not only quantify green spaces, but also predict how their distribution impacts variables such as public health, social equity, and environmental sustainability [8,27].
In the case of Ecuador, the use of the Urban Green Space Index (UGSI) is particularly relevant as a tool for understanding territorial disparities in green space provision [28]. The country’s geographical and climatic diversity, combined with pronounced socioeconomic inequalities, significantly affects how green spaces are distributed and managed across cities [29]. This is especially important considering that the urbanization process has accelerated in recent decades [30], leading to rapid growth in major cities such as Quito, Guayaquil, and Cuenca [31]. This has resulted in various issues, including the loss of green spaces due to reduced vegetation coverage and the fragmentation of urban ecosystems [32,33]. As such, Ecuadorian cities exhibit significant heterogeneity in terms of the availability and management of green spaces, highlighting the need for a comprehensive evidence-based approach to address these challenges [34]. In this sense, the UGSI offers a standardized metric to assess and compare these conditions, supporting evidence-based planning and public management strategies aimed at ensuring more equitable and sustainable urban development.
On the other hand, another important aspect for the evaluation of green spaces is public management [35,36]. This type of management plays a central role in the planning, development, and maintenance of urban green spaces [37,38]. In this sense, government entities are responsible for ensuring that urban policies and strategies prioritize the promotion of green spaces [39]. However, the effectiveness of these policies largely depends on the availability of reliable data and analytical tools that allow for the assessment of the impact of interventions [40]. In this context, the UGSI provides a useful tool for this purpose, integrating both quantitative and qualitative information on various aspects of urban green spaces [41].
The aim of this study was to analyze the UGSI in Ecuadorian cities through mathematical modeling and from a territorial perspective based on public management. To achieve this, the variables associated with governmental entities influencing the development and maintenance of urban green spaces were analyzed. Additionally, the predictor variables for the mathematical model were determined, and the corresponding quantitative databases were structured through a comprehensive analysis combining both quantitative and qualitative methodologies. Therefore, this study stands out for introducing a comprehensive territorial perspective into the assessment of the Urban Green Space Index (UGSI), incorporating variables that reflect the influence of public policies and institutional management. Unlike other research, which tends to emphasize biophysical or spatial aspects alone, this work integrates governance-related dimensions into a mathematical model. In Ecuador, studies that combine urban sustainability indicators with public management variables are still limited, making this research one of the few to explore this intersection systematically. In this sense, this study aims to contribute key information for the development of effective strategies that will benefit both present and future generations.

2. Materials and Methods

2.1. Study Area

Ecuador is a country located in the northwest of South America with a territorial extension of approximately 283,561 km2 (Figure 1a) [42]. It is divided into three regions, Costa Sierra, Oriente, and Insular, comprising a total of 24 provinces, which were included in this study (Figure 1b).
Ecuador was selected as the study area due to its increasing urban dynamics, the sustained growth of its population in metropolitan areas, and the prioritization of public and private investments in green infrastructure projects. These factors make it a strategic environment for applying a mathematical model aimed at estimating the UGSI. This approach enables the quantification of the availability and quality of green spaces in the urban areas of each province, providing a robust analytical tool to assess equity in access to natural and recreational areas, as well as to support decision making in urban planning and sustainable land management.

2.2. Methodology

The methodology applied in this study considered a quantitative research approach with an exploratory, analytical, and descriptive design. It involved the development of the mathematical model and determination of the UGSI in relation to the total area of green areas, population, and public management. This was carried out through (i) data collection, (ii) determining model variables statistical, (iii) analysis of the data and the application of a mathematical model, and (iv) model evaluation.

2.2.1. Data Collection

First, a bibliographic review was conducted, which allowed for the collection of data from the 24 provinces of Ecuador [43]. The following information was determined: demographic data (urban population by province), environmental data (total surface area of urban green spaces (m2) by province), public management data (number of green space projects and monetary investment in the projects by province), and UGSI data for the 24 provinces of Ecuador.
The data used in this study were obtained from reputable official sources, including the Ecuadorian National Institute of Statistics and Census (INEC) and government agency databases. To address potential gaps or outdated information, we cross-referenced available data with secondary sources and ensured that the most current and relevant data were utilized at the time of the study. This careful selection and validation of data sources contribute to the reliability and robustness of the findings presented in the study.

2.2.2. Determining Model Variables

The predictor variables to be analyzed in the mathematical model were established (Table 1). The variables of interest were demographic (province), environmental (urban green index, green areas, urban population, number of projects), and economic (investment value).
In this regard, population and geographic data were considered to understand the relationship between the amount of green space and population density in each province. This made it possible to analyze how the distribution of green spaces may affect access to and enjoyment of nature by the urban population. Likewise, financial aspects were considered to assess the level of investment and resources allocated to the development and maintenance of green space projects in each province. This provided a more comprehensive view of governmental policies and efforts aimed at promoting sustainable development and equity in access to green spaces.

2.2.3. Statistical Analysis and Model Development

The study is primarily based on an empirical model that incorporates theoretical components, specifically a mathematical regression model, where linear regression and statistical analysis are used to identify predictor variables, and a quantitative and predictive approach, aimed at explaining how public management variables influence UGSI.
A multiple linear regression model was developed to analyze the relationship between the predictor variables and the UGSI. The following typical regression structure used was:
IVU = β0 + β1X1 + β2X2+⋯+βnXn + ε
where IVU is the dependent variable; X1, X2, ..., XnX1 are the independent variables; β0 is the constant or intercept; and βiβi are the regression coefficients.
The codes used for the syntax in the development of the mathematical model to determine the UGSI are detailed in Appendix A. An analysis of the data was conducted for each of the variables established for this study. On the other hand, the information regarding the projects developed in relation to urban green areas was considered. Subsequently, a code was designed to graphically generate the representation of investments by province. Additionally, linear relationships between variables were analyzed, reflecting the study variables: total green areas (m2), urban population, and UGSI. Similarly, the standard deviation was analyzed. These values indicate how much the observations vary in each of the three variables. The greater the standard deviation, the greater the dispersion of the data around the mean [44].

2.2.4. Model Evaluation

Residuals were examined to assess model adequacy, including checking for normality and homoscedasticity (Appendix A). The minimum (−18.616), quartile, and maximum (50.507) values of the residuals were analyzed. To obtain residual values, considering that the residuals are the differences between the observed values and the values predicted by the model. The residual standard error was calculated to measure the average dispersion of the residuals around the regression line.
In addition, simulated data were generated to represent fluctuations in the UGSI in response to variations in investment (limited to ±3%) and the extension of green areas. These data were then plotted using MATLAB R2023a, where the horizontal axis represents time in milliseconds and the vertical axis represents the UGSI amplitude. The resulting graph made it possible to visualize how variations in investment and green area extension affect the UGSI over time, facilitating the validation of the mathematical model in its ability to keep the UGSI within the desired limits, in line with WHO standards.
Once the model was adjusted, the correlation between variables and the behavior of the UGSI was performed.

3. Results

Figure 2 presents the UGSI by province in Ecuador. It was determined that the total UGSI in the country is 13.01 m2/inhabitant. A variability in UGSI was observed across provinces. Some provinces, such as Napo and Zamora-Chinchipe, stand out with significantly high indices of 76.58 m2 per inhabitant and 63.29 m2 per inhabitant, respectively. This indicates an adequate availability of green spaces relative to their population. However, other provinces exhibit much lower indices, suggesting an unequal distribution of green spaces. This may reflect differences in urban planning, investment in green infrastructure, and attention to the needs of local communities.
Moreover, it was determined that, in 2016, 12 projects were developed with an investment of USD 2,839,905. In 2017, 20 projects were developed with a total investment of USD 1,763,092. For the year 2018, 29 projects were developed with USD 3,369,881 invested. In 2019, USD 3,696,350 were invested in 24 projects. For 2020, 33 projects were developed with an investment of USD 2,130,000. Finally, in 2021, 33 projects were developed with a total investment of USD 2,801,840.
These data highlight the importance of considering both quantitative and qualitative data when assessing the state of urban green spaces and underscore the potential of using mathematical modeling for urban sustainability planning.
Figure 3 shows the relationship between the UGSI, total green areas, and urban population. The analysis reveals that cities with larger urban populations tend to have greater total green areas, although with high dispersion, suggesting an inconsistent proportion between green areas and population. Furthermore, it is observed that cities with larger total green areas tend to have a higher urban green index, indicating a positive correlation between the total availability of green areas and the UGSI. However, cities with larger urban populations generally show a lower green index, which highlights that population density negatively affects the number of green areas available per inhabitant. This underscores the importance of planning green areas in proportion to urban growth to ensure sustainability and the well-being of residents.
Figure 4 shows the correlation level between the total green areas and the urban population. It is evident that having a large total green area in a city (with a correlation of 0.79 with the urban population) does not necessarily guarantee a high Urban Green Space Index (UGSI) for its residents. The weak correlation (0.15) between total green area and UGSI suggests that these resources may not be adequately distributed or accessible to the population. Moreover, the negative correlation (−0.21) between UGSI and urban population indicates that, as cities expand, green space per capita tends to decrease, highlighting the challenges of balancing urban growth with the provision of accessible green areas for all residents. This underscores the need for urban planning strategies that prioritize the equitable distribution and effective management of green spaces, rather than focusing solely on increasing the total green area.
Figure 5 shows the correlation between the variables. The dispersion of the data was identified, showing that the values of total green areas in relation to the urban green index are dispersed, indicating a minimal relationship compared to the values of urban population and urban green index, which are directly related as their values are aligned in the same space.
A balance point was obtained that allows for the assumption of data normality to be met, as well as its independence. Furthermore, the model’s constraints regarding the budgetary level were analyzed.
TGA = Total Green Areas
U P = U r b a n   p o p u l a t i o n
U G S I = 2.219 × 10 1 + 1.814 × 10 6 T G A 3.844 × 10 5 U P
This formula is used to calculate the UGSI, a metric that measures the amount of green space available in urban areas relative to the population. In this equation, TGA stands for the total green area (in square meters) within the urban area, and UP represents the urban population. The constant 2.219 × 101 is a baseline value that adjusts the calculation. The term 1.814 × 10−6 (TGA) indicates a very small positive influence of increasing green area on the UGSI, meaning that, as the total green area increases, the green space index rises, but the impact is relatively minor. Conversely, the term −3.844 × 10−5 (UP) represents a negative relationship between urban population size and the UGSI, suggesting that, as the population grows, the per capita green space decreases, which leads to a lower UGSI. This formula effectively models how green space availability is influenced by both the total green area and the size of the urban population, emphasizing the challenge of maintaining adequate green space as cities expand.
In this sense, the constraints of this model concerning the investment budget level are as follows.
M a x i m i z e   C = 9 T G A + ( U P )
R e s t r i c c i o n e s
A = 9.2 T G A + P U
B = 1,652,579   m m   T G A + 221,778   ( P U ) 225,641.67
D = 1,652,579   m m   T G A + 221,778   ( P U ) 10.0054
T G A 0 , ( P U ) 0
Constraint B indicates the limitations regarding the investment level per urban green area according to the increase in urban population in the country. That is, through this constraint, the appropriate investment will be determined to meet the standards set by the World Health Organization (WHO). On the other hand, constraint D indicates the limitation of the urban green index concerning the population level and urban green areas.
Figure 6 represents the behavior of the mathematical model over time, as well as the amplitude that it will have with a decrease in the maximum investment of 2% and a maximum increase of 3%, balancing the midpoint of investment, as well as the extension of green areas according to the level of urban population to obtain an UGSI that is within the limits established by the WHO.
Figure 7 shows the UGSI in Ecuador until 2027. The data reflect a fluctuating trend in the availability of green spaces per inhabitant. In 2022, the index was 15.23%, increasing to 20.79% in 2023 and decreasing by −0.76% in 2024, for a total of 20.03%. For 2026, an increase of 2.93% is shown with 22.96%. However, for 2026, a significant decrease to 15.99% was projected, which could indicate challenges in the sustainability of these spaces due to urbanization and lack of effective policies. Despite this reduction, a rebound to 20.41% is projected in 2027. In short, the projections indicate that, from 2022 to 2027, a total increase of approximately 6.08% is expected. This increase, although positive, reflects the need for a sustained effort to improve the availability of green spaces, which highlights the importance of continued commitment by local governments and communities to preserve and expand green spaces, which are essential to improving the quality of life and environmental well-being in Ecuadorian cities.
Figure 8 shows the growth of the UGSI through the relationship between the urban population (Y-axis), the urban green index (X-axis), and the total green areas (Z-axis), denoting an inverse relationship between urban population and the green space index per capita in Ecuadorian cities. In cities with approximately 50,000 (5.0 × 104) inhabitants, the total green area is 3,000,000 m2 (3.0 × 106 m2) with an index of 60 m2/inhabitant. Upon reaching 150,000 (1.5 × 105) inhabitants, the total green area decreases to 1,500,000 m2 (1.5 × 106 m2) with an index of 10 m2/inhabitant. For 200,000 (2.0 × 105) inhabitants, the total green area is 1,600,000 m2 (1.6 × 106 m2), with a rate of 8 m2/inhabitant. Finally, in cities with 300,000 (3.0 × 105) inhabitants, the rate is only 5 m2/inhabitant. This trend highlights the pressure that urbanization exerts on green spaces, underscoring the need for proactive urban planning that ensures the creation and conservation of adequate green areas to improve the quality of life of residents in growing urban environments.
The colored surface on which the data are projected reflects a pattern of change that allows us to observe how, as the urban population increases, the green area index per inhabitant tends to decrease. This decrease does not always translate into a reduction in the total area of green areas, but it does reflect a redistribution of available space, which implies increasing pressure on natural resources in urbanized areas. This suggests that the provision of green space per capita is more effective in areas with lower population density, highlighting the importance of considering population density in urban planning to ensure an adequate distribution of these resources.

4. Discussion

Numerous studies have established the importance of green spaces in urban areas [28,45,46]. These spaces, including parks, gardens, recreational areas, and ecological corridors [47], not only enhance quality of life by providing natural environments within the urban landscape, but also play a key role in environmental sustainability [3]. Additionally, they have a significant impact on the psychological and social well-being of citizens [5], offering places for recreation and relaxation that foster social cohesion [4], reduce stress levels [48,49], and promote an active and healthy lifestyle [5]. However, despite the widely recognized benefits, the unequal distribution of these spaces in many cities remains a significant challenge that requires attention in urban policies [21,50].
Incorporating participatory models into the UGSI can enhance its effectiveness by integrating community-driven insights into the planning and management of green spaces. While the UGSI currently focuses on quantitative measures, including qualitative data from residents could make the index more responsive and inclusive [51]. For example, New York City’s participatory parks model and community-driven initiatives in Bogotá and Medellín highlight how local involvement improves the sustainability and accessibility of green spaces [52,53,54]. Integrating such models into the UGSI would offer a more comprehensive assessment that includes social and cultural dimensions, helping policymakers make better-informed decisions that prioritize both the physical and social aspects of urban green spaces.
The analysis of the UGSI in Ecuadorian cities has allowed for the identification of patterns that reflect both urban growth dynamics and the distribution of green spaces in relation to the population [55]. This research highlights a common issue in many cities worldwide: the unequal distribution of green spaces as urban areas experiences accelerated population growth. In general, the results obtained in this study align with findings from previous research, which have indicated an inversely proportional relationship between population density and the availability of green areas per inhabitant. According to the study by Jensen et al. [56], in densely populated cities, the pressure on natural resources significantly increases, limiting the expansion of green spaces, a trend also observed in the main Ecuadorian cities. Specifically, in cities with more than 150,000 inhabitants, the green space index per inhabitant decreases to as low as 10 m2/inhabitant [57,58]. This behavior reflects a widely recognized pattern in global cities such as New York or São Paulo, where high levels of urbanization have led to the fragmentation of urban ecosystems and the overload of green infrastructure [59,60,61]. We believe that the analysis of the UGSI reveals an unequal distribution of green spaces, particularly in areas of high population density.
On the other hand, the results of the study show a different trend in areas of lower population density, such as in cities with around 50,000 inhabitants, where the green space index per capita reaches up to 60 m2 per capita. This finding contrasts with the work of Tao et al. [62], who observed that, in less densely populated areas, a better provision of green spaces is facilitated due to the lower pressure on available resources. This highlights the importance of incorporating population density as a key factor in urban planning [63] to ensure that green spaces are equitably distributed and accessible to all citizens [64,65].
Furthermore, the relationship between urbanization and the distribution of green areas has also been a subject of study in other regions [28,66,67]. For example, in the case of European cities, Krzyżaniak et al. [68] concluded that urban expansion processes are not always accompanied by a proportional increase in green space area, especially in rapidly growing cities. This phenomenon, like that of Ecuador, highlights the need for urban policies that consider both population expansion and the integration of green areas within urban development plans [69,70]. The authors believe that, like in this study, the importance of proactive planning and continuous monitoring is emphasized to ensure that green areas are adequate in both quantity and quality.
Furthermore, the comparison with previous studies on the use of mathematical modeling tools in green space management also reinforces the relevance of the methodology employed in this study [71,72]. The work of Li et al. [39] highlights the use of multiple regression models and spatial analysis to assess the distribution of green areas in Chinese cities, showing that such approaches allow for a better understanding of the relationship between different urban variables and their impact on the quality of the urban environment. In this regard, the mathematical model used in this Ecuadorian study, which incorporates variables such as the total area of green spaces, urban population, and investment in expansion projects [73], provides a useful tool for visualizing the dynamics between these factors and optimizing decision making in public policies [51].
The research also emphasizes the importance of citizen participation in green space management, an aspect that has been widely discussed in the literature. According to Wang et al. [74], the lack of community participation in urban planning can lead to an unequal distribution of resources, resulting in social exclusion and reduced effectiveness in managing public spaces. In the Ecuadorian context, limited citizen participation in urban decision making has been identified as a challenge that needs to be addressed to improve the quality of projects and ensure they meet the real needs of the residents.
Despite advancements in understanding the distribution of green spaces, the results also highlight some persistent challenges in Ecuadorian cities. The scarcity of updated data on green areas and the lack of integration between sectoral policies are recognized limitations in similar studies [73,74]. Yu et al. [75] emphasizes that the fragmentation of urban policies and the lack of precise data hinder the efficient planning of green spaces, a challenge also observed in the Ecuadorian case. These issues underscore the need for greater cooperation between local authorities, urban planners, and the scientific community to create more comprehensive and reliable databases [76] that can serve as the foundation for formulating more effective public policies.
Previous research on the UGSI has predominantly focused on single-case studies or specific cities, often without considering the broader regional or national context [56]. Many studies have also used simplified models that fail to incorporate a range of variables influencing the availability and quality of urban green spaces [20]. This search differentiates itself by taking a more holistic approach, analyzing UGSI across multiple cities in Ecuador while incorporating variables such as total green areas, urban population, and investment in green space projects. Additionally, while the existing literature often overlooks the role of public management in shaping green space policies, this study explicitly addresses how governmental factors can influence the distribution and accessibility of urban green spaces. This gap in the literature is addressed in our work, offering a more comprehensive understanding of the UGSI and its implications for urban planning.
In this context, this study on the UGSI in Ecuadorian cities, when compared with international studies, confirms that urban growth and population density are key factors in the distribution of green spaces. However, it also highlights the importance of integrated urban policies that consider both demographic characteristics and the environmental needs of cities while promoting active citizen participation. The results obtained, supported by mathematical modeling, provide a solid foundation for future interventions, enabling a more equitable distribution of green spaces and contributing to the improvement of quality of life in Ecuadorian cities.

5. Conclusions

This study demonstrates the effectiveness of using mathematical modeling, specifically the UGSI, to assess and predict the availability and distribution of green spaces in rapidly urbanizing cities. The results underscore the potential of such models to support decision making in urban sustainability planning, offering a data-driven approach to optimize green space distribution.
The UGSI varies widely among Ecuadorian provinces, with Napo (76.58 m2/inhabitant) significantly exceeding the national average of 13.01 m2/inhabitant. This demonstrates a need for targeted investment in green spaces, focusing on provinces lagging behind to address disparities and promote equitable access to the benefits of urban green infrastructure. Strategic investment can improve not only the UGSI, but also related factors like public health and community well-being in underserved regions.
Using mathematical modeling, it has been confirmed that, as the population increases, pressure on green spaces becomes evident not only in quantitative terms, but also in their distribution and accessibility. While some urban areas manage to maintain or slightly expand total green cover, per capita availability decreases significantly, suggesting a mismatch between urban growth and environmental provision. This trend reinforces the importance of integrating population density metrics into urban green space planning. Rather than focusing solely on expanding the total amount of green space, urban planners must ensure that these areas are equitably distributed and accessible across demographic gradients. The findings advocate for adaptive planning frameworks that respond to urban growth patterns and prioritize environmental equity as a pillar of urban resilience.
This study identifies challenges such as the lack of up-to-date data and fragmented policies in Ecuador. It emphasizes the need for better data collection systems and greater coordination between urban planners, local authorities, and citizens to enhance the effectiveness of green space policies and ensure long-term sustainability in urban environments. Policymakers should focus on maintaining and restoring existing green spaces while promoting public–private partnerships for effective management. Additionally, using tools like the Urban Green Space Index (UGSI) can support continuous monitoring and guide decision making. These actions will help policymakers improve urban sustainability and green space availability.
In response to the urban planning challenges identified in our study, we recommend prioritizing equitable access to green spaces, especially in marginalized areas, to ensure that all residents benefit from these resources. In this regard, green spaces should be integrated into new developments and infrastructure projects, while strengthening public management to ensure their preservation, restoration, and equitable distribution. Community participation should be encouraged to foster a sense of ownership and responsibility for these areas. Furthermore, attracting investment in green infrastructure projects and utilizing data and analytical tools, such as the UGSI, can guide better decision making and resource allocation, thus creating more sustainable, inclusive, and resilient urban environments in Ecuadorian cities.
Finally, to further enhance the Urban Green Space Index (UGSI), several improvements could be considered. Integrating real-time data through remote sensing technologies, such as satellite imagery or drones, would provide up-to-date information on the state of green spaces, allowing for more dynamic and responsive assessments. This would enable continuous monitoring and timely interventions. Additionally, applying the UGSI in different geographical contexts, such as rural or peri-urban areas, could expand its applicability, offering insights into green space distribution in both urban and non-urban settings. Adapting the index to different environmental, social, and economic contexts would improve its accuracy in understanding green space management across diverse regions. Lastly, incorporating factors like biodiversity, environmental health, and climate resilience into the UGSI would broaden its scope, offering a more comprehensive view of urban ecosystems and their contributions to sustainability. Expanding the model in this way would enhance its usefulness in policy making and urban planning, fostering more resilient and equitable green spaces.

Author Contributions

Conceptualization, A.D.H.-A. and J.G.P.G.; methodology, A.D.H.-A., J.G.P.G., S.P.M.S., C.S.A.G., J.F.V.U., E.P.S.C., V.F.N.S., and R.F.S.C.; software, A.D.H.-A. and C.S.A.G.; validation, A.D.H.-A., J.F.V.U., R.F.S.C., and V.F.N.S.; formal analysis, A.D.H.-A. and V.F.N.S.; investigation, A.D.H.-A., J.G.P.G., S.P.M.S., C.S.A.G., J.F.V.U., E.P.S.C., V.F.N.S., and R.F.S.C.; resources, A.D.H.-A., J.G.P.G., S.P.M.S., C.S.A.G., J.F.V.U., E.P.S.C., V.F.N.S., and R.F.S.C.; data curation, A.D.H.-A.; writing—original draft preparation, A.D.H.-A., J.G.P.G., S.P.M.S., C.S.A.G., J.F.V.U., E.P.S.C., V.F.N.S., and R.F.S.C.; writing—review and editing, A.D.H.-A., J.G.P.G., S.P.M.S., C.S.A.G., J.F.V.U., E.P.S.C., and V.F.N.S.; visualization, A.D.H.-A. and C.S.A.G.; supervision, A.D.H.-A., J.G.P.G., S.P.M.S., C.S.A.G., J.F.V.U., E.P.S.C., V.F.N.S., and R.F.S.C.; project administration, A.D.H.-A. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

All the data generated and analyzed during this study are included in this published article.

Acknowledgments

The authors of this article thank the Escuela Superior Politecnica de Chimborazo (ESPOCH) for creating research spaces and opportunities for academic and professional growth.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

Model Development

The codes were established for the syntax used in the development of the mathematical model to determine the UGSI. An analysis of the data was conducted for each of the variables established for this study (Figure A1), where the urban green index (m2/inhab.) was considered as the dependent variable and the total green areas (m2) and urban population number projects as independent variables. Regarding the total green areas in the urban sector, a total of 42,317,094 m2 was obtained, with 1,878,968 inhabitants in the urban population and a total UGSI of 76,580 points in 2021 (Figure A1).
Figure A1. Data analysis by variable.
Figure A1. Data analysis by variable.
Urbansci 09 00232 g0a1
On the other hand, the information regarding the projects developed in relation to urban green areas was considered (Figure A2). It was determined that, in 2016, 12 projects were developed with an investment of USD 2,839,905. In 2017, 20 projects were developed with a total investment of USD 1,763,092. For the year 2018, 29 projects were developed with USD 3,369,881 invested. In 2019, USD 3,696,350 were invested in 24 projects. For 2020, 33 projects were developed with an investment of USD 2,130,000. Finally, in 2021, 33 projects were developed with a total investment of USD 2,801,840.
Figure A2. Projects developed in relation to urban green areas.
Figure A2. Projects developed in relation to urban green areas.
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Subsequently, a code was designed to graphically generate the representation of investments by province. Additionally, linear relationships between variables were analyzed, reflecting the study variables: total green areas (m2), urban population, and UGSI. In the main diagonal, the matrix contains the variances of the variables, which indicate how much these variables individually vary in relation to their mean values. The values outside the main diagonal represent the covariances, which indicate how the variables are linearly related to each other. A positive covariance indicates that the variables tend to increase together, while a negative covariance indicates that one variable tends to decrease when the other increases The standard deviation was analyzed. To obtain residual values, it was considered that the residuals are the differences between the observed values and the values predicted by the model (Figure A3).
Figure A3. Multiple linear regression model.
Figure A3. Multiple linear regression model.
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Figure A4 shows the histogram of the model’s residuals. An error level was presented that allowed for the reduction in noise in the data, thus identifying two outliers, which are visually observed in the box plot, indicating that the error quartiles are very low. Additionally, the scatter plot demonstrates that the data fit a normal distribution, as there is no extensive variability of the data relative to the mean.
Figure A4. Histogram of residuals.
Figure A4. Histogram of residuals.
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Additionally, the balance between the adjusted values was analyzed through confidence intervals with a 97.5% confidence level (Figure A5). It was determined that the UGSI ranges between 1.26 and 3.17, which falls within the parameters established by the WHO. On the other hand, the total green areas included in the model range between 4.81 × 10⁻7 and 3.14 × 10⁻6, with a decreasing urban population ranging from 6.54 × 10⁻5 to 1.14 × 10⁻5.
Figure A5. Balance between the adjusted values.
Figure A5. Balance between the adjusted values.
Urbansci 09 00232 g0a5

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Figure 1. Study area: (a) location of Ecuador in South America; (b) provinces of Ecuador.
Figure 1. Study area: (a) location of Ecuador in South America; (b) provinces of Ecuador.
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Figure 2. UGSI by province.
Figure 2. UGSI by province.
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Figure 3. Correlation of variables of the mathematical model data.
Figure 3. Correlation of variables of the mathematical model data.
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Figure 4. Correlation of variables: (a) total green areas vs. UGSI; (b) urban population vs. UGSI.
Figure 4. Correlation of variables: (a) total green areas vs. UGSI; (b) urban population vs. UGSI.
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Figure 5. Dispersion analysis of the mathematical model data.
Figure 5. Dispersion analysis of the mathematical model data.
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Figure 6. Behavior of the mathematical model over time.
Figure 6. Behavior of the mathematical model over time.
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Figure 7. Projection of the urban green index in Ecuador until 2027.
Figure 7. Projection of the urban green index in Ecuador until 2027.
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Figure 8. Growth of the UGSI per inhabitant in relation to the urban population size and total green areas.
Figure 8. Growth of the UGSI per inhabitant in relation to the urban population size and total green areas.
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Table 1. Predictor variables for the mathematical model.
Table 1. Predictor variables for the mathematical model.
VariableDefinition
Total green areas (m2)Square meters corresponding to green areas in a zone or region
Urban populationNumber of inhabitants in a region
Urban green index (m2/inhab.)Proportion of green areas per m2 per inhabitant
Number of projectsNumber of green area expansion projects
Investment valueMonetary value of the green area expansion projects
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Hernández-Allauca, A.D.; Gavilánez, J.G.P.; Salazar, S.P.M.; Guadalupe, C.S.A.; Uvidia, J.F.V.; Castañeda, E.P.S.; Silva, V.F.N.; Chávez, R.F.S. An Analysis of the Urban Green Space Index in Ecuadorian Cities Through Mathematical Modeling: A Territorial Analysis. Urban Sci. 2025, 9, 232. https://doi.org/10.3390/urbansci9060232

AMA Style

Hernández-Allauca AD, Gavilánez JGP, Salazar SPM, Guadalupe CSA, Uvidia JFV, Castañeda EPS, Silva VFN, Chávez RFS. An Analysis of the Urban Green Space Index in Ecuadorian Cities Through Mathematical Modeling: A Territorial Analysis. Urban Science. 2025; 9(6):232. https://doi.org/10.3390/urbansci9060232

Chicago/Turabian Style

Hernández-Allauca, Andrea Damaris, Jorge Gualberto Paredes Gavilánez, Sandra Patricia Miranda Salazar, Carla Sofía Arguello Guadalupe, Juan Federico Villacis Uvidia, Eduardo Patricio Salazar Castañeda, Vilma Fernanda Noboa Silva, and Roberto Fabián Sánchez Chávez. 2025. "An Analysis of the Urban Green Space Index in Ecuadorian Cities Through Mathematical Modeling: A Territorial Analysis" Urban Science 9, no. 6: 232. https://doi.org/10.3390/urbansci9060232

APA Style

Hernández-Allauca, A. D., Gavilánez, J. G. P., Salazar, S. P. M., Guadalupe, C. S. A., Uvidia, J. F. V., Castañeda, E. P. S., Silva, V. F. N., & Chávez, R. F. S. (2025). An Analysis of the Urban Green Space Index in Ecuadorian Cities Through Mathematical Modeling: A Territorial Analysis. Urban Science, 9(6), 232. https://doi.org/10.3390/urbansci9060232

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